Arguing that theism isn't necessarily irrational - Part 2: The Roots of Logic

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Arguing that theism isn't necessarily irrational - Part 2: The Roots of Logic

This is the second in my series of essays.
Again, this should be uncontroversial and I don't expect to get a huge amount of opposition here.
This one even involves an implicit refutation of some of the claims of pre-suppositionalist theology,
The idea is that the first two essays will remind us of some subtle points that will be picked up later on in the more controversial arguments.

The Roots of Logic
The last essay took at the root and purpose of reason.
This one concentrates on a particular method within reason - logic.
Once again, we'll be looking at root and purpose.
Not because logic needs justifying - logic needs to be in place before we can justify things, but so that we can recognise why logic is appropiate so judge when and where to apply it.
For logic to be applicable, only one thing has to be in place - language.
Once we have language, i.e. we grasp and understand the concepts involved (and that's pretty much necessary for any kind of questioning or debate to even start) logic comes out of it. The most famous rule of logic is the law of non-contradiction.

The Law of Non-Contradiction: 'P & not P' cannot be true
And why it holds in a debate[/b]
Consider the following conversation:
"You're an idiot."
"No I'm not!"
"I know you're not, but you're still an idiot."
"I told you, I'm not an idiot."
"I don't disagree, you're not an idiot but you're still an idiot."

The speaker on the right is using the word 'not', but he might as well not be as it doesn't seem to mean anything to the speaker on the left. It becomes quite clear that ignoring the law of non-contradiction makes the word 'not' meaningless. Seeing as we are reasoning in a language where we use the word 'not' as we do, the law of non-contradiction comes naturally.
Whatever our picture of the world, it can only be a picture if we are using language correctly to describe it. If we are abusing our language when what are we actually saying?
So if our position contains a contradiction then that shows a problem with our picture, that it doesn't really make sense as it stands.
That is why the law of non-contradiction holds within a debate.

Logical Inference
Alongside the law of non-contradiction there is another law.
The Law of the Excluded Middle: Either 'P' is true or 'not P' is true
This holds for the same reason as the law of non-contradiction.
It is another consequence of the meanings of the words 'or' and 'not'.
Using these two rules of logic we can build a method of logical inference.
A valid logical inference is when you prove that if some premises are true, then a conclusion is true.
For example:

Premise 1) Unicorns have horns
Premise 2) Sam is a unicorn
Conclusion: Sam has a horn

If you accept that premise 1 and premise 2 are true then the conclusion must also be true. This can be used to defend a statement against an opponent if it can be shown that it leads from premises that the opponent holds. By why is this. Why is a valid inference considered to be 'infallible'?
It's because that if an inference is valid, to accept the premises while denying the conclusion is to make a contradiction.
To deny that Sam has a horn while agreeing that Sam is a unicorn and that all unicorns have horns is to contradict yourself.

Methods of proof tend to work as follows:
1) Show that the premises contradict the denial of the conclusion.
2) By the Law of Non-Contradiction, if you hold these premises then the denial of the conclusion cannot be true.
3) By the Law of Excluded Middle, if the denial of the conclusion is false then the conclusion must be true.
4) So if you accept the premises then you must also accept the conclusion.

When and where is logic applicable?
Logic is best applied when the concepts in question are clearly defined.
Mathematics is the practice of logic.
Mathematical concepts are so well defined that mathematical problems can often be solved purely on logic, and when they can't, this too can be proved in advance using logic.
The language of Physics is very mathematical, and logic tends to be very applicable in science too. Once the concepts are defined it can be quite clear when there is a contradiction and problems can be spotted with relative ease.
Theories can be constructed from the ground up, starting from basic axioms as foundations.

Not all of our concepts are so crystal clear.
Our language has a whole range of concepts, ranging from mathematic ones that have very strict definitions to very loose ones that appear to elude strict definition altogether. Concept like 'love' tend to be so loose that an attempt to nail a strict definition will almost certainly be incorrect. 'Love' is a concept for poetry rather than logic, because rather than trying to nail strict rules, poetry lets the concept display it's true nature through loose examples.

This leads some people to prefer to avoid loose language in debate as it makes it much harder, maybe impossible, to get watertight conclusions. The thing is, are all questions worth asking supposed to have such definite answers? If we have a question that arises in the form of a loose language, would trying to re-phrase the question in a mathematical language lead us to a clear answer, or would it just change the question and lead the original question unanswered?
Like other methods, it seems that there is a time and place for strict logical method.
While some kind of logic will always applicable, it won't always give such definite answers, and it won't always be so obvious whether a contradiction is really a contradiction.
A circle is most certainly not a square, but whether love and hate are as incompatable isn't quite so obvious.


Strafio
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bump?

bump?


Rev_Devilin
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Strafio

Strafio wrote:
bump?

Wink

Okie dokie,............... but

Logic and or mathematics , are limited, fundamentally so, Kurt Gödel incompleteness theorems, quantum physics, and even reason itself, are also limited as I've demonstrated in a previous post, and if your purpose is to show that theism is not necessarily irrational, then your choice of limited tools, is incorrect, as irrational falls into the discipline of psychology, (psychology, the psychology of reasoning) (logic, the correct principles of reasoning)

I understand what you are trying to do, but I believe you are trying to use automotive maintenance tools to make a fine suit

? why not use psychology + reason, ? wouldn't they be a more appropriate choice of tools for the job

 


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limited?  If by "limited"

limited?  If by "limited" you mean that they can not tell us everything, then you are absolutely right.  But they have to be limitied in this world of uncertaintly, becuase logic and mathematics are absolute.  They tell us absolute truth, the arrive at absolute conclusions based on the premises in their arugment. 

I think "limited" is the wrong word.  They are correct, and that is all they need to be.  If they were anything else, then they would not have the same use that they do. 


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RationalDeist

RationalDeist wrote:

limited? If by "limited" you mean that they can not tell us everything, then you are absolutely right. But they have to be limitied in this world of uncertaintly, becuase logic and mathematics are absolute. They tell us absolute truth, the arrive at absolute conclusions based on the premises in their arugment.

I think "limited" is the wrong word. They are correct, and that is all they need to be. If they were anything else, then they would not have the same use that they do.

No they are limited because they are not absolute, please read Kurt Gödel incompleteness theorems, for information on how these disciplines are fundamentally flawed


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Sorry for the delay,

Sorry for the delay, Strafio.  Our jump in traffic over the last week has left me a bit bogged down just trying to read everything that's been posted.

Quote:
For logic to be applicable, only one thing has to be in place - language.

Not strictly true.  A man could theoretically live in complete isolation and never develop language, yet be capable of using logic.  I believe the only necessity is the capability to form abstractions.

 

Quote:
The most famous rule of logic is the law of non-contradiction.

You need to start with the law of identity, lest you presume part of the law of non-contradiction.

 

Quote:
Premise 1) Unicorns have horns
Premise 2) Sam is a unicorn
Conclusion: Sam has a horn

You realilze that Sam might have ten horns, right?  This argument is valid, but you've inadvertantly demonstrated an interesting problem that often crops up in debates.  This is why we must be so careful to state our premises in precise language.

 

Quote:
Logic is best applied when the concepts in question are clearly defined.

Formal logic can only be applied when the concepts are clearly defined.  Informal logic can use vague terms, but the conclusion will be as doubtful as the vaguest term.

 

Quote:
Mathematics is the practice of logic.

I smell an equivocation.  While logic can be represented symbolically with mathematics, I don't think you can completely justify this statement.

 

Quote:
Theories can be constructed from the ground up, starting from basic axioms as foundations.

Theories must be constructed from the ground up, starting from basic axioms.  We skip the axiomatic steps most of the time, but that's because they've been so well established.

 

Quote:
Not all of our concepts are so crystal clear.

This is a fault of the concepts, not of logic.

 

Quote:
Concept like 'love' tend to be so loose that an attempt to nail a strict definition will almost certainly be incorrect. 'Love' is a concept for poetry rather than logic, because rather than trying to nail strict rules, poetry lets the concept display it's true nature through loose examples.

Love has many definitions that are often used interchangeably.  The fact that most people have not thought out the exact meaning of the word does not have any bearing on the fact that each element of it is describable.  Again, the existence of nebulous terms has no bearing on the validity of logical arguments containing precise language.  You're just pointing out that some people try to use logic with vague terms.

We're going to get right back to the same spot.  People who use "fuzzy" logic might be acting rationally if they don't know any better, or have rationally decided that fuzzy logic is ok for the task at hand, but that does not affect the objective external validity or rationality of the conclusions they might reach.

 

Quote:
If we have a question that arises in the form of a loose language, would trying to re-phrase the question in a mathematical language lead us to a clear answer, or would it just change the question and lead the original question unanswered?

If a question cannot be asked in precise language, it is either too incoherent to ask or there is not sufficient knowledge to ask it properly.  In either case, there are logically valid ways to deal with such questions, and we can judge the rationality of the questioner in accordance with them.

 

Quote:
A circle is most certainly not a square, but whether love and hate are as incompatable isn't quite so obvious.

Because of the fault of the definitions, not the reality of the emotions.

 

Atheism isn't a lot like religion at all. Unless by "religion" you mean "not religion". --Ciarin

http://hambydammit.wordpress.com/
Books about atheism


Strafio
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Hambydammit wrote:

Hambydammit wrote:

Sorry for the delay, Strafio. Our jump in traffic over the last week has left me a bit bogged down just trying to read everything that's been posted.


No worries.
Despite my impatience, it's actually better for me if people take their time over these essays rather than try and get instant answers.

Strafio wrote:
For logic to be applicable, only one thing has to be in place - language.

Hambydammit wrote:
Not strictly true. A man could theoretically live in complete isolation and never develop language, yet be capable of using logic. I believe the only necessity is the capability to form abstractions.

There might be an argument that language is necessary for such abstractions, but I don't need it for my point. I was saying that language is sufficient for a logic to be applicable, rather than necessary.

Strafio wrote:
The most famous rule of logic is the law of non-contradiction.

Hambydammit wrote:
You need to start with the law of identity, lest you presume part of the law of non-contradiction.

Why is that?

Hambydammit wrote:
While logic can be represented symbolically with mathematics, I don't think you can completely justify [that maths is the practice of logic].

It's the impression I got doing Maths at university.
It might be I'm wrong, but I'm not relying on this as a literal claim.
Much of my points here are to 'give the idea' rather than state literal absolutes.

Strafio wrote:
Theories can be constructed from the ground up, starting from basic axioms as foundations.

Hambydammit wrote:
Theories must be constructed from the ground up, starting from basic axioms. We skip the axiomatic steps most of the time, but that's because they've been so well established.

Bear in mind that I was using 'theory' in the colliquial sense rather than the strict scientific sense. Another point is that axioms tend to come after, i.e. they are written to fit the theory that's already in place. The axioms of Arithmetic were worked out in the 19th century, after we'd been counting and adding for thousands of years.

Strafio wrote:
Not all of our concepts are so crystal clear.

Hambydammit wrote:
This is a fault of the concepts, not of logic.

So it's the concepts I should be suing then? lol! I wasn't looking for someone to blame. I was simply stating what logic depends on.

Hambydammit wrote:
Again, the existence of nebulous terms has no bearing on the validity of logical arguments containing precise language. You're just pointing out that some people try to use logic with vague terms.

Yes. I am actually.
The point is that not all of our language is precise and not all of our questions are written in precise language. Some important questions cannot be re-phrased in a more precise language and to try to is to just miss the point in them and ask a different question altogether.

You're right that science should be talked about in precise language, that where we use imprecise language it's a means to an end until we devellop a more precise terminology. This doesn't hold in general.

Hambydammit wrote:
If a question cannot be asked in precise language, it is either too incoherent to ask or there is not sufficient knowledge to ask it properly. In either case, there are logically valid ways to deal with such questions, and we can judge the rationality of the questioner in accordance with them.

