# Rational, Irrational, and Arational.

Topher
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Rational, Irrational, and Arational.

Here is how I'm defining these terms in relation to each other.

Rational means not irrational.

Irrational means not rational.

Arational means not rational AND not irrational.

Thus, only things within the class of reason can be classified as being rational or irrational. Everything outside of that class (i.e. things not based on reason) would be arational, so saying, for example, "football is rational", or this "cup is irrational" would be category errors.

Discuss.

"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring" -- Carl Sagan

tothiel
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So,'Rational' is something

So,

'Rational' is something that not only exist within the realm of reason, but is also congruent with it.  (I.E. I'm cold so I put on a sweater.)

'Irrational' is something that also exist within the realm of reason, but fails to be a congruent product of it's correct counter part. (I.E. I'm cold so I take off my clothes and go stand in the snow.)

'Arational/non-rational' is something that has no relation to reason in the first place. (I.E. Something instinctive/intuitive/exist in nature.)

Is this correct?

As through a glass darkly you seek yourself,
But the light grows weak while under Yggdrasil. --clutch

HisWillness
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Topher wrote:Thus, only

Topher wrote:

Thus, only things within the class of reason can be classified as being rational or irrational. Everything outside of that class (i.e. things not based on reason) would be arational, so saying, for example, "football is rational", or this "cup is irrational" would be category errors.

Ha! I love it!

But wouldn't that limit the realm of "arational" to things without the capacity for rationality? As long as an agent had the capacity to be rational, but exhibited irrational behaviour, that behaviour would still concern rationality by its conspicuous absence. Furthermore, rocks and stars would be arational, but even pencils and tables, which are the result of a rational process, could not be arational if that's what you're getting at with "based on reason".

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence

Hambydammit
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I guess if you have to have

I guess if you have to have a word for things that are not subject to reason, that's as good a word as any, but it sort of seems like a-unicornist.  It's perfectly valid, but what's the point?

In Strafio's post about religious belief vs. rational belief, I kept returning to the point that arational is simply special pleading when applied to anything that requires reason.  I guess I just don't like throwing out another word to be conflated.

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

Topher
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tothiel wrote:So,'Rational'

tothiel wrote:

So,

'Rational' is something that not only exist within the realm of reason, but is also congruent with it.  (I.E. I'm cold so I put on a sweater.)

'Irrational' is something that also exist within the realm of reason, but fails to be a congruent product of it's correct counter part. (I.E. I'm cold so I take off my clothes and go stand in the snow.)

'Arational/non-rational' is something that has no relation to reason in the first place. (I.E. Something instinctive/intuitive/exist in nature.)

Is this correct?

Yes.

"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring" -- Carl Sagan

Topher
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Hambydammit wrote:I guess if

Hambydammit wrote:

I guess if you have to have a word for things that are not subject to reason, that's as good a word as any, but it sort of seems like a-unicornist.  It's perfectly valid, but what's the point?

In Strafio's post about religious belief vs. rational belief, I kept returning to the point that arational is simply special pleading when applied to anything that requires reason.  I guess I just don't like throwing out another word to be conflated.

Well I agree with Strafio that there are arational things (intuition, instinct, etc), I just don't think religion is in that category.

The point to my post was someone I was discussing this with held the view that everything rational was called 'rational', and everything else was 'not rational', including things that have nothing to do with reason (e.g. "the weather isn't rational" ). I think "not rational' implies irrational. To me, rational, irrational, not rational, not irrational are all indicators of reason so it makes no sense to even apply them to things that have nothing to do with reason, hence the term arational.

"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring" -- Carl Sagan

Topher
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HisWillness wrote:Topher

HisWillness wrote:

Topher wrote:

Thus, only things within the class of reason can be classified as being rational or irrational. Everything outside of that class (i.e. things not based on reason) would be arational, so saying, for example, "football is rational", or this "cup is irrational" would be category errors.

But wouldn't that limit the realm of "arational" to things without the capacity for rationality?

That's the point.

HisWillness wrote:
As long as an agent had the capacity to be rational, but exhibited irrational behaviour, that behaviour would still concern rationality by its conspicuous absence.

Right.

HisWillness wrote:
Furthermore, rocks and stars would be arational, but even pencils and tables, which are the result of a rational process, could not be arational if that's what you're getting at with "based on reason".

