# Tautology

In my wanderings debating on a catholic forum I've had an argument thrown at me involving Tautologies, using them as an example of things that require no observable empirical testing to be true. I'm pretty sure this is merely a quick lead in to show that God is one of these things that doesn't require observable empirical testing to be true

I just thought I'd run my response by the crowd here first, to see if anybody else has any thoughts on this particular topic, as I've not seen this kind of thing argued before.

"Agreed. And now, we can agree that there are truths which do not require observable

empirical testing. They are true in their inherent rationality.

I give more credit to our rational faculty than you do, Phooney. You only accept what you can

prove has been demonstrated by whatever physical observable science is available at any given

time. I say our rational faculty can lead us into higher truths."

This is very interesting. I will take some time at some stage to read up on tautologies in

propositional logic. I have already mentioned such things that are proven through retortion,

like me saying "I exist". The inherent truth of tautologies is something else that I am happy to

concede. I think it is safe to say that yes tautologies are true by definition, but they don't

neccesarily have any correspondence reality or existence. Your unicorn tautology is a good

example, just because a unicorn eats hay or it doesn't, says nothing about whether unicorns

exist. Also, while true, they are incoherent if you or nobody else knows what a unicorn is, with

as much meaning to people as complete gibberish. Just as a logically sound argument is only true

when the premises are true, despite being logically sound.

Are you saying "God exists" is a tautology or something?

"There are mathematical truths, for example, which cannot be tested empirically."

Sure, such as we can say that the number 5,392,292,748,173,290,098,234,329,293,239,726,239,923 is

a number, but nobody will ever count to it. Luckily for us such mathematical truths are built on

simpler truths, that allow us to satisfactorily prove complicated concepts that we are, I agree,

unable to test empirically.

"It is not uncommon for a physicist to say, "we know x is mathematically true, but we

cannot prove it observably."

reality and existence. The example I have brought up earlier in this thread and in the last one

was loop vortex theory, which was mathematically sound and matched observations, but has been

proven to not be an accurate model of the universe.

coincidentally, I requested and received a book for Christmas called "What we Believe but Cannot

Prove: Science in the Age of Certainty" which I am looking forward to reading, but it is a few

books down in the list at the moment.

"If you could BOLD or something my stuff or your stuff when you respond, I could get

through it more quickly..."

them ever since, I will try to use it from now on. I see by quote 669 that you have some

problems with it as well!

#1I didn't really understood your conversation with the guy (maybe cause I'm not an english speaker... or maybe I'm just stupid but anyways)

Is he talking about the ontological argument for the existance of God ?

Cause if he is... The problem with that argument is that you have to pull a definition of God directly out of your ass before commencing the logical analysis of it : "God is the most perfect thing there is... Therefor, He exists."

Pulling things out of your ass can be nothing more than bullshit (or humanshit if you prefer).

Si Dieu existe, c'est Son problème !

If God exists, it's His problem !--Graffiti on the walls of the Sorbonne (France), May 1968

romancedlife.blogspot.com

#2Logical tautologies are always true. If it could conceivably be false, it's not a tautology. As an example of a tautology, regardless of what truth-value you assign to X, the statement "X or ~X" will be true.

I have the same suspicion as Girl Dancing in Orbit. It sounds like an ontological or presuppositional argument is about to be made. You can find refutations of all those arguments online. I intend to write articles for each ontological argument (and other arguments) but I've only written about Anselm's Classic Ontological Argument so far. Here it is:

"Thus even the fool is compelled to grant that something greater than which cannot be thought exists in thought, because he understands what he hears, and whatever is understood exists in thought. And certainly that greater than which cannot be understood cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater. If, therefore, that than which greater cannot be thought exists in thought alone, then that than which greater cannot be thought turns out to be that than which something greater actually can be thought, but that is obviously impossible. Therefore something than which greater cannot be thought undoubtedly exists both in thought and in reality.... And you, Lord God, are this being."

ReformulationX is "something than which nothing greater can be thought"

(1) If someone understands X then X exists in thought

(2) Someone understands X

(3) X exists in thought (modus ponens from 1-2)

(4) X exists solely in thought (beginning of proof by contradiction)

(5) Someone could conceive of Y such that Y has all the properties of X but Y exists in reality

(6) To exist in reality is greater than to exist in thought alone (axiom)

(7) Y would therefore be greater than X (from 4-6)

( X would therefore not be the greatest conceivable (from 7)

(9) Contradiction with the definition of X (from

(10) X (i.e. God) exists not only in thought but also in reality (proof by contradiction from 4-9)

Refutation: Proof by ContrapositionX is "the greatest conceivable credit card with an infinite amount of cash on it in all conceivable currencies"

(1) If I understand X, then X obviously exists in thought

(2) I understand X

(3) X exists in thought (from 1-2, modus ponens)

(4) X exists solely in thought (beginning of proof by contradiction)

(5) I can conceive of Y such that Y has all the properties of X, but Y exists in reality

(6) To exist in reality is greater than to exist in thought alone (axiom)

(7) Y is therefore greater than X (from 4-6)