Here we reach our disagreement.
Your position here on language is extremely controversial.
If you mean this simply for professional science then not many would disagree - science as a practice suits this kind of approach. If you're claiming that we should make language precise in general... can you justify such a claim?
It's common sense that our language is very diverse and generally suits it's purpose. Certain purposes require more precise language and in those areas a more precise language has develloped. But sometimes we have other forms of language that aren't so precise, but still have their uses and bring us questions of interest. The claim that we should always be precise is quite a claim of practical reason, and not one I think that you can justify.


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Rev_Devilin wrote: No they

Rev_Devilin wrote:
No they are limited because they are not absolute, please read Kurt Gödel incompleteness theorems, for information on how these disciplines are fundamentally flawed

There's no flaw.
There just exists certain statements that are true that can't be proved to be so. It's not a big deal.


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Strafio wrote: Rev_Devilin

Strafio wrote:
Rev_Devilin wrote:
No they are limited because they are not absolute, please read Kurt Gödel incompleteness theorems, for information on how these disciplines are fundamentally flawed
There's no flaw. There just exists certain statements that are true that can't be proved to be so. It's not a big deal.

evil religion wrote:

in fact its arguably the most important theory in the whole of the philosophy of mathematics.

It begs fundamental questions about the nature of mathematics and its place in the universe.

If there are mathematical truths or patterns that are not provable then what does this mean? Is maths part of the universe for us to discover? Or is it a human construct? If its a human construct then why are there tuths that are unprovable? Where do these truths come from (*before you think it please fuck of theists - God is not an explanation). If something is unprovable or falsifibale for that matter (even in principle) is that thing true even if it holds for all cases?

 It's not a big deal. arguably the most important theory in logic, is not a big deal, interesting ? what other fundamental logical principles do you disregard with such casual ease ?

Rev_Devilin wrote:

and if your purpose is to show that theism is not necessarily irrational, then your choice of limited tools, is incorrect, as irrational falls into the discipline of psychology, (psychology, the psychology of reasoning) (logic, the correct principles of reasoning)

I understand what you are trying to do, but I believe you are trying to use automotive maintenance tools to make a fine suit

? why not use psychology + reason, ? wouldn't they be a more appropriate choice of tools for the job

cough


Hambydammit
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Forgive me if some of my

Forgive me if some of my comments were a bit pedantic, but we're talking about the vagueries of language and how it affects logic, right? I figured you'd want to be as precise as possible. I think your essay could use some cleaning up in that regard.

My statement about the specificity of language with regard to logic is not as controversial as you're taking it. Let me try to be more clear. Bear in mind the distinction that I've drawn between the belief in something and a specific person's belief in the same thing. I hold that there is a fallacy of equivocation at the heart of your argument, and that it is based on a fundamental misunderstanding of RRS's position.

* For any formal proof, language must be precise.

* For any informal proof, language can be vague.

* Within any informal proof, the conclusion is necessarily as uncertain as the vaguest concept within the premises.

* In the context of day to day living, many decisions based on fuzzy logic can be described as rational with regard to the individual making the decision.

* These decisions might be objectively irrational based on precise logic, or the conclusions might be incoherent, and thus irrational.

Your conclusion seems to rest on the necessity of language for logic, despite your claim to the contrary. If only abstraction is necessary for logic, then logic can function in spite of the limitations of language. In other words, conclusions which are communicated imprecisely through language are not in themselves flawed. Rather, it is the limitations of language which create a perception that logic is incomplete.  In still more words, the communication is flawed, not the logic.

Quote:
It's common sense that our language is very diverse and generally suits it's purpose. Certain purposes require more precise language and in those areas a more precise language has develloped. But sometimes we have other forms of language that aren't so precise, but still have their uses and bring us questions of interest. The claim that we should always be precise is quite a claim of practical reason, and not one I think that you can justify.

Well, I'm not going to mention how often common sense fails. (Oops... just mentioned it.) You keep talking about certain purposes in very vague language, asserting that imprecise logic is logical in at least one instance where language is insufficient to describe the premises completely. This is a positive claim that must be justified, not just asserted. I realize you have a lot of essay left after this, but unless you have some kind of marvelous proof hiding up your sleeve, it appears to me that you're simply mentioning the difference between formal and informal logic. On this point, we have no disagreement.

In neither of these essays have I seen anything that dissuades me from the belief that theism is irrational, but individuals, because of ignorance could rationally hold a theist position.

Ok... a couple of the nitpicky things:

Quote:

Hambydammit wrote:
You need to start with the law of identity, lest you presume part of the law of non-contradiction.

Why is that?

The law of non-contradiction says that a thing cannot be both true and false. As stated, there is a presumption of the existence of a thing. The law of identity establishes the axiomatic existence of self, which is a thing. Therefore, existence is established, and we may discuss non-contradiction as a corrolary to existence.

Quote:
It's the impression I got doing Maths at university.
It might be I'm wrong, but I'm not relying on this as a literal claim.
Much of my points here are to 'give the idea' rather than state literal absolutes.

I took exception to the italicized the in your statement, "Math is the practice of logic. It's nitpicking, to be sure, but chimps use logic and don't know a damn thing about math. We can describe their thought processes mathematically using game theory, but math, strictly speaking, is the codification of the practice of logic.

Frankly, I would strongly consider stating literal absolutes if I were you.  You're trying to argue that "giving the idea" constitutes a basis for valid logic, but it's well established that logic needs precision.  I doubt you're going to convince many philosophers if you don't find a way to precisely explain how precision isn't necessary. 

Quote:
Bear in mind that I was using 'theory' in the colliquial sense rather than the strict scientific sense. Another point is that axioms tend to come after, i.e. they are written to fit the theory that's already in place. The axioms of Arithmetic were worked out in the 19th century, after we'd been counting and adding for thousands of years.

It's true that we often discover axioms after the fact, but they exist independently of the knowledge of their existence. Without a human to observe, chimps would still exist, and the law of non-contradiction would still be in force.

 

Atheism isn't a lot like religion at all. Unless by "religion" you mean "not religion". --Ciarin

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Strafio
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Rev_Devilin wrote: Strafio

Rev_Devilin wrote:

Strafio wrote:
Rev_Devilin wrote:
No they are limited because they are not absolute, please read Kurt Gödel incompleteness theorems, for information on how these disciplines are fundamentally flawed
There's no flaw. There just exists certain statements that are true that can't be proved to be so. It's not a big deal.

evil religion wrote:

in fact its arguably the most important theory in the whole of the philosophy of mathematics.

It begs fundamental questions about the nature of mathematics and its place in the universe.

If there are mathematical truths or patterns that are not provable then what does this mean? Is maths part of the universe for us to discover? Or is it a human construct? If its a human construct then why are there tuths that are unprovable? Where do these truths come from (*before you think it please fuck of theists - God is not an explanation). If something is unprovable or falsifibale for that matter (even in principle) is that thing true even if it holds for all cases?

It's not a big deal. arguably the most important theory in logic, is not a big deal, interesting ? what other fundamental logical principles do you disregard with such casual ease ?


It was a big deal at the time because it refuted a philosophy of mathematics that was widely held, one that had OTT expections on logic.

In maths, a statement is considered true if it logically follows from the axioms. There exist methods where a computational function is applied. These methods take the premises and conclusion and return a 'true' or a 'false' depending on whether inference is valid.

It turns out that not all logical inferences can be decided by an algorithm. All it means is that not every logical dispute can be settled by an algorithmic method. There are some quite serious consquences, but to topics that only mean anything in the obscure details that you'd only come across if the foundations of mathematics was a particular field of yours - i.e. there aren't any serious consequences for philosophy in general.

Godel's theory is continually being brought up by people who have seen the wording of the conclusion and misunderstood what it has meant. The fact that there are true statements 'out there' that cannot be 'proved' makes things sound quite mysterious, but when you see what kind of statements they are, what it means for them to not be 'provable' and see why they aren't, the theorem really turns out to be not such a big deal as it is often made out to be by those who don't understand it.

I've worked through it at university and can recognise when someone hasn't understood it, but I don't have the expertise on the subject to give a real explanation on it. Instead I will refer you to a post by the the RRS logicia who perhaps kills a kitten everytime he sees the theorem being abused by someone who doesn't understand it.

Rev_Devilin wrote:

and if your purpose is to show that theism is not necessarily irrational, then your choice of limited tools, is incorrect, as irrational falls into the discipline of psychology, (psychology, the psychology of reasoning) (logic, the correct principles of reasoning)

I understand what you are trying to do, but I believe you are trying to use automotive maintenance tools to make a fine suit

? why not use psychology + reason, ? wouldn't they be a more appropriate choice of tools for the job


Although psychology might give us insight into why a person might be rational/irrational, whether something is rational or irrational is surely a philosophical task. So I'm not sure how psychology would help on this question. Even if there is an argument from psychology I'd rather argue from philosophy as that's my subject so one I can make proper arguments from.

As it happens, some of the later essays do make use of the psychology of reason, so perhaps you'll see what you were looking for there? Until then, you'll just have to be patient! Sticking out tongue


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Do you believe that there

Do you believe that there are any non-definitional logical truths?


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It depends what you mean by

It depends what you mean by 'definition'.
Sometimes we use it as synonymous for 'meaning' in which case then yes. Logic follows from the meaning/rules-of-use of language.

Definition isn't the only way that words have meaning though.
Definition is when we can nail a word's meaning in terms of other words. Many words aren't like that and we have to rely on a natural grasp of language to see how we generally use them.

Hambydammit wrote:
My statement about the specificity of language with regard to logic is not as controversial as you're taking it. Let me try to be more clear. Bear in mind the distinction that I've drawn between the belief in something and a specific person's belief in the same thing. I hold that there is a fallacy of equivocation at the heart of your argument, and that it is based on a fundamental misunderstanding of RRS's position.

* For any formal proof, language must be precise.

* For any informal proof, language can be vague.

* Within any informal proof, the conclusion is necessarily as uncertain as the vaguest concept within the premises.

* In the context of day to day living, many decisions based on fuzzy logic can be described as rational with regard to the individual making the decision.

* These decisions might be objectively irrational based on precise logic, or the conclusions might be incoherent, and thus irrational.


The premise in bold is the controversial one.
It makes the assumption that all language is potentially translatable into a more precise form. This was what Wittgenstein set out to refute in his philosophical investigations and is generally out of favour in contemporary philosophy.
Now, even if you had been satisfied with this lame argument from authority I just gave, I still wouldn't be. What I'll do next is pick up my Wittgenstein book and see if I can pick out the arguments/observations that convinced me.

I imagine that the argument in your favour would be to point out that unless these words are random then there clearly ways to apply them and ways not to. These ways are ultimately describable, even if a word is so complex that the rules are extremely numerous.
This is the bit where I'd point out that language and logic is rooted in a practice that is judged by practical reason. That treating these words as 'complex definitions' is no use to our real practice, and that treating them as words to complex to define, words that we rely on our intuitive grasp of them, is the only way to deal with them.

You have to remember that language depends on our practical/psychological needs, and expecting all words to be nailable into explicit definitions misses this point.

Quote:
Your conclusion seems to rest on the necessity of language for logic, despite your claim to the contrary. If only abstraction is necessary for logic, then logic can function in spite of the limitations of language. In other words, conclusions which are communicated imprecisely through language are not in themselves flawed. Rather, it is the limitations of language which create a perception that logic is incomplete. In still more words, the communication is flawed, not the logic.