I don't merely mean 'based on reason'. It would be nonsensical to call a pencil or a table, in of itself, rational or irrational, even though they are the result of rational processes.

"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring" -- Carl Sagan

HisWillness
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Topher wrote:HisWillness

Topher wrote:

HisWillness wrote:
Furthermore, rocks and stars would be arational, but even pencils and tables, which are the result of a rational process, could not be arational if that's what you're getting at with "based on reason".

I don't merely mean 'based on reason'. It would be nonsensical to call a pencil or a table, in of itself, rational or irrational, even though they are the result of rational processes.

It would be nonsensical, but since the topic seemed tongue-in-cheek, I thought you were playing. Especially if you were setting up a parody of the universe as a giant mind (an argument I've yet to see completed).

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence

Topher
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HisWillness wrote:Topher

HisWillness wrote:

Topher wrote:

HisWillness wrote:
Furthermore, rocks and stars would be arational, but even pencils and tables, which are the result of a rational process, could not be arational if that's what you're getting at with "based on reason".

I don't merely mean 'based on reason'. It would be nonsensical to call a pencil or a table, in of itself, rational or irrational, even though they are the result of rational processes.

It would be nonsensical, but since the topic seemed tongue-in-cheek, I thought you were playing. Especially if you were setting up a parody of the universe as a giant mind (an argument I've yet to see completed).

LOL no it wasn't a joke.

What is the universe as a giant mind argument? Pantheism?

"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring" -- Carl Sagan

aiia
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HisWillness wrote:...the

HisWillness wrote:

...the universe as a giant mind...

lol

HisWillness
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Topher wrote:What is the

Topher wrote:

What is the universe as a giant mind argument? Pantheism?

I think it's "panENtheism", but I occasionally confuse the two. It's the idea that the universe itself is an all-permeating mentality. I've been discussing it with Eloise, but I haven't heard the punchline yet. So far the idea seems to hinge on quantum information being interpreted as colloquial information. That is, stuff the brain processes. If that were the case, EVERYTHING would be either rational or irrational, since mentality is all-permeating. (Cue dramatic music.)

Yeah. Like I said, I haven't really gotten to the point where I could defend it as a concept. I'm still curious about some aspects.

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence

inspectormustard
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The question "is it moral or

The question "is it moral or immoral to be rational or irrational?" is

a) Amoral

b) Arational

c) Amoral and arational

It would be nice if everything used the same prefix-ation, but common knowledge makes things difficult. For example:

Moral - of, pertaining to, or concerned with the principles or rules of right conduct or the distinction between social right and wrong.

Immoral - violating moral principles; not conforming to the patterns of conduct usually accepted or established as consistent with principles of personal and social ethics.

Amoral - not involving questions of right or wrong; without moral quality; neither moral nor immoral.

Typically, when people hear the word amoral they defer to the anthropomorphic second definition: "having no moral standards, restraints, or principles; unaware of or indifferent to questions of right or wrong." In most people's judgment an amoral person is by default immoral. I also think people work some kind of mad logic to arrive that the conclusion that it is immoral to be irrational by falsely associating the negative prefix with right and wrong. This thought process can be carried to atheism as well.

BobSpence
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I'm not sure I would define

I'm not sure I would define the categories exactly as in the OP, but it is making an important point.

I have seen many posters responding with the implicit assumption that if some proposition can not be proved by reasoned argument, it is 'irrational', whereas in many cases in may better fit into the 'arational' or perhaps 'non-rational' in the sense that it is purely a matter of personal preference.

The other assumption I see is that when something cannot be logically, deductively 'proved' it is automatically 'irrational', even if it is about something which, while it cannot be provedcan be shown to be a perfectly reasonable working assumption, based on some version of Occam's Razor applied to the balance of evidence. This I would still class as 'rational'.

I would reserve 'irrational' for a conclusion which flies in the face of significant counter evidence.

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

Topher
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BobSpence1 wrote:I'm not

BobSpence1 wrote:

I'm not sure I would define the categories exactly as in the OP, but it is making an important point.

I have seen many posters responding with the implicit assumption that if some proposition can not be proved by reasoned argument, it is 'irrational', whereas in many cases in may better fit into the 'arational' or perhaps 'non-rational' in the sense that it is purely a matter of personal preference.