( X is therefore not the greatest conceivable (from 7)

(9) Contradiction with the definition of X (from

(10) X not only exists in thought, but in reality (from 4-9, proof by contradiction)

(11) X exists solely outside my pocket (beginning of proof by contradiction)

(12) We can conceive of Y such that Y has all the properties of X, but Y is inside my pocket

(13) To exist inside my pocket is greater than to exist outside (axiom)

(14) Y is therefore greater than X (from 11-13)

(15) X is therefore not the greatest conceivable (from 14)

(16) Contradiction with the definition of X (from 15)

(17) X not only exists in reality, but also inside my pocket (from 10-16, proof by contradiction)

(18) If Anselm's argument is sound then my argument is sound

(19) If my argument is sound then X is inside my pocket

(20) X is not inside my pocket

(21) If X is not inside my pocket then my argument is not sound (contraposition of 19)

(22) My argument is not sound (from 20-21, modus ponens)

(23) If my argument is not sound then Anselm's argument is not sound (contraposition of 18)

(24) Anselm's argument is not sound (from 22-23, modus ponens)

Explanation of the Argument's Failure:The argument fallaciously broadens the argument's scope in premise 6. It says "to exist in reality" rather than saying "to think of X as existing in reality." Anselm fallaciously changed the scope from the realm of ideas to the realm of external reality and offers no justification for doing so. The argument's wording connotes an implicit assumption that ideas necessarily agree with external reality. Because the conclusion in 10 depends on the truth of premises 9, 8, 7, and 6, the argument is unpersuasive because premise 6 contains an unwarranted and false assumption.

A more appropriate wording of premise 6 does not avoid the problem though. One could word the premise as stating, "to think of X as existing in reality is greater than existing in thought alone." However, that would be false. To exist in thought is the same as to exist in thought, it is not greater. The argument in this form is unpersuasive because the conclusion in 10 depends on the truth of premises 9, 8, 7, and 6, but premise 6 is false.

An even more appropriate wording of premise 6 is possible though. One could reword it so it says, "to think of X as existing in reality is greater than to think of X as existing in thought alone." This wording does not fallaciously change the scope of the argument from the realm of ideas to the realm of external reality in premise 6. The premise could be accepted as axiomatically true. A proof by contradiction attempt can now be made. With this modification of premise 6, though, the argument now fallaciously changes the scope from the realm of ideas to the realm of external reality in the conclusion—now the conclusion contains the unwarranted and false assumption that ideas necessarily agree with external reality. If one removes this false assumption and consequently reword the conclusion as saying, "X not only exists in thought but that X exists in reality is also a part of that thought," that would just be a very verbose way of saying, "Theists think God is real." That doesn't prove God's existence outside the realm of ideas.

There is no way to reword the premises so it doesn't contain that unwarranted and false assumption while simultaneously having "God exists in reality" as a conclusion that logically follows from the premises.

(Stupid emoticons! When you see one, interpret that section as the number eight followed by a right parenthetical bracket.)

Stultior stulto fuisti, qui tabellis crederes!

#3Tautologycan refer to: (from google)Tautology (logic), a statement of propositional logic which can be inferred fromany proposition whatsoeverTautology (rhetoric), use oflanguageredundant.... IE = stupid shit !

I can hear the buddhists laughing, GOD ??? those that make GOD assumptions are fucking nuts .... like kelly cleverly says ....

, when they asked buddha "what about god" , he replied "who cares" ,

I love that old buddha story guy .....

Atheism Books.

#4Thanks, Visual_Paradox for that comprehensive breakdown of the ontological arguement. I didn't really think my 'opponent' was going for such, and indeed she didn't in the end.

What I was anticipating was something, much simpler along the lines of

1"there are truths which don't require any empirical observation"

2"god is one of those truths"

Using tautologies as an example of such a thing and basically assuming a strawman of my position, namely that I had asserted the only possible truths are things we have already tested and observed.

She never did finish this argument though, as I said that a tautology doesn't neccesarily have anything to do with reality, like the "a unicorn eats hay or it doesn't" tautology she presented.

The other example she tried to use to prove the above point was mathematics, in that there are mathematical equations, values etc that have been proven without any empirical observation. While I agreed that this was the case, I pointed out that in my understanding, such proofs were only able to be made due to building on prior proofs, which if you go back far enough gets down to a simple enough level of mathematics that must have been observed empirically. As far as I know, mathematics begins with counting, and you count 'things'. 1 rock and 1 more rock equals 2 rocks, every time (so far)!

#5Really, the question is "can we just think something into existence."

Uh, no.

#6I'm glad you liked my analysis of Anselm's Classic Ontological Argument. I have extended it to explain two more problems with the argument and created a new formal argument against Anselm's Classic Ontological Argument

Saint Anselm of Canterbury once posed an ontological argument that sought to demonstrate the existence of deity from thought alone. He said, "Thus even the fool is compelled to grant that something greater than which cannot be thought exists in thought, because he understands what he hears, and whatever is understood exists in thought. And certainly that greater than which cannot be understood cannot exist only in thought, for if it exists only in thought it could also be thought of as existing in reality as well, which is greater. If, therefore, that than which greater cannot be thought exists in thought alone, then that than which greater cannot be thought turns out to be that than which something greater actually can be thought, but that is obviously impossible. Therefore something than which greater cannot be thought undoubtedly exists both in thought and in reality.... And you, Lord God, are this being."