Hmmm...
Your argument makes a cou[ple of leaps that I am not happy with.
1) Although I agree that I've not given a conclusive argument that logic must be linguistic, it's mostly because I'm having a hard time working exmaples of 'non-linguistic' logic. I suspect that your claim comes from a narrow definition of language.
2) Say that we had established that there was 'non-lingusitic' logic, it would not follow that it was working 'ahead' and that our language was trying to keep up with it. While this might be true in some cases, there are also cases where our language consitutes our patterns of thinking.
3) Such 'abstractions' would be limited in content, i.e. to patterns in perception etc.
So even if (2) held for our language for describing the world, our language for science, it would not follow that it held

Having said that, my argument is a lot stronger if I stop you at (1).
Although the burden of proof is on me, I need to know what I am arguing against before I can go on. Could you give me examples or some other kind of description of non-linguistic logic?
(If you can't then I guess that my argument is that the idea of 'non-lingusitic' logic is incoherent! Sticking out tongue)

Quote:
You keep talking about certain purposes in very vague language, asserting that imprecise logic is logical in at least one instance where language is insufficient to describe the premises completely. This is a positive claim that must be justified, not just asserted.

That's fair enough. There is only one point I am trying to establish so far:
Logic/reason is rooted in our practice and is therefore to be judged in terms of practical reason to our everyday life.
If you accept this (which you do, right?) we can get onto the next question which is whether 'imprecise language' is justifiable in this way.

Quote:
In neither of these essays have I seen anything that dissuades me from the belief that theism is irrational, but individuals, because of ignorance could rationally hold a theist position.

And neither will you in the next two either.
The first four essays do two things:
1) Emphasise the bit in bold.
2) Explore the practical roots of logic that will later be used to build an argument to show that by practical rationality, such an 'ignorance' can be justified to be rationally preferable, under certain conditions.

Quote:
The law of non-contradiction says that a thing cannot be both true and false. As stated, there is a presumption of the existence of a thing. The law of identity establishes the axiomatic existence of self, which is a thing. Therefore, existence is establshed, and we may discuss non-contradiction as a corrolary to existence.

Hmmm...
I'm not sure this is right.
For example. the law of identity establishing the existence of a 'thing' doesn't sound like the law of identity to me.
In formal logic the law of identity merely defines the symbol '=' and not all formal logic systems make use of this symbol. This means that there are formal logic systems out there with the law of non-contradiction and no law of identity.
(If you dispute this I'll do some reading up on it and try and quote some proper logicians on it)

More importantly, your point is only relevent if I was trying to build a linguistic system from scratch. This is a common practice in formal logic, but it wasn't what I was trying to do here. What I was trying to justify it to the 'layman' who has their natural grasp of language, but isn't sure that the 'law of non-contradiction' should always apply.
It was to show a sceptic that the law of non-contradiction is a consequence of correctly following the English language.

Quote:
Frankly, I would strongly consider stating literal absolutes if I were you. You're trying to argue that "giving the idea" constitutes a basis for valid logic, but it's well established that logic needs precision. I doubt you're going to convince many philosophers if you don't find a way to precisely explain how precision isn't necessary.

There's an obvious argument why not.
Consider what is necessary for literal absolutes and then consider that these are the things that we are questioning/observing, so literal absolutes are out of the question.

Quote:
It's true that we often discover axioms after the fact, but they exist independently of the knowledge of their existence. Without a human to observe, chimps would still exist, and the law of non-contradiction would still be in force.

I agree that the axioms were 'discovered' rather than 'invented', but lets remind ourselves of the context in which we brought this up. You said that a theory must be built upon its axioms, but axioms are more often discovered within an existing theory.

The bit in bold I still disagree with, but you can refute me by showing an example of non-linguistic logic. Btw, I should qualify this statement a bit by anticipating a possible counter example:
You might show me psychological experiements on pre-linguistic children or non-linguistic animals and show that they attempt certain puzzles in a way that might be considered logical.
The kind of 'logic' I am talking about here specifically involves the 'law of non-contradiction', and that I am certain cannot be separated from language.
I'll watch this space to see what you come up with! Smiling


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Quote: It makes the

Quote:
It makes the assumption that all language is potentially translatable into a more precise form.

No. You seem hung up on language, and I'm not sure why. As I've pointed out, one does not need language to think logically.

Quote:
What I'll do next is pick up my Wittgenstein book and see if I can pick out the arguments/observations that convinced me.

After you do, I'll still be puzzled at your insistence to link my argument to language.

Quote:
I imagine that the argument in your favour would be to point out that unless these words are random then there clearly ways to apply them and ways not to. These ways are ultimately describable, even if a word is so complex that the rules are extremely numerous.
This is the bit where I'd point out that language and logic is rooted in a practice that is judged by practical reason.

This is not very clear. Logic has ways of dealing with imprecise language, and critical thinking dictates certain conclusions when we are faced with it. When you say "practical reason" I am hearing "critical thinking." Is that an accurate interpretation? If so, then good critical thinking applies to a conclusion a level of doubt commensurate to the level of doubt accumulated in the premises. Thus, we can say that a conclusion based on imprecise language is dubious, whereas a conclusion based on precise language is highly probable, and one based on precise language and deduction is certain. It's the heirarchy or reliability.

Quote:
. That treating these words as 'complex definitions' is no use to our real practice, and that treating them as words to complex to define, words that we rely on our intuitive grasp of them, is the only way to deal with them.

This just feels like a naked assertion to me. It appears to beg the same question as any argument from wonder. To say that a word is not precisely defined is far different than saying it cannot be precisely defined.

Could you please provide justification for these two classes of words -- "Those which can be precisely defined" and "Those which cannot?"

How do we know which is which? How do we assign the final verdict, when words are imprecisely defined for different reasons -- cultural plasticity, scientific ignorance, philosophical uncertainty, etc? The presence of different causes for vague language is a confounding variable, but it is not a justification for the conclusion that vague language is inevitable.

Furthermore, when language is vague, is it truly because the language is vague, or is it because the concept to which it refers is vague?

Quote:
You have to remember that language depends on our practical/psychological needs, and expecting all words to be nailable into explicit definitions misses this point.

You seem to be missing my point, which is that our practical/psychological needs are not relevant to the external validity of a particular argument. Even though we feel like we need to reach a conclusion about whether or not we love someone, the correct logical conclusion is that if we cannot define love, we cannot answer the question with certainty. Once we know this, we can assess our understanding of the word love with a level of doubt, and treat our conclusion with the same uncertainty. This is rational, and it is not somehow "outside of logic." It is using imprecise logic in a very logical way.

Quote:
1) Although I agree that I've not given a conclusive argument that logic must be linguistic, it's mostly because I'm having a hard time working exmaples of 'non-linguistic' logic. I suspect that your claim comes from a narrow definition of language.

I had to chuckle for a minute before writing a reply to this. Yes. Your imprecise language is making it hard for me to formulate a reply to the concept in your head. Nevertheless, the concept in your head is either externally rational or irrational, regardless of whether you or I can communicate it.

Quote:
2) Say that we had established that there was 'non-lingusitic' logic, it would not follow that it was working 'ahead' and that our language was trying to keep up with it. While this might be true in some cases, there are also cases where our language consitutes our patterns of thinking.

I don't think I've mentioned a hierarchy of logic having to do with the use of language.

There are cases where our language communicates our patterns of thinking.

Quote:
Although the burden of proof is on me, I need to know what I am arguing against before I can go on. Could you give me examples or some other kind of description of non-linguistic logic?

Watch any discovery channel special on primates. When we give an ape a task and they figure out how to do it, they're using logic. Before you argue that we humans are communicating a task to them, or that the task is itself symbolic, consider that an ape in the wild uses the same facilities for naturally occuring puzzles. Unless you're willing to ascribe language to inanimate objects, I don't see how you're going to object to non-linguistic logic's existence.

When I have two pieces of wood -- a sphere and a cube, and there is a circular hole in front of me, regardless of whether I've ever learned language, I can pick the correct piece of wood to put through the hole 100% of the time. That's using logic -- spacial reasoning, rudimentary syllogism, and cause/effect induction.

Quote:
Logic/reason is rooted in our practice and is therefore to be judged in terms of practical reason to our everyday life.
If you accept this (which you do, right?) we can get onto the next question which is whether 'imprecise language' is justifiable in this way.

No, I don't accept this. Our practice is rooted in logic/reason, and our practical reason is to be judged in terms of logic/reason.

To be precise, I don't claim to be able to establish a dividing line between instinctive behaviors and cognitive choices, and frankly, that's a matter for another discussion. The level of your argument seems to be at the level where humans are reacting to thoughts, not instincts or reflexes.

Quote:
2) Explore the practical roots of logic that will later be used to build an argument to show that by practical rationality, such an 'ignorance' can be justified to be rationally preferable, under certain conditions.

And, as I've repeatedly said, I have no quarrel with your assertion that ignorance can lead to a locally rational event, despite the externally objective irrationality of the decision.

Quote:
For example. the law of identity establishing the existence of a 'thing' doesn't sound like the law of identity to me.
In formal logic the law of identity merely defines the symbol '=' and not all formal logic systems make use of this symbol. This means that there are formal logic systems out there with the law of non-contradiction and no law of identity.
(If you dispute this I'll do some reading up on it and try and quote some proper logicians on it)

I guess to be precise, I should say that existence is axiomatic through retortion. I don't think it's important to quibble over that point. I was only pointing out that at a very fundamental level, the statement "A thing cannot contradict itself" presumes that a thing exists. This is why they always put identity before non-contradiction in the logic texts.

Don't waste time on this unless you just want to. It doesn't appear to be relevant to your argument.

Quote:
It was to show a sceptic that the law of non-contradiction is a consequence of correctly following the English language.

That's fine, but as I've said before, you have a daunting task ahead of you, and imprecise language isn't going to get it done.

Quote:
Consider what is necessary for literal absolutes and then consider that these are the things that we are questioning/observing, so literal absolutes are out of the question.

Pardon me. I was using your words in my reply. To rephrase, I would consider using language as precisely as possible if you intend to convince philosophers of your argument. As you've seen, my primary objections are that 1) I don't think you've defined "reason" well enough, 2) I don't think you've defined language properly, 3) I don't think you've defined "irrational" well enough, and 4) I don't think you've defined logic well enough.

Notice that I separate reason, logic, and irrational. I believe you are equivocating between the three, and it would be unthinkable for me to let you off the hook without insisting on precise definitions of all three, and precise formulation of your argument using only well defined terms.

Quote:
The kind of 'logic' I am talking about here specifically involves the 'law of non-contradiction', and that I am certain cannot be separated from language.

Well, I'm glad you got around to mentioning this! Smiling

Once again, imprecise language has caused a severe problem. In a sense, every self aware creature knows of the law of contradiction. When an ape touches its forehead after seeing a dot on the forehead of the ape image in the mirror, it recognizes that the image is not the same as itself. It knows that it is a discreet being, whether it can articulate this knowledge or not.

We could further say that simply acting rationally demonstrates an understanding of the law of non-contradiction. (I am speaking only of creatures who are self aware. Instinctive behaviors, such as ants following the scent trail of the ants in front of them, are not rational in the strictest sense.) Anytime a creature capable of abstract problem solving attempts to solve a problem based on what it perceives, it is relying on the law of non-contradiction. If it were not so, any potential solution to a problem would be considered rational, for anything could be anything else.

 

 

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I think that what Godel did

I think that what Gödel did was devise a way to rigorously prove a really fundamental point which can invalidate many arguments, including apparently formally valid logical arguments, namely self-reference.

The classic examples are "This statement is false." or "The next sentence is false. The previous sentence is true."

One implication of this is that you cannot, even in principle, prove the validity of any formal logical system using the system itself.

When any of the initial propositions of an argument are not simple assertions about the attributes of clearly definable entities, subtle and not-so-subtle problems can arise. When the propositions are about ideas and more complex concepts, and even about the validity or otherwise of another argument, and so on, the self-reference loops may not be readily apparent.