The other assumption I see is that when something cannot be logically, deductively 'proved' it is automatically 'irrational', even if it is about something which, while it cannot be provedcan be shown to be a perfectly reasonable working assumption, based on some version of Occam's Razor applied to the balance of evidence. This I would still class as 'rational'.

I would reserve 'irrational' for a conclusion which flies in the face of significant counter evidence.

I would say irrational is best used for when no attempt has been made to apply reason, and in that sense, someone can misuse reason, or not use it (say, due to ignorance), but if they were genuinely attempting to be rational, then I wouldn't say they're rational; they just made an error. Obviously if they ignore correction, then they're irrational.

"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring" -- Carl Sagan

Hambydammit
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For my use, rational is

For my use, rational is something that is both valid and true, or is valid and believed to be true.  In other words, a person who believed that he had won the lottery would be acting rationally to take his ticket to the lottery office, even though the ticket was actually not a winner.

This is why I accept some theist belief as locally rational.  (I use local as a way to say "within one's set of knowledge.&quot  If someone doesn't know that the concept of supernatural is irrational, it can be rational for them to believe in the supernatural.  Likewise, if someone has been deceived or unknowingly misled, they can act rationally based on untrue information.

Someone who has been given knowledge that supernatural is irrational, and continues to believe, is now irrational, in my usage.  I recognize that belief is not a choice, but I don't see how that has any bearing on the terminology.  Belief is belief, and irrational is irrational.

Now that I've given it some thought, I think I would only apply arational to things which require no reason.  "Beer bottle" is arational.  However, I don't like using it on things which use reason, but for which there are no incorrect answers.  If you ask me if I want steak or chicken, and I choose chicken, that's a rational decision because it's based on the fact that 1) I prefer chicken, and 2) My action can be stated logically:

1) I prefer chicken to steak.

2) I desire that which I prefer.

3) If I choose steak, I will get steak

4) If I choose chicken, I will get chicken.

5) If I offer no choice, I am uncertain what I will get.

Therefore, of the three options, choosing chicken is the most rational, given my preference and desire to get my preference.

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

BobSpence
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I definitely agree

I definitely agree with Hambydammit that it is fair to say someone is being rational as long as their conclusions or beliefs are reasonably consistent with their current state of 'knowledge', even if that 'knowledge' is in error. Even if it can be shown that by careful logical analysis, their beliefs are no consistent, it would be unfair to call them 'irrational' if the inconsistency is not particularly obvious. Making errors in a somewhat complex chain of reasoning does not make someone 'irrational', tht should be reserved for the case when someone refuses to acknowledge a blatant error when clearly demonstrated, and is unable to logically defend their conclusion.

There is always going to be a gray area, but when people persistently refuse to accept a mountain of clear counter-evidence, and continue to 'defend' their views by explicitly non-rational 'arguments', such as "I just know it has to be true", "God spoke to me", etc - that's irrational.

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

HisWillness
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BobSpence1 wrote:There is

BobSpence1 wrote:

There is always going to be a gray area, but when people persistently refuse to accept a mountain of clear counter-evidence, and continue to 'defend' their views by explicitly non-rational 'arguments', such as "I just know it has to be true", "God spoke to me", etc - that's irrational.

I'd contend that's being a vapid slathering moron, but I see your point. It's probably in harmony with the original post, seing as "irrational" in your example actively opposes rationality, and doesn't bypass it completely (which would make it "arational" ).

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence

drummermonkey
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Topher wrote:Here is how I'm

Topher wrote:

Here is how I'm defining these terms in relation to each other.

Rational means not irrational.

Irrational means not rational.

Arational means not rational AND not irrational.

Thus, only things within the class of reason can be classified as being rational or irrational. Everything outside of that class (i.e. things not based on reason) would be arational, so saying, for example, "football is rational", or this "cup is irrational" would be category errors.

Discuss.

Well, unfortunately if we define rational, irrational and arational in this way it seems that we run into contradictions. Here's how:

1. S is Rational iff S is not irraional.

2. S is irrational iff S is rational.

3. S is arational iff S is not rational and not irrational.

Suppose S is arational.