His argument can be reformulated as:

X is "something than which nothing greater can be thought"

1. If someone understands X then X exists in thought

2. Someone understands X

3. X exists in thought [modus ponens from 1-2]

4. X exists solely in thought [beginning of proof by contradiction]

5. Someone could conceive of Y such that Y has all the properties of X but Y exists in reality

6. To exist in reality is greater than to exist in thought alone [axiom]

7. Y would therefore be greater than X [from 4-6]

8. X would therefore not be the greatest conceivable [from 7]

9. Contradiction with the definition of X [from 8]

10. X (i.e. God) exists not only in thought but also in reality [proof by contradiction from 4-9]

The first problem with the argument concerns the definition of X. If greatness entails existence, why would anyone accept a definition that includes greatness? Wouldn't the dispute between theists and atheists center upon the inclusion of greatness in the definition then? An atheist could simply say, "You have presented no reason to accept greatness as being part of X's definition," and Anselm's argument collapses. After all, if there's no reason to accept the definition, there's no reason to accept any reasoning that relies on it.

Another problem concerning the definition of X is that X is defined as being greater than what can be thought. It follows from that definition that whatever is thought is Not-X. Thinking of Y necessitates thinking of X but X cannot be thought. You cannot think of X or Y. If neither exist in thought, a proof by contradiction attempt cannot be made. Thus:

1. If X is greater than what can be thought, whatever is thought is not X

2. X is greater than what can be thought

3. Whatever is thought is not X [from 1-2, modus ponens]

4. If whatever is thought is not X, X doesn't exist in thought

5. X doesn't exist in thought [from 3-4, modus ponens]

6. If X doesn't exist in thought, X cannot be compared with Y

7. X cannot be compared with Y [from 5-6, modus ponens]

8. If X cannot be compared with Y, Anselm's proof by contradiction attempt failed

9. Anselm's proof by contradiction attempt failed [from 7-8, modus ponens]

10. If Anselm's proof by contradiction attempt failed, Anselm's conclusion does not follow

11. Anselm's conclusion does not follow [from 9-10, modus ponens]

The final noteworthy problem is premise 6 saying "to exist in reality" rather than "to think of X as existing in reality." This indicates an assumption that the realm of ideas and of external reality necessarily agree with one another which is self-evidently false. Because the conclusion depends on premises 6-9 being true, the argument is unpersuasive because 6 entails a false assumption. The premise could be reworded as "to think of X as existing in reality is greater than to think of X as existing in thought alone" and that can be accepted as axiomatically true (if the definition is accepted). If we pretend that the proof by contradiction attempt can be made, there is yet another problem with the argument. The conclusion would then contain that aforementioned false assumption. If you remove the entailment of it, the premise would say "X not only exists in thought but that X exists in reality is a part of that thought," which is a wordy way of saying "theists think a deity exists." That, however, doesn't prove the existence of a deity outside the realm of ideas.

By leveraging definitions that necessarily entail certain conclusions and by assuming the realm of ideas and of external reality necessarily agree, other arguments can be made that result in conclusions that can be empirically shown to be false. In the following argument I have done just that and shown, through this proof by contraposition, that Anselm's argument is unsound. Thus:

X is "the greatest conceivable credit card with an infinite amount of cash on it in all conceivable currencies"

1. If I understand X, then X obviously exists in thought

2. I understand X

3. X exists in thought [from 1-2, modus ponens]

4. X exists solely in thought [beginning of proof by contradiction]

5. I can conceive of Y such that Y has all the properties of X, but Y exists in reality

6. To exist in reality is greater than to exist in thought alone [axiom]

7. Y is therefore greater than X [from 4-6]

8. X is therefore not the greatest conceivable [from 7]

9. Contradiction with the definition of X [from 8]

10. X not only exists in thought, but in reality [from 4-9, proof by contradiction]

11. X exists solely outside my pocket [beginning of proof by contradiction]

12. We can conceive of Y such that Y has all the properties of X, but Y is inside my pocket

13. To exist inside my pocket is greater than to exist outside [axiom]

14. Y is therefore greater than X [from 11-13]

15. X is therefore not the greatest conceivable [from 14]

16. Contradiction with the definition of X [from 15]

17. X not only exists in reality, but also inside my pocket [from 10-16, proof by contradiction]

18. If Anselm's argument is sound then my argument is sound

19. If my argument is sound then X is inside my pocket

20. X is not inside my pocket

21. If X is not inside my pocket then my argument is not sound [contraposition of 19]

22. My argument is not sound [from 20-21, modus ponens]

23. If my argument is not sound then Anselm's argument is not sound [contraposition of 18]

24. Anselm's argument is not sound [from 22-23, modus ponens]

Stultior stulto fuisti, qui tabellis crederes!