I think Wittgenstein attempted to address the point about the necessity to distinguish the different levels of complexity of the input propositions to a logical argument, represented by the symbols used in the formal statement of a logical argument, basically as either 'simples' or 'complexes'.

On the problem of dealing with 'fuzzy' real-world ideas, this requires inductive reasoning and the formal treatment of probabilities and 'likelihood'. Simple binary (TRUE/FALSE) logic is inadequate to handle this regime, which is where Science resides, although it is the essential foundation.

Handling ever more complex and subtle concepts, theories, analyses only become manageable when we recognise specific complex structures of simple 'facts' which each map closely to observed structures in observed reality, and encapsulate complex logical arguments which describe relationships between such complexes in higher level rules and theorems.

Elementary arithmetic is absolutely based on basic logic, but adds new 'operations' such as addition, subtraction, multiplication and division, as well as 'number' itself. IOW a simple math calculation could. in principle, be expressed in elementary logic statements, but it would not be practical to do arithmetic this way. This progressive encapsulation of simpler ideas in 'higher-level' concepts is what allows us to handle ever more sophisticated ideas.

In physical science, we see this hierarchy from sub-atomic particles, which are organised into atoms, in turn into molecules, into solids liquids and gasses, into identifiable macroscopic entities like rocks, planets, stars, etc. We need these different levels of description to allow us to keep the number of concepts we have to juggle in our theories manageable. Imagine trying to explain the chemistry of fermentation in terms of the interactions of sub-atomic particles....

A roughly comparable analogy in the field of math would be trying to describe Differential Calculus in the basic laws of logic.

There is an important distinction which needs to be made between the fields of logic/math and empirical science.

Logic/math are rigorously derived from an irreducible set of axioms, so the truth or falsity, or even its decidability (per Gödel), of any statement of math or logic can in principle be established in absolute terms.

Empirical science inevitably includes a level of uncertainty. I think of this as a basic trade-off - Science comes with incredibly useful theories which describe the way various observable attributes of reality interact, to a high, while inevitably imperfect, degree of accuracy.

Every time we go up a level of description in Science, such as from sub-atomic particles to atoms to molecules, there will be subtle aspects of their behaviour and properties which may be lost, or at least covered by statistical averages. As long as the estimated probability of those approximations leading to serious error is small, we are reasonably justified in not having to continually allow for them, except under specific rare circumstances. We are justified because of the immense explanatory and/or predictive power of the higher-level description.

Probably the most extreme example of this would be the prediction of Quantum Theory that there is a non-zero probability that all our constituent particles could suddenly shift six feet to the left, maybe on the other side of a wall. The extremely low value of this probability means that we can safely ignore it in all but theoretical terms. We should also recognise that the probability that the particles would re-appear in close enough to their original relative position and velocity that we would remain otherwise intact and alive is vastly smaller than the possibility of a wholesale shift itself, or the probability that only some of our atoms jumped.

Modern science very much takes into account the fuzziness of real-world observations. Ideas of error bounds, degrees of correlation, ways of estimating the level of confidence we are justified in placing in any theory or scientific argument are drummed into students of science and engineering, or certainly should be. I can remember this from the first physics lectures at University I attended. It seemed a little boring at the time, but I realize now how fundamentally important it was.

 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

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Thanks, Bob!

Thanks, Bob!

(By the way, it's nice to see you posting more these days!)

I think, upon further reflection, that there is a kind of composition error in Strafio's argument, based on the fundamental difference between axiomatic systems and probability systems. It seems that he wants to say that since higher level computations are confounded by uncertainty, the syllogistic label of irrational should not apply to deviances in strict logic at other levels.

As Richard Dawkins says, "Premature erections of alleged philosophical problems are often a smokescreen for mischief." In other words, we can nitpick all day about whether or not a person on a local level is acting within boundaries that we call rational, but to compare this level of day to day logic with the more rigid demands of academic philosophy is akin to a category error, or maybe a fallacy of composition.

 

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Thanks Hamby!

Thanks Hamby!

Yeah I felt a definite void in my life, and using the knowledge and understanding I have accumulated over my life to hopefully shed some light on discussions like this seems a worthy use of my time. I think I realized that drifting away from this interchange of ideas was contributing to my feeling of 'something missing'.

Clarifying my own ideas in the process of finding ways to express them is immensely useful to me as well.

Back to the thread: 

The conflation of formal systems like logic and math with empirical inductive techniques of studying 'reality' is one of my pet peeves. This includes the 'problem of induction'. Arrgh!

EDIT: The 'problem of induction' just demonstrates the inadequacy of logic by itself to allow us to address empirical reality, without building all these higher level tools on the base of fundamental logic rules.

Whenever I hear someone refer to propositions like 'square circles' as examples of things that God can't do to disprove omnipotence, or 'all bachelors are unmarried' as a demonstration that we can make statements that can be absolutely true, I fume.

They are in a fundamentally different category to assertions about existence or otherwise of specific entities, or their attributes, and are usually irrelevant to the argument. They are either tautologies or simple contradictions.

There are essentially absolute statements about reality that I think are valid, such as "I am absolutely certain that we will never achieve absolute certainty about many propositions about the world".

An example of a proposition relevant to this board would be, say, the existence of Jesus as portrayed in the Bible. I quite happily describe anyone asserting certainty of a historical Jesus as irrational in the wider sense. Note it is the assertion of certainty I am attacking here, not the proposition that there might have been a historical Jesus.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

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Before we go on, you asked

Before we go on, you asked me what I meant by Practical Reason.
Practical reason is about using reason to guide and evaluated action.
"Should I jump or shouldn't I?"
I refer to practical reason a lot so I thought I'd better get that clarified.

Reading through your posts, I guess my definition of logic was a bit narrow. Perhaps I should have said 'logic as it applies to argument'.
I've decided not to counter point your last reply as I feel like it would just be attacking details so I've decided to try and re-state my position in a fresh way.

Logic is about rule following.
When a system of formal logic is defined, it is defined as a set of rules that you follow. Logical rules for that system have meaning within the system, and outside that system they are irrelevent.
So the logic that's applicable will depend on the grounding rules of the system.
Any disagreement so far?

'Language games' are also rule based systems. Therefore they will have logical rules. These logical rules will be determined by the rules of the language game they are within. The language games with the word 'and' and 'not' will also have the rule of non-contradiction as this is a consequence of how we use the words. This is what the OP was trying to show.

So we have rules of logic being dependent on the rules of the system that they are based within. An example of such a system is the language game. What are the rules of the language game based on? The rules of the language game devellop through our everyday practices that we use our language for.
They evolve to suit our 'form of life'.
If we are judging a language game then we are judging the very practice that it is based upon, so such judgements can only be a form of practical reason.

So when we debate, the rules of logic are dependent on the system, the system being the 'language game' that we are 'playing' at that moment in time. And if we are to judge language games, (e.g. language where the definitions are imprecise) then we do so on practical terms. That is, we work out whether using language in that way serves any purpose to our life at all.
Language games with loose rules still have rules so in that respect some kind of logic is applicable, but the logic isn't as absolute as it is in systems where the concepts are precisely defined. That's why we can apply strict calculus to mathematics, whlie concepts like 'love' tend to be left to poetry where trying to apply a strict calculus would be seen to be missing the point.
Nevertheless, it still seems to make sense to make statements like:
"If he loved me then he wouldn't beat me", as there are rules that apply to fuzzier concepts.

So logic is strict or fuzzy depending on the system/language game that it is based in and systems/language games are to be evaluated through practical reason. This is the conclusion I am trying to push here.
So the claim that concepts should be precise isn't a claim of logic, it's a claim of practical reason. The claim that certain concepts can't be simplified into precise definitions is also a claim of practical reason.

If you agree with this conclusion then I'll hint where I'm taking this in regards to the atheist vs theist debate.


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Logic is a list of rules,

Logic is a list of rules, ok, but rules rigorously derived from the basic starting points involving progressively more elementary propositions. The most important use in discussion is to identify logical fallacies.

For 1 proposition, we have the law of non-contradiction that it cannot both be true and not true at the same time.

For 2 propositions:

if for all cases where A is true then B is true, it is invalid to assume that if B is true A must be true, unless we can also show that whenever A is false, B is false.

For 2 propositions:

If A is true whenever B and C are both true, it is invalid to assume that A must be false when B or C are false, unless we can show that A is only true when both B and C are true.

If A is true whenever B or C are true, it is invalid to assume that A is false whenever both B and C are false, unless this can be separately shown.

etc.

These are not arbitrary rules and are not context dependent. The limitation is that the propositions A, B, C, etc have to be precisely nailed down assertions or observations, that can only be true or false.

To handle other cases, we need more complex extensions, such as multivalued logic, which starts to shade into mathematics. There are also extensions to cover statements where the propositions are about groups of elementary entities, with qualifiers like All, Some, None.

Some birds cannot fly, so if A is a bird, it may be able to fly, but not necessarily.

This extends further to statements involving probabilities, and so on.

So it is not the rules which change in different contexts, it is the level of logic we need to use. All these levels are extensions from simple binary logic, and are all rigorously derived. So to handle the sorts of concepts involved in Theist/Atheist arguments, we need to have logic which can handle all of these aspects.

Bear in mind that I think the main value of this formal logic is to check for clearly fallacious conclusions, rather than establish their truth value. It can only show that the conclusions are not inconsistent with the initial assumptions or propositions.

To establish the plausibility or likelihood of the conclusions on a really solid foundation strictly requires analysis which goes beyond logic, into rules of inference, Bayesian theory, etc. If we don't this, and of course we don't in ordinary discussions on these topics, we cannot claim to have established much, unless the strengths and weaknesses of the various arguments are very obvious. A lot of philosophical writing falls into this category.

The point I am trying to make is that we do have tools of logic to address these more 'fuzzy', probabilistic topics, where some sort of judgement is called for in assessing the strength of the various points. There is inevitably going to be a strong subjective element in the assessment, but logic and related tools can help.

 EDIT: The bottom line is that if a statement in language is shown to be inconsistent with the appropriate level of logic, it is invalid, period.

 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

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I think Maths can't fully

I think Maths can't fully be shown to be consistent with logic, and I think this means that at least some axioms are in some sense arbitrary, and could logically be different

I am not sure off-hand what this would be in general, but in Geometry the key axiom is about parallel lines. If you assume, with Euclid, that there is one and only one straight line that can be drawn through a given point that will never intersect an adjacent line, you get Euclidean geometry, or the geometry of 'flat' space.

If you assume that many lines can meet this condition, you have negatively curved space, if you assume none, you get positively curved space, also known as Riemannian space.

 

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

"Theology is now little more than a branch of human ignorance. Indeed, it is ignorance with wings." - Sam Harris

The path to Truth lies via careful study of reality, not the dreams of our fallible minds - me

From the sublime to the ridiculous: Science -> Philosophy -> Theology


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Following this thread and

Following this thread and have just a quick question for Strafio:

I've seen you go a couple of rounds before with people over the uses of Godel's theorem without, apparently, accepting that most people are not referring to the incompleteness theorem itself, but rather its implications for formal systems as worked out by Hofstadter and others.

Are you persuaded by Devilin and Bob's use of the (extended version of) Godel's theorem in this thread?  Not to sidetrack your main line of argument, but I think it's important to clarify because of the effect that it has on your conclusions.

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Textom wrote: Following

Textom wrote:

Following this thread and have just a quick question for Strafio:

I've seen you go a couple of rounds before with people over the uses of Godel's theorem without, apparently, accepting that most people are not referring to the incompleteness theorem itself, but rather its implications for formal systems as worked out by Hofstadter and others.


Change 'not accepting' to 'not realizing'.
It completely passed me by.
Are these conclusions like it cannot be proved that maths is consistent, and things like that?