So S is not rational and not irrational. by definition (3).

So S is not rational. by our original pressuposition.

But by definition (2), then S is irrational.

But S is not irrational, because S is arational.

Thus a contradiction is reached, S is both not irrational and irrational.

We can also redefine Araitionality to mean that Arational means both irrational AND rational. But this seems absurd.

inspectormustard
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drummermonkey wrote:Well,

drummermonkey wrote:

Well, unfortunately if we define rational, irrational and arational in this way it seems that we run into contradictions. Here's how:

1. S is Rational iff S is not irraional.

2. S is irrational iff S is not rational.

3. S is arational iff S is not rational and not irrational.

Suppose S is arational.

So S is not rational and not irrational. by definition (3).

So S is not rational. by our original pressuposition.

But by definition (2), then S is irrational.

But S is not irrational, because S is arational.

Thus a contradiction is reached, S is both not irrational and irrational.

We can also redefine Araitionality to mean that Arational means both irrational AND rational. But this seems absurd.

Bad monkey, no banana! Reread your argument in the form of fruits and veg:

1. S is a vegetable if-and-only-if S is not a fruit.
2. S is a fruit if-and-only-if S is not a vegetable.
3. S is a mineral if-and-only-if S is not a fruit and not a vegetable.

Suppose S is a mineral.
So S is not a fruit and not a vegetable. by definition (3).
So S is not a vegetable. by our original pressuposition (1).
But by definition (2), S is a fruit.
But S is not a fruit, because S is a mineral.
Thus a contradiction is reached, S is both not fruit and fruit.

In case that doesn't show you the error of your ways, let's do an in depth analysis of the definitions. Given the operator "iff," which has a truth table as such:

 p q p <-> q F F T F T F T F F T T T

Letting V be rational, F be irrational, and M be arational, a truth table for the situation may be written thusly:

 V(S) F(S) M(S) V(S) <-> 'F(S) F(S) <-> 'V(S) M(S) <-> ('F(S)&'V(S)) F F T F F T F T F F T F T F F T F F

Since the 3 establishing columns on the left match the 3 conclusion columns on the right, we can say that the given definitions are correct. Now, go learn to logic.

HisWillness
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inspectormustard wrote:Bad

inspectormustard wrote:

Bad monkey, no banana! Reread your argument in the form of fruits and veg:

When online, inspectormustard employs only the finest fruits and vegetables FTW.

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence

QuasarX
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Hambydammit and BobSpence1

Hambydammit and BobSpence1 have touched on an issue I've been thinking of lately.  I think there's a distinction between saying an idea is rational/irrational, an action is rational/irrational, and a person is rational/irrational.

BobSpence1 wrote:
Even if it can be shown that by careful logical analysis, their beliefs are no consistent, it would be unfair to call them 'irrational' if the inconsistency is not particularly obvious. Making errors in a somewhat complex chain of reasoning does not make someone 'irrational', tht should be reserved for the case when someone refuses to acknowledge a blatant error when clearly demonstrated, and is unable to logically defend their conclusion.

This is a good distinction between saying the thoughts are irrational versus the person is irrational.  The person might be making every effort to be as rational as possible, but might still overlook something and come to an irrational conclusion about something.  They would still, for the most part, be a rational person when all things are considered, but the conclusion would still be rightly said to be irrational.

Hambydammit wrote:
1) I prefer chicken to steak.

2) I desire that which I prefer.

3) If I choose steak, I will get steak

4) If I choose chicken, I will get chicken.

5) If I offer no choice, I am uncertain what I will get.

This is a good example for the idea I had.  An action can't be inherently rational or irrational, therefore all actions would be inherently arational.  However, an action would be either rational or irrational for purposes of achieving a specific goal.  That is to say, the action would either help one achieve the goal, or it would not (having no effect is still not helping).

In this example, if the goal is to get the food which is most desired, then #4 would be the rational choice.  If, however, the goal is instead to select the most healthy choice, then either #3 or #4 might be the rational choice, depending on the current condition of the chooser and what nutrients his/her body would most benefit from.

Hambydammit
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Quote:An action can't be

Quote:
An action can't be inherently rational or irrational, therefore all actions would be inherently arational.  However, an action would be either rational or irrational for purposes of achieving a specific goal.

[/cue balloon drop and "The Price is Right" Theme Music]

Ladies and Gentlemen, We have a winner!

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

drummermonkey
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inspectormustard

inspectormustard wrote:

drummermonkey wrote:

Well, unfortunately if we define rational, irrational and arational in this way it seems that we run into contradictions. Here's how:

1. S is Rational iff S is not irraional.

2. S is irrational iff S is not rational.

3. S is arational iff S is not rational and not irrational.

Suppose S is arational.

So S is not rational and not irrational. by definition (3).

So S is not rational. by our original pressuposition.

But by definition (2), then S is irrational.

But S is not irrational, because S is arational.

Thus a contradiction is reached, S is both not irrational and irrational.

We can also redefine Araitionality to mean that Arational means both irrational AND rational. But this seems absurd.

Bad monkey, no banana! Reread your argument in the form of fruits and veg:

1. S is a vegetable if-and-only-if S is not a fruit.
2. S is a fruit if-and-only-if S is not a vegetable.
3. S is a mineral if-and-only-if S is not a fruit and not a vegetable.

Suppose S is a mineral.
So S is not a fruit and not a vegetable. by definition (3).
So S is not a vegetable. by our original pressuposition (1).
But by definition (2), S is a fruit.
But S is not a fruit, because S is a mineral.
Thus a contradiction is reached, S is both not fruit and fruit.

In case that doesn't show you the error of your ways, let's do an in depth analysis of the definitions. Given the operator "iff," which has a truth table as such:

 p q p <-> q F F T F T F T F F T T T

Letting V be rational, F be irrational, and M be arational, a truth table for the situation may be written thusly:

 V(S) F(S) M(S) V(S) <-> 'F(S) F(S) <-> 'V(S) M(S) <-> ('F(S)&'V(S)) F F T F F T F T F F T F T F F T F F

Since the 3 establishing columns on the left match the 3 conclusion columns on the right, we can say that the given definitions are correct. Now, go learn to logic.

Wow, I guess I really should go back and learn logic. Or perhaps not. Obviously your analogous argument is really bad, since both (1), (2), and (3) are obviously false. The argument may be valid but it's certainly not sound. My argument was in inductive form, and it only proves one thing, you can't say that something is Arational, this is troubling since in giving these definitions it was thought that perhaps we can label something Arational in the first place, distinguishing it from the Irrational and Rational. Otherwise by the given definitions we derive a contradiction. Still don't believe me? I'll use a Fitch style proof to give a deductive proof. For those of you not schooled in deductive logic, formal proofs and the rules of formal logic, I apologize.

Premises

1. Rational (a) iff ~Irrational (a).

2. Irrational (a) iff ~Rational (a).

3. Arrational (a) iff (~Rational (a) & ~Irrational (a)).

Begin a subproof assuming (4):

4. Arational (a).                                          Beginning of the subproof with our assumption.

5. ~Rational (a) & ~Irrational (a).              Biconditional Elimination from 3 and 4.

6. ~Rational (a)                                          Conjunction Elimination from 5.

7. Irrational (a)                                           Biconditional Elimination from 6 and 2.

8. ~Irrational (a)                                        Conjunction Elimination from 5.

9. Irrational (a) & ~Irrational (a)                Conjunction Introduction from 7 and 8.

So we've reached a contradiction and that ends our subproof.

So given our subproof 4 - 10 it is a matter of tautological fact that something cannot be Arrational. or 11.

10. ~Arratioinal (a)                                     Negation Introduction 4 - 9.

Therefore, we have two options: first we can abandon the idea of Arrationality. Or second we can complete the definition of Arrationality to get around these difficulties by adding something else to the definition. I think it's probably more parsimonious to do the former. We don't really need the idea of Arrationality, since usually the standards for rationality applies to those capable of actually having propositional attitudes, or beliefs.

I was never meaning to suggest that there wasn't anything there with these definitions, I was just suggesting that there are severe problems with them as is.

QuasarX
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drummermonkey

drummermonkey wrote:

Premises

1. Rational (a) iff ~Irrational (a).

2. Irrational (a) iff ~Rational (a).

3. Arrational (a) iff (~Rational (a) & ~Irrational (a)).

Your premises don't quite fit the original proposition.  You're using iffs instead of ifs.