Quote:

Are you persuaded by Devilin and Bob's use of the (extended version of) Godel's theorem in this thread? Not to sidetrack your main line of argument, but I think it's important to clarify because of the effect that it has on your conclusions.


Again, I'm not sure of the effect it has on my conclusions.
I don't even see the relevence of Godel's results to the position I have put forward. Maybe I'm too focused on other issues to notice the point at hand, but I saw all the discussion on Godel as a red herring side-track.

I'll take another look by all means, but it might be that you need to spell it out to me.


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BobSpence1 wrote: These are

BobSpence1 wrote:
These are not arbitrary rules and are not context dependent.

So you say, but can you justify why not?
I don't consider the rules of logic to be arbitrary, I consider them to be rooted in whatever 'language game' we are playing at that moment in time. (Are you familiar with Wittgenstein and his terminology?)

Why do we use the rules of logic and not some other rules?
I think that when you try and answer this question you will see where I am coming from.

Quote:
The limitation is that the propositions A, B, C, etc have to be precisely nailed down assertions or observations, that can only be true or false.

Here you're describing one set of rules.
Perhaps we could call it the rules of the 'observation language game'. A sentence is true if it describes something observed and false if it contradicts something observed.
This is the kind of language we use when we make statements like:
"There is a blue chair over in that corner."

That sentence describes an observation that can either be true or false.
Take a similar sentence:
"There is a blue seat over in that corner."
Often we would use the sentences synonymously, but this sentence has actually broken the rules that would allow it to be a purely observational sentence.
When we call something a 'seat', it means that we think it would be good to 'sit' upon, so by calling something a seat we have inserted a kind of human value into the sentence.

The langauge of science deals purely in observation, so keeps itself free from such 'value concepts' in it's language. That's why the logic we use in scientific language is based around the observation language game. However, this observation language clearly isn't the only one important to us as human beings. We have a range of language uses, each with their own variations and rules to follow. In that sense, the concepts that appear in these 'language games' will have different rules to those of the 'observation langauge game'.

Quote:
The bottom line is that if a statement in language is shown to be inconsistent with the appropriate level of logic, it is invalid, period.

This appears to sum up the big premise behind your position that I disagree with. You appear to place the rules of logic as more fundamental as the rules of a language. i.e. language must conform to the rules that you call 'logic', rather than logic being a natural consequence of following the rules of our language.

If so, where did these rules come from and why are they so fundamental?
I can answer that question for language:
Language develloped out of our practical use of it in the real world.
"Hello" has a purpose as a greeting that the law of non-contradiction appears to bare no relevent whatsoever.
The reason why the rules of language are so fundamental to any debate is that they are necessary for debate to be possible. Hence if we are asking a question, you either reject the question as meaningless or you answer it on the terms of the language.

I think that many people in this community have made an error in that they have assumed that the pure observation language of science is the language that all others must be based on or reducible to. My only guess is that they found the language of science so successful in dealing with scientific matters that they fell in love with it or got used to it or got into the habit of trying to re-phrase questions to fit it, and began to assume that it was the language that they should always try and use to answer questions.

I don't see how such an assumption can be justified.


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Strafio wrote:

Strafio wrote:
BobSpence1 wrote:
These are not arbitrary rules and are not context dependent.
So you say, but can you justify why not? I don't consider the rules of logic to be arbitrary, I consider them to be rooted in whatever 'language game' we are playing at that moment in time. (Are you familiar with Wittgenstein and his terminology?) Why do we use the rules of logic and not some other rules? I think that when you try and answer this question you will see where I am coming from.

I think the rules are independent of language. The kind of logic, (basic binary logic, inductive, etc) that may be appropriate to apply to analyse a particular statement in a particular discussion will indeed be dependent on, as you put it, whatever 'language game' we are playing at that.

And I agree that logical analysis in any formal sense may not be appropriate way to understand or test the validity of a given statement., especially if we are talking about very subjective things like values.

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Quote:
The limitation is that the propositions A, B, C, etc have to be precisely nailed down assertions or observations, that can only be true or false.
Here you're describing one set of rules. Perhaps we could call it the rules of the 'observation language game'. A sentence is true if it describes something observed and false if it contradicts something observed. This is the kind of language we use when we make statements like: "There is a blue chair over in that corner." That sentence describes an observation that can either be true or false. Take a similar sentence: "There is a blue seat over in that corner." Often we would use the sentences synonymously, but this sentence has actually broken the rules that would allow it to be a purely observational sentence. When we call something a 'seat', it means that we think it would be good to 'sit' upon, so by calling something a seat we have inserted a kind of human value into the sentence. The langauge of science deals purely in observation, so keeps itself free from such 'value concepts' in it's language. That's why the logic we use in scientific language is based around the observation language game. However, this observation language clearly isn't the only one important to us as human beings. We have a range of language uses, each with their own variations and rules to follow. In that sense, the concepts that appear in these 'language games' will have different rules to those of the 'observation langauge game'.

This argument is really just a demonstration of what I just said. Once you use a term like 'seat' which is one step away from a simple object reference, you complicate the applicabiity of logic to it. In this instance, I would say it is still reasonable to analyse it logically, but as you say you have introduced another level of reference. But even that can still be described logically, by explicitily acknowledging the subjective element.

It may require us to analyse the form of the object and assess how closely it conforms to a range of possible confiqurations which have been judged as suitable for use as a seat. We may only be able to assert a probability that the people involved in the discussion will agree that it meets their standards for an acceptable 'seat'.

You refer to 'true or false', which means you are assuming a particular level of logic, ie, simple binary logic. Which may indeed be not appropriate to the next form of statement, but does not exclude forms of logic expanded to encompass uncertainty and 'sets', where terms like 'some' and 'all' and 'none' are formal qualifiers.

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The bottom line is that if a statement in language is shown to be inconsistent with the appropriate level of logic, it is invalid, period.
This appears to sum up the big premise behind your position that I disagree with. You appear to place the rules of logic as more fundamental as the rules of a language. i.e. language must conform to the rules that you call 'logic', rather than logic being a natural consequence of following the rules of our language. If so, where did these rules come from and why are they so fundamental?

From starting points like the law of non-contradiction, which simply means a statement that asserts a simple contradiction is invalid.

Like a statement that "That chair has three legs" in the same context with another statement clearly referring to the same object, at the same time, that asserts that it has four legs. Such an example is so obviously mistake that we hardly need formal logical analysis to detect it.

Surely such a contradiction is a pretty fundamental error - the rest of logic is a rigorous elaboration of the implications of this fundamental observation as more propositions are involved.

But for progressively more subtle fallacies that depend on more complex sets of assertions may require explicit analysis to detect.

And of course there are types of discussion where logic analysis is really not relevant, especially when we are tossing around highly subjective and personal wants and desires and feelings.

But if we make an assertion of fact about non-subjective reality, logic or science may be applicable, depending on the nature of the assertion.

In a sense, language 'rules' share something with logic, namely they are both ways to formally describe things we ordinarily do without explicitly thinking of the 'rules'. Language 'rules' are about communicating with others, logic 'rules' are about 'reasoning'.

Quote:

I can answer that question for language: Language develloped out of our practical use of it in the real world. "Hello" has a purpose as a greeting that the law of non-contradiction appears to bare no relevent whatsoever. The reason why the rules of language are so fundamental to any debate is that they are necessary for debate to be possible. Hence if we are asking a question, you either reject the question as meaningless or you answer it on the terms of the language. I think that many people in this community have made an error in that they have assumed that the pure observation language of science is the language that all others must be based on or reducible to.

It is appropriate to use science as the model if we attempting to establish or at least debate the objective truth status of some proposition, which surely applies to the context of a debate.

I would agree that that is not appropriate to all communication.

Quote:

My only guess is that they found the language of science so successful in dealing with scientific matters that they fell in love with it or got used to it or got into the habit of trying to re-phrase questions to fit it, and began to assume that it was the language that they should always try and use to answer questions. I don't see how such an assumption can be justified.

Surely it is still appropriate in answering questions about objective reality. You may have too narrow a view of the areas of knowledge to which science, or scientific style argument, can apply. Many tedious ongoing 'debates' are precisely due to differences in the way different people use and understand various key words, which is precisely where trying to get everyone to re-phrase things in more precise terms is essential.

If someone finds difficulty doing this, it may be that they indeed have not got a clear idea of just what they are talking about, and are just regurgitating second-hand concepts, or arguments they have just accepted uncritically from someone else or some web-site.

If the question is about what is your favourite food, or sport, or film, whatever, of course the language of science is inappropriate, along with a whole range of things people talk about.

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BobSpence1 wrote: I think

BobSpence1 wrote:
I think the rules are independent of language. The kind of logic, (basic binary logic, inductive, etc) that may be appropriate to apply to analyse a particular statement in a particular discussion will indeed be dependent on, as you put it, whatever 'language game' we are playing at that.

So we could say that:
"A logical rule is appliccable when it coincides with a rule of the language game that we are playing at that moment in time."
Or even generalise it from 'language game' to 'practice' in general, right?

Whether we call 'fuzzy logic' logic or not is just naming.
All I want to show that 'fuzzy logic' is equivalent to logic in that it's a rule of reasoning that coincides/is justified by the rules of the 'practice' we are going at that moment in time.

BobSpence1 wrote:
And I agree that logical analysis in any formal sense may not be appropriate way to understand or test the validity of a given statement., especially if we are talking about very subjective things like values.

If the question is about what is your favourite food, or sport, or film, whatever, of course the language of science is inappropriate, along with a whole range of things people talk about.


This is kind of what I've been looking for.
I just want to make some points here:
1) There are still 'logical' rules to subjective language too.
E.g. You can contradict your friend's tastes but you're not supposed to contradict your own.
So there's still a kind of logic to subjective language.

2) If the language of science and the language of value are a black and white then there are several shades of grey in between that mix things up in lots of ways.
For instance, I noted in the last post that we would treat "There's a blue chair over there" and "There's a blue seat over there" as synonyms, but there is actually a subtle difference as 'seat' brings in a value concept wheras the 'chair' sentence is purely observational.

BobSpence1 wrote:

This argument is really just a demonstration of what I just said. Once you use a term like 'seat' which is one step away from a simple object reference, you complicate the applicabiity of logic to it. In this instance, I would say it is still reasonable to analyse it logically, but as you say you have introduced another level of reference. But even that can still be described logically, by explicitily acknowledging the subjective element.

It may require us to analyse the form of the object and assess how closely it conforms to a range of possible confiqurations which have been judged as suitable for use as a seat. We may only be able to assert a probability that the people involved in the discussion will agree that it meets their standards for an acceptable 'seat'.


No disagreement here.
I just want to note what we're doing here.
We notice that the language game has expanded from the purely observational language game, so our methods of reasoning must account for the new rules involved. As you have noted, the key element is how people use the word 'seat', what criteria we would generally apply, etc.

Strafio wrote:
You appear to place the rules of logic as more fundamental as the rules of a language. i.e. language must conform to the rules that you call 'logic', rather than logic being a natural consequence of following the rules of our language. If so, where did these rules come from and why are they so fundamental?

BobSpence1 wrote:
From starting points like the law of non-contradiction, which simply means a statement that asserts a simple contradiction is invalid. Like a statement that "That chair has three legs" in the same context with another statement clearly referring to the same object, at the same time, that asserts that it has four legs. Such an example is so obviously mistake that we hardly need formal logical analysis to detect it.
Surely such a contradiction is a pretty fundamental error - the rest of logic is a rigorous elaboration of the implications of this fundamental observation as more propositions are involved.

Again, no disagreement here but I want to make some remarks on what you're saying here. You say that the law of non-contradiction doesn't need to be justified as it is so obvious. It is indisputable to everyone's intuitive common sense.