Edit:

Okay, rereading this, I don't think I explained it well enough.  You're interpretation was:

R <=> ~I

I <=> ~R

A <=> ~R & ~I

which would imply that A was always false.  But, if you start with this:

R => ~I

I => ~R

A => ~R & ~I

it works as intended.

Topher wrote:

Rational means not irrational.

Irrational means not rational.

Arational means not rational AND not irrational.

The issue is you interpreted "means" to mean "equals" and not to mean "implies".

HisWillness
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drummermonkey wrote:I'll use

drummermonkey wrote:
I'll use a Fitch style proof to give a deductive proof. For those of you not schooled in deductive logic, formal proofs and the rules of formal logic, I apologize.

Apology accepted.

If I'm not entirely wrong, inspectormustard was having a bit of fun with you. The original idea (at least as I understood it) is the introduction of three sets: things rational, irrational, and arational. The definitions weren't presented using formal logic, so there is some interpretation there. Rational and irrational are mutually exclusive, and arational is exclusive of both rational and irrational by virtue of it being untouched by rationality or its absence.

drummermonkey wrote:
I was never meaning to suggest that there wasn't anything there with these definitions, I was just suggesting that there are severe problems with them as is.

Maybe that's because you've formed false relationships between the sets. If "rational" were a set, and "irrational" were defined as all things not rational, then I'd understand your problem. But that's not how it was originally expressed. The first two sets simply had no items in common. Now along comes "arational", defined as items not being in either of the first sets.

This seems fairly straightforward to me, but ... Topher, am I misunderstanding the first basic part of your argument?

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence

drummermonkey
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HisWillness

HisWillness wrote:

drummermonkey wrote:
I'll use a Fitch style proof to give a deductive proof. For those of you not schooled in deductive logic, formal proofs and the rules of formal logic, I apologize.

Apology accepted.

If I'm not entirely wrong, inspectormustard was having a bit of fun with you. The original idea (at least as I understood it) is the introduction of three sets: things rational, irrational, and arational. The definitions weren't presented using formal logic, so there is some interpretation there. Rational and irrational are mutually exclusive, and arational is exclusive of both rational and irrational by virtue of it being untouched by rationality or its absence.

drummermonkey wrote:
I was never meaning to suggest that there wasn't anything there with these definitions, I was just suggesting that there are severe problems with them as is.

Maybe that's because you've formed false relationships between the sets. If "rational" were a set, and "irrational" were defined as all things not rational, then I'd understand your problem. But that's not how it was originally expressed. The first two sets simply had no items in common. Now along comes "arational", defined as items not being in either of the first sets.

This seems fairly straightforward to me, but ... Topher, am I misunderstanding the first basic part of your argument?

Hmmm I see your point. I think I might have misunderstood "means". My impression was that when we use that term we are given definitions, traditionally in analytic philosophy when we give a definition or analysis of something we use a biconditional. However if we use set theory that might change things to get around my original objection. But it's difficult to construe things in terms of set theory. I understand what rationality might be, it is when an epistemic agent has justification or sufficient evidence plus other things (properly functioning, having properly orientated cognitive mechanisms etc). Irrational cannot just be the negation of the rational, it's when an epistemic agent doesn't have justification or sufficient evidence.

Given how it was defined however we are told that it is the negation of rational. We are told it means "not rational". Now we can define Arational as just the negation of irrational and rational. But I don't think we really need the term "arational", these objects we are given are just not epistemic agents. So the second definition of "irrational" is just false. Arationality would just be everything outside the realm of "epistemic agents" but then we don't even need to talk about rationality for these things, nor is it entirely that interesting to those that talk about rationality. If I were to state Arationality it would probably look something like this:

S is Arational iff a. ~(S is Rational & S is Irrational) &

b. S is not an epistemic agent.

inspectormustard
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drummermonkey wrote:

drummermonkey wrote:

HisWillness wrote:

drummermonkey wrote:
I'll use a Fitch style proof to give a deductive proof. For those of you not schooled in deductive logic, formal proofs and the rules of formal logic, I apologize.

Apology accepted.

If I'm not entirely wrong, inspectormustard was having a bit of fun with you. The original idea (at least as I understood it) is the introduction of three sets: things rational, irrational, and arational. The definitions weren't presented using formal logic, so there is some interpretation there. Rational and irrational are mutually exclusive, and arational is exclusive of both rational and irrational by virtue of it being untouched by rationality or its absence.

drummermonkey wrote:
I was never meaning to suggest that there wasn't anything there with these definitions, I was just suggesting that there are severe problems with them as is.

Maybe that's because you've formed false relationships between the sets. If "rational" were a set, and "irrational" were defined as all things not rational, then I'd understand your problem. But that's not how it was originally expressed. The first two sets simply had no items in common. Now along comes "arational", defined as items not being in either of the first sets.

This seems fairly straightforward to me, but ... Topher, am I misunderstanding the first basic part of your argument?

Hmmm I see your point. I think I might have misunderstood "means". My impression was that when we use that term we are given definitions, traditionally in analytic philosophy when we give a definition or analysis of something we use a biconditional. However if we use set theory that might change things to get around my original objection. But it's difficult to construe things in terms of set theory. I understand what rationality might be, it is when an epistemic agent has justification or sufficient evidence plus other things (properly functioning, having properly orientated cognitive mechanisms etc). Irrational cannot just be the negation of the rational, it's when an epistemic agent doesn't have justification or sufficient evidence.

Given how it was defined however we are told that it is the negation of rational. We are told it means "not rational". Now we can define Arational as just the negation of irrational and rational. But I don't think we really need the term "arational", these objects we are given are just not epistemic agents. So the second definition of "irrational" is just false. Arationality would just be everything outside the realm of "epistemic agents" but then we don't even need to talk about rationality for these things, nor is it entirely that interesting to those that talk about rationality. If I were to state Arationality it would probably look something like this:

S is Arational iff a. ~(S is Rational & S is Irrational) &

b. S is not an epistemic agent.

Ordinarily I'm all for whatever pedantry we can dig up, but sir you have gone too far!

Perhaps this Venn Diagram will serve to illustrate the original (to me, blindingly obvious) point:

BobSpence
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All this show how tricky it

All this show how tricky it can be applying analysing strict logical analysis to ordinary speech - we 'know; what we mean, and often our listeners/readers extract the same meaning from it, but it is so easy to make logical slips.

The initial 'problem' here was in 'defining' rational as not irrational, and irrational as not rational, which both allow 'arational' into the definition.

Whereas they are best treated, as seems finally resolved, as three mutually exclusive states.

Rational => an opinion, conclusion, decision, based on making logical inferences from already accepted propositions;

Irrational => basing conclusions on arguments which can easily be shown to be logically invalid, or non-sequiters;

Arational => applicable to decisions which only involve personal tastes, or values.

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

HisWillness
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drummermonkey wrote:S is

drummermonkey wrote:

S is Arational iff a. ~(S is Rational & S is Irrational) &

b. S is not an epistemic agent.

I don't think you even have to go that far. If S is not an epistemic agent, it's automatically arational, and all three categories are mutually exclusive. So epistemic agents get two categories, and everything else (since it has nothing to do with rational processes at all) is arational. Just like inspectormustard's diagram.

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence

drummermonkey
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inspectormustard

inspectormustard wrote:

drummermonkey wrote:

HisWillness wrote:

drummermonkey wrote:
I'll use a Fitch style proof to give a deductive proof. For those of you not schooled in deductive logic, formal proofs and the rules of formal logic, I apologize.

Apology accepted.

If I'm not entirely wrong, inspectormustard was having a bit of fun with you. The original idea (at least as I understood it) is the introduction of three sets: things rational, irrational, and arational. The definitions weren't presented using formal logic, so there is some interpretation there. Rational and irrational are mutually exclusive, and arational is exclusive of both rational and irrational by virtue of it being untouched by rationality or its absence.

drummermonkey wrote:
I was never meaning to suggest that there wasn't anything there with these definitions, I was just suggesting that there are severe problems with them as is.

Maybe that's because you've formed false relationships between the sets. If "rational" were a set, and "irrational" were defined as all things not rational, then I'd understand your problem. But that's not how it was originally expressed. The first two sets simply had no items in common. Now along comes "arational", defined as items not being in either of the first sets.

This seems fairly straightforward to me, but ... Topher, am I misunderstanding the first basic part of your argument?