This appears to fit my idea that it follows naturally from our language use of the words 'not' and 'and'. If you go back to the OP, I did a thought experiment to the consequences to if we allowed contradictions. The consequences was that the word 'not' fell to pieces and became meaningless.
For someone to be able to debate they need to grasp the language, which means that they are automatically following the rules of that language.
This would explain why the law of non-contradiction is so intuitively obvious to us, as it is a result of following the rules that we are already doing so in our language.

BobSpence1 wrote:
It is appropriate to use science as the model if we attempting to establish or at least debate the objective truth status of some proposition, which surely applies to the context of a debate.

I'd say that what rules of logic we use will depend on what the language is of the propositions that we are debating.

BobSpence1 wrote:
Surely it is still appropriate in answering questions about objective reality. You may have too narrow a view of the areas of knowledge to which science, or scientific style argument, can apply.

This might be pedantic of me, but I think that your idea of 'objective truth' might be a bit narrow.

BobSpence1 wrote:
Many tedious ongoing 'debates' are precisely due to differences in the way different people use and understand various key words, which is precisely where trying to get everyone to re-phrase things in more precise terms is essential.

But do you accept the possibility that there are words that just cannot be re-phrased into more precise terms?
If the language we use is based on our needs as people, surely a variety of words will crop up that don't seem to fit any kind of precise definition, and that any attempt to do so just appears to lose everything that made that word that word, i.e. you've just made a brand new word rather than made the old one more precise.

There seem to be a lot of words that are important to us that evade strict definition in this way. 'Love' is a famous example. Wittgenstein used the word 'game' as an example, claiming that whatever strict definition you tried to lay down as to what constitutes a 'game', you could find a counter example to that definition.

BobSpence1 wrote:
If someone finds difficulty doing this, it may be that they indeed have not got a clear idea of just what they are talking about, and are just regurgitating second-hand concepts, or arguments they have just accepted uncritically from someone else or some web-site.

That is also a possibility.
Again, it depends on the subject matter.
Science is applied to subject matters where precision is both possible and favourable.
Sometimes we are talking in other subject matters.

I'd like to draw a summary here of the points I am trying to make in this topic. I'd be interested to see how plausible you find them given my arguments.

1) Logical methods are rules, and like all rules there's a time and a place when they should or shouldn't be applied.

2) When in discussion or thought, the 'language game' or 'practice' we are following determines which rules are applicable.
Concepts like 'truth' and 'falsity' also depend on the language game at hand.

3) So if a statement follows from the rules of its language game then it cannot be illogical. We can, however, criticise the very language game on the ground of practical reason.
E.g. If I invented a language game where the only two rules were: "BobSpence is wrong" is always true and
"Strafio is right" is always true
then "Strafio is right" would be a tautology given the game.
You could then point out that such a 'language game' is pointless and there's no reason why we would want to abide by such rules in real life.

You will notice that you defended precision on an argument of practicality, showing how imprecision mixes up debates.
Now I will bring the relevence of religion into this.
If religion is a practice/'language game' in its own right, then logical evaluation would be based on the rules of this practice. To evaluate the practice would be a matter of practical reason on whether this practice was beneficial to a person's life?
Do you agree that is how we would evaluate a religious practice?

Whether such a religious practice could be justifiable is a question for a later essay. I just want to get agreement here on how we would go about evaluating such a practice.
If so, the rationality of a religious belief would be evaluatable in two possible ways:
1) Whether the belief follows the rules of the language game/practice it is grounded in
2) Whether the language game/practice that it is grounded in is beneficial to our lives

In a sense, the same applies to science.
The only difference with science, as far as I can see, is that we can answer condition (2) with an obvious yes.


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Strafio wrote:

Strafio wrote:

Again, no disagreement here but I want to make some remarks on what you're saying here. You say that the law of non-contradiction doesn't need to be justified as it is so obvious. It is indisputable to everyone's intuitive common sense. This appears to fit my idea that it follows naturally from our language use of the words 'not' and 'and'. If you go back to the OP, I did a thought experiment to the consequences to if we allowed contradictions. The consequences was that the word 'not' fell to pieces and became meaningless. For someone to be able to debate they need to grasp the language, which means that they are automatically following the rules of that language. This would explain why the law of non-contradiction is so intuitively obvious to us, as it is a result of following the rules that we are already doing so in our language.

I think this may be an incomplete view of the law of non-contradiction. I do not believe that the reason I find contradictory things to be non-sensical is because of my language. I am horrible at memorizing language, I am better at understanding concepts. Therefore, intuitively from my point of view, if it was simply a rule, then I would not be able to remember it well, or it would not sit with me.

This is my intuitive reason to reject it. My logical reason to reject it is this: the law of non-contradiction preceeds logic, but it does not preceed reason. We can observe axioms using our reason. Saying "I think therefore I exist" does not require the use of logic, it simply requires an examination of the consequences of thinking otherwise (if I did not exist, how could I be thinking?)

Now, I think it is safe to say that when we our founders were developing language, they attempted to say "that berry is poisonous and that berry is not poisonous." They would have quickly realized the absurdity of this statement, or they would have quickly died. Beyond this, however, by using reason that human would have realized that the berry can not be both poisonous and non-poisonous, since one kills him and the other does not and it can only be one, and not the other--since he has eaten berries that do not poison him.

Now, Hamby might interject and call this "logic" but I say that he was simply "reasoning." He was trying to come to a conclusion about language that made sense.

 

In all, when the first humans were developing language, they would have found that it had to follow the law of non-contradiction.  Animals, before they ever use langauge (practically none do) are able to follow the law of non-contradiction.  The Gazelle says "Lions are dangerous"  he does not claim that lions are both dangerous and not dangerous.  His instinct does not allow him to have a contradiction on this subject, and neither would have our ancestors.  They could have applied this "instinct" (i view it as an incomplete term) to their language.  Therefore reason preceeds language, and the law of non-contradiction is not a corrollary of our language (although language can be used to understand such a law).

 


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Strafio wrote: Textom

Strafio wrote:
Textom wrote:

Following this thread and have just a quick question for Strafio:

I've seen you go a couple of rounds before with people over the uses of Godel's theorem without, apparently, accepting that most people are not referring to the incompleteness theorem itself, but rather its implications for formal systems as worked out by Hofstadter and others.

Change 'not accepting' to 'not realizing'. It completely passed me by. Are these conclusions like it cannot be proved that maths is consistent, and things like that?

Yes, in a sense.  But beyond even that--thinkers like Hofstadter have shown that the implications of Godel's theorem suggest that any formal system can't be used to make meaningful statements about itself. A system of meaning or representation always "breaks" when you turn it back on itself.

Quote:
Quote:

Are you persuaded by Devilin and Bob's use of the (extended version of) Godel's theorem in this thread? Not to sidetrack your main line of argument, but I think it's important to clarify because of the effect that it has on your conclusions.

Again, I'm not sure of the effect it has on my conclusions. I don't even see the relevence of Godel's results to the position I have put forward. Maybe I'm too focused on other issues to notice the point at hand, but I saw all the discussion on Godel as a red herring side-track. I'll take another look by all means, but it might be that you need to spell it out to me.

I should have said "premises" rather than "conclusions."   I think Dev's point is that logic can't be used to support itself.  The statement "Logic is logical" can't be accommodated or evaluated within the system of logic.  So attempting to use reason to show that something is rational has the same problem.

So, yes, that and 5 bucks will get you a bowl of soup.  The fact that the argument is based on a tautology shouldn't stop you from making it anyway.  But I agree with Devlin it's important to acknowledge.  You may even actually be able to use it to support part of your argument somehow.

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I used to have a Dawkins

I used to have a Dawkins quote on my sig. I hope I'm quoting it right. If not, it's a damn close paraphrase:

"Premature erection of alleged philosophical problems is often a smokescreen for mischief."

This saying always comes to mind when someone starts invoking Godel in the "theism is not irrational" discussion. I've yet to see anyone make a meaningful argument out of it. Put very simply, mathematicians and philosophers can argue the minutia of this stuff with regard to AI and such for a century, and I fail to see how it has any bearing at all on the dependence of thought on logic and logic on tautology. The theorem doesn't (as far as I can tell) have any effect on certainty within deduction, and (as todangst has demonstrated) there are ways to link induction to deduction, so we're left with something like this:

A: Logic is axiomatic to knowledge.

T: Yeah, but Godel!

A: Um. Yes. It's a theorem, and logic is axiomatic to knowledge.

T: Yeah, but we don't know.

A: You just admitted we do.

T: How?

A: You thought.

T: But I can't be sure because of Godel

A: (bangs head against wall and leaves.)

 

 

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As you probably know, I

As you probably know, I still don't agree, Hamby, that Tod has sucessfully linked deduction to induction.  My careful examination of his arguments suggests that the only link between induction and deduction there is the unsupported labeling of the former as the latter.

Nobody needs to use Godel to restate the fundamental logical fact that induction can never produce a conclusion that is known to be true. 

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Textom wrote: As you

Textom wrote:

As you probably know, I still don't agree, Hamby, that Tod has sucessfully linked deduction to induction. My careful examination of his arguments suggests that the only link between induction and deduction there is the unsupported labeling of the former as the latter.

Nobody needs to use Godel to restate the fundamental logical fact that induction can never produce a conclusion that is known to be true.

And neither can logic. All it can show is locical consistency of premises and conclusions.

At least induction can produce useful estimates of likelihood, which logic cannot do by itself.

Any coherent argument even, an inductive one, is built around a series of IF...THEN, and similar, statements, which are essentially logical, even when the substance of the statements are expressions about relative or 'absolute' probability.

Favorite oxymorons: Gospel Truth, Rational Supernaturalist, Business Ethics, Christian Morality

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A: Logic is axiomatic to


A: Logic is axiomatic to knowledge.

T: Yeah, but Godel!

A: Um. Yes. It's a theorem, and logic is axiomatic to knowledge.

T: Yeah, but we don't know. say that an infinite will-not contradict itself at some point

A: Um.. errrr ummmmm eeerrrr but

T : (bangs head against wall Wink)

 

logic is an incredibly powerful tool, but it has limits therefore one can-not derive absolute truth from its conclusions, conclusions with an incredibly high probability of truth yes, but it lacks absolute certainty

logic is a tool understanding its limitations or the limitations of any tool will help oneself in its correct use and application, diminishing returns in certainty Wink oh my

A: Yeah, but this is just mathematics, what has mathematics ever done for us

T: that would be just about everything wouldn't it (bangs head against wall and leaves Wink.) 


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Bob Spence wrote: And

Bob Spence wrote:
And neither can logic.

I'm gonna have to go ahead and call this statement factually incorrect, Bob.  Deductive logic can produce conclusions that are known to be true.

That's why it's important to acknowledge the difference.

But I'm pulling this thread off the line of Strafio's main argument now, so I'll stop. 

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Quote: As you probably

Quote:
As you probably know, I still don't agree, Hamby, that Tod has sucessfully linked deduction to induction.

I'm only speaking for myself, as I don't know Tod's opinion on this, but I'm not trying to say that the link between induction and deduction makes induction certain. That would be nonsense, since induction is about probability. All I'm saying is that induction is not just plucked out of thin air. When theists argue using Godel, or the problem of induction, they don't even understand what the problem of induction is!

Quote:
My careful examination of his arguments suggests that the only link between induction and deduction there is the unsupported labeling of the former as the latter.

I don't want to derail this thread further by speculating for todangst. He's the guy with the letters after his name, and I'd just as soon let him speak for himself. However, the crux of my argument stands regardless of whether there is a link between induction and deduction. (That's really a bit out of my expertise.)