Hmmm I see your point. I think I might have misunderstood "means". My impression was that when we use that term we are given definitions, traditionally in analytic philosophy when we give a definition or analysis of something we use a biconditional. However if we use set theory that might change things to get around my original objection. But it's difficult to construe things in terms of set theory. I understand what rationality might be, it is when an epistemic agent has justification or sufficient evidence plus other things (properly functioning, having properly orientated cognitive mechanisms etc). Irrational cannot just be the negation of the rational, it's when an epistemic agent doesn't have justification or sufficient evidence.

Given how it was defined however we are told that it is the negation of rational. We are told it means "not rational". Now we can define Arational as just the negation of irrational and rational. But I don't think we really need the term "arational", these objects we are given are just not epistemic agents. So the second definition of "irrational" is just false. Arationality would just be everything outside the realm of "epistemic agents" but then we don't even need to talk about rationality for these things, nor is it entirely that interesting to those that talk about rationality. If I were to state Arationality it would probably look something like this:

S is Arational iff a. ~(S is Rational & S is Irrational) &

b. S is not an epistemic agent.

Ordinarily I'm all for whatever pedantry we can dig up, but sir you have gone too far!

Perhaps this Venn Diagram will serve to illustrate the original (to me, blindingly obvious) point:

Oh stop busting my chops, inspectormustard, I never went too far. I have never said any glaring falsities. Nor did I tell anyone to “go learn logic”. If anything I was encouraging clarity. If we were talking about set theory and sets, we should have used terms that set theorists use, not language that mean particular things in formal and informal logic. Even if we were to use set theory language we have to be careful and be clear about what sets we are talking about. When we say “not in set A” we usually mean all the elements that are not in the set A. When we use “and” as in “set A and set B” we usually mean the set including all the elements in set A united with all the elements in set B. When we combine “not” and “and” we have to be even more careful. Furthermore, your ven diagram is wrong, at least how I suggested we ought to define arational, and I think it kind of abandons what the original poster was after. Tell me, which ven diagram do you find is more parsimonious (a) or (b)? The way you articulated it, what was meant was a glaringly, blindingly obvious point, represented in (b). On the other hand (a) is what I suggest we are after, and we should mean. In both diagrams, yellow is the elements that are "arational", blue indicates the elements that are "irrational" and white are the elements that are "rational" or undefined elements. I can assure you, in set theory the two diagrams mean very different things:

a)

b)

illeatyourdog
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Rational

Rational Scientists

Irrational Creationists

Arational Women

. . . . The door is this way right?  I'll just let myself out.

" Why does God always got such wacky shit to say? . . . When was the last time you heard somebody say 'look God told me to get a muffin and a cup tea and cool out man'?" - Dov Davidoff

HisWillness
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drummermonkey wrote:Oh stop

drummermonkey wrote:
Oh stop busting my chops, inspectormustard

Thank you for at least taking it like a man (not gender specific - anyone jumping on me for that will get the suplex) instead of whining or dodging. This is, after all, the land of busting chops.

I think your diagram b is exactly the same Venn diagram as inspectormustard's, except that inspectormustard has "all else" labelled, and his "reason" region isn't clearly enclosed.

Personally, I'd consider "rational" the only positive statement of the three, and the rest only relevant by their relationship to rational. Having two types of "not rational" seems helpful, considering the original point that "this rock is irrational" is nonsensical. The rock never even had a chance to be rational! Why are we picking on the rock like that? Won't someone think of the rock?

Saint Will: no gyration without funkstification.
fabulae! nil satis firmi video quam ob rem accipere hunc mi expediat metum. - Terence

Nordmann
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Quote:1. S is a vegetable

Quote:

1. S is a vegetable if-and-only-if S is not a fruit.
2. S is a fruit if-and-only-if S is not a vegetable.
3. S is a mineral if-and-only-if S is not a fruit and not a vegetable.

Suppose S is a mineral.
So S is not a fruit and not a vegetable. by definition (3).
So S is not a vegetable. by our original pressuposition (1).
But by definition (2), S is a fruit.
But S is not a fruit, because S is a mineral.
Thus a contradiction is reached, S is both not fruit and fruit.

It is a tomato.

I would rather have a bottle in front of me than a frontal lobotomy