When someone claims that the problem of induction is a supporting argument for something that is Vanishingly* improbable, they are both misunderstanding and misusing the issue. The probability that induction doesn't work is so Vanishingly small that everyone on the planet could spend their lives writing zeros and we might not express it fully. It's so staggeringly preposterous that it literally isn't worth conversation except to theoretical philosophers, and even then, it could be argued that the only person benefitting from such a conversation would be the girl behind the counter selling them coffee.

Furthermore, if we take the Argument from the Problem of Induction seriously, then, again borrowing from Daniel Dennett, we are playing with the philosophical net down, and we might as well just stop talking because we will never be able to agree on anything. Literally. Even the fact that we can never agree won't be in agreement. It's preposterous.

Quote:
Nobody needs to use Godel to restate the fundamental logical fact that induction can never produce a conclusion that is known to be true.

That's more like my point. Godel is a red herring in arguments about things being rational or irrational in the context of Strafio's thesis. In short, the problem of induction has a Vanishingly small probability of contributing anything to a discussion of day to day critical thinking.

 

*Daniel Dennett, in Darwin's Dangerous Idea, coins the words Vastly and Vanishingly, with the capital letters, to deal with numbers that are "very much more than astronomically" big or small, respectively. If you're familiar with the idea of the Library of Mendel, you know what I'm talking about. In short, we're dealing with numbers that exceed the number of atoms in the universe.

 

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Hambydammit wrote: . In

Hambydammit wrote:

. In short, we're dealing with numbers that exceed the number of atoms in the universe.

Wot more than one ? Wink  ( hypothetical spinoff of the many worlds interpretation, the entire universe is just one single atom in superposition, my apologies I couldn't resist )


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Textom wrote: I think

Textom wrote:

I think Dev's point is that logic can't be used to support itself. The statement "Logic is logical" can't be accommodated or evaluated within the system of logic. So attempting to use reason to show that something is rational has the same problem.

So, yes, that and 5 bucks will get you a bowl of soup. The fact that the argument is based on a tautology shouldn't stop you from making it anyway. But I agree with Devlin it's important to acknowledge. You may even actually be able to use it to support part of your argument somehow.


I guess it's interesting in general, I was just questioning the relevence it had to my post.
My 'grounding' of logic in the OP was to show that if we were to ignore the law of non-contradiction then our language would break down. Seeing as any debate pre-supposes that language is in place, the law of non-contradiction will hold in any such debate.

That's why I didn't see why Godel was brought in.


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Uncertainty, The more

Uncertainty,

The more complex the logical argument get's, the less likely it is to be true, diminishing returns of certainty, uncertainty and contradictions are part of everyday life, there it is

It is how one deals with uncertainty and contradictions, is it not

What is the rational response to uncertainty and contradictions,

I don't know I am uncertain, (vs) I know with absolute certainty the flying spaghetti monster bridges this uncertainty

? can you see where this is going

 


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Rev_Devilin

Rev_Devilin wrote:

Uncertainty,

The more complex the logical argument get's, the less likely it is to be true, diminishing returns of certainty, uncertainty and contradictions are part of everyday life, there it is

It is how one deals with uncertainty and contradictions, is it not

What is the rational response to uncertainty and contradictions,

I don't know I am uncertain, (vs) I know with absolute certainty the flying spaghetti monster bridges this uncertainty

? can you see where this is going 

 

I can't, not when you are basing it off Godel's

In Godel's we know when the truth value of something cannot be certain, it has to be such and such an entity within such and such a system.  Unless you can demonstrate that Strafio's arguments are such entities within the system of logic, your entire premise that Godel's theorem will lead to some kind of uncertaintly in the logical conclusion is pretty much unfounded.

This is just my own perspective after giving a quick read to the Wikipedia page of Godel's and reading a few of the comments here, so feel free to call me out if I don't know what I am talking about.  But as far as I can tell, Godel's theorem only applies to very specific instances; instances that are known because of Godels theorem!

In other words, it doesn't demonstrate much of a problem. 


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Hambydammit

Hambydammit wrote:

Quote:
As you probably know, I still don't agree, Hamby, that Tod has sucessfully linked deduction to induction.

I'm only speaking for myself, as I don't know Tod's opinion on this, but I'm not trying to say that the link between induction and deduction makes induction certain. That would be nonsense, since induction is about probability. All I'm saying is that induction is not just plucked out of thin air. When theists argue using Godel, or the problem of induction, they don't even understand what the problem of induction is!

Quote:
My careful examination of his arguments suggests that the only link between induction and deduction there is the unsupported labeling of the former as the latter.

I don't want to derail this thread further by speculating for todangst. He's the guy with the letters after his name, and I'd just as soon let him speak for himself. However, the crux of my argument stands regardless of whether there is a link between induction and deduction. (That's really a bit out of my expertise.)

When someone claims that the problem of induction is a supporting argument for something that is Vanishingly* improbable, they are both misunderstanding and misusing the issue. The probability that induction doesn't work is so Vanishingly small that everyone on the planet could spend their lives writing zeros and we might not express it fully. It's so staggeringly preposterous that it literally isn't worth conversation except to theoretical philosophers, and even then, it could be argued that the only person benefitting from such a conversation would be the girl behind the counter selling them coffee.

Furthermore, if we take the Argument from the Problem of Induction seriously, then, again borrowing from Daniel Dennett, we are playing with the philosophical net down, and we might as well just stop talking because we will never be able to agree on anything. Literally. Even the fact that we can never agree won't be in agreement. It's preposterous.

Quote:
Nobody needs to use Godel to restate the fundamental logical fact that induction can never produce a conclusion that is known to be true.

That's more like my point. Godel is a red herring in arguments about things being rational or irrational in the context of Strafio's thesis. In short, the problem of induction has a Vanishingly small probability of contributing anything to a discussion of day to day critical thinking.

 

*Daniel Dennett, in Darwin's Dangerous Idea, coins the words Vastly and Vanishingly, with the capital letters, to deal with numbers that are "very much more than astronomically" big or small, respectively. If you're familiar with the idea of the Library of Mendel, you know what I'm talking about. In short, we're dealing with numbers that exceed the number of atoms in the universe.

I'm gona go out on a limb here and flat out disagree with everything portrayed here. While I agree that there is no rational purpose (rather than being philosophically complete) to giving serious question to induction, that doesn't mean one can go around setting up probability values for it. If this world is a program, there is nothing that we can say which can put a probability on this world not being a program. Is there a purpose in thinking it might be a program in our daily decisions? Of course not, but you can't just set a probability to it, even if it makes you feel more comftorable. You just have to live your life deluding yourself into believing that the world you see around you is absolute, and that empiricle induction will always work, it doesn't mean you can somehow place a probability to this. You cannot know the future.

 

Edit: then again, this is all just very nit-picky, so if you didn't even respond to it I would fully understand. It really isn't worth derailing this thread over.  The truth is that I mostly agree with you, I just don't agree with your evaluation of probability on somehting that cannot be possibly known.  Saying "the probability of the Flying Spaghetti monster is such and such" is a useless statment--you cannot possibly ascribe a number to such a thing.


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RationalDeist wrote:   I

RationalDeist wrote:
 

I can't, not when you are basing it off Godel's

In Godel's we know when the truth value of something cannot be certain, it has to be such and such an entity within such and such a system. Unless you can demonstrate that Strafio's arguments are such entities within the system of logic, your entire premise that Godel's theorem will lead to some kind of uncertaintly in the logical conclusion is pretty much unfounded.

This is just my own perspective after giving a quick read to the Wikipedia page of Godel's and reading a few of the comments here, so feel free to call me out if I don't know what I am talking about. But as far as I can tell, Godel's theorem only applies to very specific instances; instances that are known because of Godels theorem!

In other words, it doesn't demonstrate much of a problem.

Godel's Smile is only part of this, reason which can contradict itself, also plays its part, "Godel's only affects mathematics", many would argue it affects much more, but lets say you are correct, what does mathematics effect ? just about everything Wink ok it only affects specific equations in a mathematical model I hear you cry, well no it shows that the more complex the system is the less likely it is to be true, diminishing returns in certainty,

 ? but what has all this to do with whether it is rational or not to hold a believe in the flying spaghetti monster

It's part of the groundwork for Strafio's thesis which will undoubtedly end in linguistics, somehow using logic reason language and a small sledgehammer, to argued that theism can be logically rational, (good luck Strafio,  I don't think you can do it, but so far this has been the best argument I've seen) anyway rather than working against Strafio's argument this information could actually help reinforce her argument, generally an atheist position is about truth not about sides, atheist in general will argued for the truth no matter what the conclusions

But...... Wink

Where was I going 

Uncertainty is in the domain of science

Certainty is in the domain of religious belief  "in sure and certain hope of the resurrection to eternal life"

Belief or faith with absolute certainty in any kind of system religious or scientific is necessarily irrational,

And now we have moved to psychology as for why this is so, as irrational is a psychological term

 


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Quote: While I agree that

Quote:
While I agree that there is no rational purpose (rather than being philosophically complete) to giving serious question to induction, that doesn't mean one can go around setting up probability values for it.

Like I said, this goes a bit beyond my focus in logic and philosophy, but consider an application of Bayes theorem where we take the entire history of humanity, complete with every single use of valid induction with true data.  Though the numbers would be wild estimates at best, how precise do you need to be when the resulting probability would be so infintessimally different from one that we could add or subtract astronomically large margins of error and still be essentially one?

 

Quote:
If this world is a program, there is nothing that we can say which can put a probability on this world not being a program. Is there a purpose in thinking it might be a program in our daily decisions? Of course not, but you can't just set a probability to it, even if it makes you feel more comftorable.

You've clearly misunderstood what I'm saying because you're agreeing with me.   There are things to which we cannot assign a probability because we have no way to discuss them coherently.  As I've demonstrated dozens of times, anyone who claims to say anything about an incoherent concept is basically full of shit.

 

Quote:
You just have to live your life deluding yourself into believing that the world you see around you is absolute, and that empiricle induction will always work, it doesn't mean you can somehow place a probability to this. You cannot know the future.

I just demonstrated that if we wanted to, we could come up with a number that would be basically accurate if we had the data to plug into the formula.

In any case, you're still agreeing with me.  Invoking Godel is mistaken in the context of the problem of induction, and invoking the problem of induction is mistaken in the context of critical thinking, which is what the OP is talking about.

 

Quote:
Saying "the probability of the Flying Spaghetti monster is such and such" is a useless statment--you cannot possibly ascribe a number to such a thing.

The FSM is an incoherent concept, and cannot be expressed as a probability.  There is a true number of times that induction has been used in the history of man, and there is a true number of times that it's been valid.  Though we don't have these numbers at our disposal, we can talk about them coherently.

You're right, though.  It's all nitpicky stuff.  To be honest, this whole thread is a gigantic splooge of nitpicky stuff that doesn't have much to do with the topic.   

Atheism isn't a lot like religion at all. Unless by "religion" you mean "not religion". --Ciarin

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Textom wrote:

Textom wrote:

Bob Spence wrote:
And neither can logic.

I'm gonna have to go ahead and call this statement factually incorrect, Bob. Deductive logic can produce conclusions that are known to be true.

That's why it's important to acknowledge the difference.

But I'm pulling this thread off the line of Strafio's main argument now, so I'll stop.

But the only things that logic can show to be true are statements which are at a deep level, tautologies, ie implicit in the premises. So it is really important to keep in mind the difference between the nature and significance of deductive and inductive 'truth'.

Logic can show inconsistencies between informal conclusions and the premises on which those conclusions are based.

It can point to implications of the starting premises, but if those premises do not abolutely accurately correspond to reality, cannot 'prove' those implications must be true in reality.

It is really, really important to 'acknowledge the difference' between deductive 'truths' which can be 'uncovered' and proved by logic, and 'truths' about the existence, attributes, structure, modes of interaction, etc of perceived entities in the world, or the universe itself, which inevitably have a level of uncertainty about them, after explicit contradictions have been eliminated.

It is related to the stupid argument about omnipotence when someone asks if God can create a 'square circle'. It is the failure to distinguish between things which seem to be highly unlikely, from historical observation and inductive reasoning, like water flowing against the force of gravity, and statements which are not meaningful by their very nature, like square circles, married bachelors, etc.

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Rev_Devilin

Rev_Devilin wrote:

Uncertainty,

The more complex the logical argument get's, the less likely it is to be true, diminishing returns of certainty, uncertainty and contradictions are part of everyday life, there it is

It is how one deals with uncertainty and contradictions, is it not


The thing is, Godel's theorem only applied to propositions that have particular conditions.
Such propositions aren't coming up in the debates that we're doing here. If we came across the type of proposition in our debate that Godel's theorem applied to then Godel's theorem would suddenly be of interest.
Until then, I'm not sure it is.

Rev_Devilin wrote:

Godel's Smile is only part of this, reason which can contradict itself, also plays its part


I don't see a contradiction in Godel.
It just accepts that some propositions aren't provable by computational methods. Once again, these propositions have unusual properties which are unlikely to show up in real debate.
If they were there then we would be able recognise them.

Quote:
it shows that the more complex the system is the less likely it is to be true, diminishing returns in certainty

Again, it shows nothing of the sort.
It shows that certain propositions with certain properties (and these properties are clearly recognisable) aren't provable. What's more, it does nothing to refute the propositions in maths that are provable. If we find a theorem in mathematics that appears to be true but we cannot prove, we might have reason to suspect that it is of a Godel type.
I think that Hilbert's Tenth theorem has been shown to be both unprovable and undisprovable.

Quote:
this information could actually help reinforce her argument,

Um... dude?
As it happens, I don't see how Godel helps my position.
I can only see it as an excuse for scepticism towards logic, but that comes off as an argument from ignorance and I'm not a fan of that.
What I'm rather doing is trying to show that the rules of logic depend on the rules of the game. First Order Logic, the language of mathematics and Godel's theorem is one such game.
A theology might have it's own language game and therefore its own rules of logic.

Quote:

And now we have moved to psychology as for why this is so, as irrational is a psychological term


You keep bringing this up.
Could you expand on what you mean by this?
If you are saying what I think you are, it would lead to an argument that myself and Hamby have already had. I tried to show that it didn't make sense to call a belief irrational, given a certain meaning of irrational, but Hamby countered that he was using a different definition of irrational.
He accepted that this definition might not be what people normally use, that people might get the wrong idea and get offended by it, but he says that controversy makes a good motivator to get people debating, and I agree.

Either way, I'd like to hear what you have to say on the psychological definition of 'irrational' and how it affects the debate at hand.


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BobSpence1 wrote: It is

BobSpence1 wrote:

It is related to the stupid argument about omnipotence when someone asks if God can create a 'square circle'.


I've always found the 'rock paradox' to be the atheist's equivalent to the ontological argument. A blatant sophistry that frustrates the opposition because they cannot instantly work out why.


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Rev_Devilin

Rev_Devilin wrote:
RationalDeist wrote:

I can't, not when you are basing it off Godel's

In Godel's we know when the truth value of something cannot be certain, it has to be such and such an entity within such and such a system. Unless you can demonstrate that Strafio's arguments are such entities within the system of logic, your entire premise that Godel's theorem will lead to some kind of uncertaintly in the logical conclusion is pretty much unfounded.

This is just my own perspective after giving a quick read to the Wikipedia page of Godel's and reading a few of the comments here, so feel free to call me out if I don't know what I am talking about. But as far as I can tell, Godel's theorem only applies to very specific instances; instances that are known because of Godels theorem!

In other words, it doesn't demonstrate much of a problem.

Godel's Smile is only part of this, reason which can contradict itself, also plays its part, "Godel's only affects mathematics", many would argue it affects much more, but lets say you are correct, what does mathematics effect ? just about everything Wink ok it only affects specific equations in a mathematical model I hear you cry, well no it shows that the more complex the system is the less likely it is to be true, diminishing returns in certainty,

as far as I know, Godel's doesn't say any such thing.  But I will let someone more learned in it to discuss this with you. 

 

Quote:
? but what has all this to do with whether it is rational or not to hold a believe in the flying spaghetti monster

It's part of the groundwork for Strafio's thesis which will undoubtedly end in linguistics, somehow using logic reason language and a small sledgehammer, to argued that theism can be logically rational, (good luck Strafio, I don't think you can do it, but so far this has been the best argument I've seen) anyway rather than working against Strafio's argument this information could actually help reinforce her argument, generally an atheist position is about truth not about sides, atheist in general will argued for the truth no matter what the conclusions

We will get to this when we get to this.

 

Quote:
But...... Wink

Where was I going

Uncertainty is in the domain of science

Certainty is in the domain of religious belief "in sure and certain hope of the resurrection to eternal life"

certainty is the domain of philosophy and math.  When we are uncertain, we even know it.  Tautologies can never be wrong within their own structures, only the axioms are things which can have a truth or a falsehood.  Obviously you are not an idealist, but you should see that logic and math are absolutes.  Even Godel's knows when it is uncertain, therefore it is absolute about being uncertain.

Quote:
Belief or faith with absolute certainty in any kind of system religious or scientific is necessarily irrational,

really?  Didn't you just make an absolute statement? 

Since you obviously did, then on what grounding did you base that statement?  You thought you were thinking logically, which allowed you to make absolute statements.  But your statement which was said delt with itself.  Strange how I now know that the truth of your statement is uncertain Smiling

 

Quote:
And now we have moved to psychology as for why this is so, as irrational is a psychological term

Hamby thinks it should be defined differently.  Personally, I don't think any person can be "irrational" in that they will always try and make the best decisions they can at the time, but w/e. 


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Hambydammit wrote:Like I

Hambydammit wrote:

Like I said, this goes a bit beyond my focus in logic and philosophy, but consider an application of Bayes theorem where we take the entire history of humanity, complete with every single use of valid induction with true data. Though the numbers would be wild estimates at best, how precise do you need to be when the resulting probability would be so infintessimally different from one that we could add or subtract astronomically large margins of error and still be essentially one?

Hamby, you are missing the entire point.  We are talking about humanity, a very short eyeblink of the history of what we can observe to be the universe.  Pretty much anything outside of that time frame is possible, but pointless to try and create wild extrapolations.

But I think we agree.  I am just being too nitpicky  Being this concise is not really necessary.  (to be more concise, I was talking about the universe and the history of it.  There may, for instance, a time variable universal constant, etc. that we are not observing.  I find this unlikely, but it is hard to say for sure.  And even if it were true, it would not change the universe enough to make it only 6,000 years old, so it is not applicable to any kind of religious argument.)

 

Quote:
You've clearly misunderstood what I'm saying because you're agreeing with me. There are things to which we cannot assign a probability because we have no way to discuss them coherently. As I've demonstrated dozens of times, anyone who claims to say anything about an incoherent concept is basically full of shit.

I understand now what you mean.  Sorry for the inconvienience.

Quote:

I just demonstrated that if we wanted to, we could come up with a number that would be basically accurate if we had the data to plug into the formula.

In any case, you're still agreeing with me. Invoking Godel is mistaken in the context of the problem of induction, and invoking the problem of induction is mistaken in the context of critical thinking, which is what the OP is talking about.

Right, I did say that I was mostly being nitpicky. 

Quote:
The FSM is an incoherent concept, and cannot be expressed as a probability. There is a true number of times that induction has been used in the history of man, and there is a true number of times that it's been valid. Though we don't have these numbers at our disposal, we can talk about them coherently.

You're right, though. It's all nitpicky stuff. To be honest, this whole thread is a gigantic splooge of nitpicky stuff that doesn't have much to do with the topic.

Ok, good to see we agree.  /arguments 


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Strafio wrote: Rev_Devilin

Strafio wrote:
Rev_Devilin wrote:

Uncertainty,

The more complex the logical argument get's, the less likely it is to be true, diminishing returns of certainty, uncertainty and contradictions are part of everyday life, there it is

It is how one deals with uncertainty and contradictions, is it not

The thing is, Godel's theorem only applied to propositions that have particular conditions. Such propositions aren't coming up in the debates that we're doing here. If we came across the type of proposition in our debate that Godel's theorem applied to then Godel's theorem would suddenly be of interest. Until then, I'm not sure it is.

THANK YOU.  I read through it and I could have swore that this was, if not a corrolary, a fairly obvious conclusion.

The absolute of tautology stands, Godel's does nothing to bring it down Smiling 

 

I agreed with everything else you said as well.

 


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Strafio wrote: Rev_Devilin

Strafio wrote:
Rev_Devilin wrote:

 

And now we have moved to psychology as for why this is so, as irrational is a psychological term

You keep bringing this up. Could you expand on what you mean by this? If you are saying what I think you are, it would lead to an argument that myself and Hamby have already had. I tried to show that it didn't make sense to call a belief irrational, given a certain meaning of irrational, but Hamby countered that he was using a different definition of irrational. He accepted that this definition might not be what people normally use, that people might get the wrong idea and get offended by it, but he says that controversy makes a good motivator to get people debating, and I agree. Either way, I'd like to hear what you have to say on the psychological definition of 'irrational' and how it affects the debate at hand.

Rational or irrational are defined by what the majority of people in a society do or do not do in that society

Smile wasn't that easy

 

 


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RationalDeist

RationalDeist wrote:

Belief or faith with absolute certainty in any kind of system religious or scientific is necessarily irrational,

 

really? Didn't you just make an absolute statement?

Since you obviously did, then on what grounding did you base that statement? You thought you were thinking logically, which allowed you to make absolute statements. But your statement which was said delt with itself. Strange how I now know that the truth of your statement is uncertain Smiling

Good we are making progress Wink

http://en.wikipedia.org/wiki/Axiomatization

Diminishing returns in certainty for your edification

 

Now if you would care to indulge me a little

what is ? ten divided by three , is there a true false or uncertain answer to this worded question ?


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Rev_Devilin wrote:

Rational or irrational are defined by what the majority of people in a society do or do not do in that society

Smile wasn't that easy


I don't like that definition...
It means that once upon a time it was rational to be racist or rational to think strange old women were witches that needed burning.
I'm thinking that was too easy there Dev! Sticking out tongue


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In psychological terms the

In psychological terms the majority rules, in any given society

The truth (or to within a degree of certainty Wink ) is usually incredibly simple, many things in today's society that your-self consider perfectly rational, may be considered highly irrational in a future society, crazy isn't it Wink but can you deny the truth of it ?


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Rev_Devilin

Rev_Devilin wrote:
Strafio wrote:
Rev_Devilin wrote:

 

And now we have moved to psychology as for why this is so, as irrational is a psychological term

You keep bringing this up. Could you expand on what you mean by this? If you are saying what I think you are, it would lead to an argument that myself and Hamby have already had. I tried to show that it didn't make sense to call a belief irrational, given a certain meaning of irrational, but Hamby countered that he was using a different definition of irrational. He accepted that this definition might not be what people normally use, that people might get the wrong idea and get offended by it, but he says that controversy makes a good motivator to get people debating, and I agree. Either way, I'd like to hear what you have to say on the psychological definition of 'irrational' and how it affects the debate at hand.

Rational or irrational are defined by what the majority of people in a society do or do not do in that society

wasn't that easy

Wait a sec, theism would be rational under that definition in any society where >50% adhere to it. I recall that being the argument against lobbying to have theism listed as a mind disorder -- that behavior is gauged by social norms. So a delusion, no matter how profound, can't be called abnormal if the majority is afflicted. Rationality, I think, though, needs justification, not just mass.