I think therefore i am.....

begbert2, i didn’t think formality was so necessary. i figured you would have no trouble figuring out it was modus ponens, and figuring out which lines were used (which you did have no trouble doing).

i also didn’t realize you would try to make such a distinction between:

E(x) s.t. P(x)

and:

Ex(P(x))

even after i said i was using “there exists an x” as a second-order property. is there anything wrong with the following formulation, short of its lack of formality:

Ex,y (T(x) -> H(y)).
Et(T(t))
:. Ei(H(i))

other than its demonstration isn’t as powerful as you’d like it to be? E(x) is not intended as a predicate. my fault for symbolizing it like one.

you do a great job explaining why my existence should be taken as an axiom. i would be at a loss to explain anything if i didn’t.

i’ve already explained that my criticism is that “i think therefore i am” does not demonstrate anything, as a logical argument. if you do not wish to disagree with me on that any more, i have nothing more to add. that “i exist”, i have no qualms with. saying that it can be demonstrated through proof does indeed take the argument into a logical forum, and is a statement i disagree with.

again, i erred originally in phrasing the proposition that way. as i said, it didn’t occur to me that using “exists” as a predicate was a bad idea. so i’ll try to stay away from it from now on. i meant to in my “proof”. instead of saying “~E(x) -> ~H(x)”, i would now say you can’t say H(x) without saying Ex(H(x)).

i think this is more a comment on the way we give properties to things, and the meaning of existence. H(x) -> E(x) seems to make sense, but it doesn’t have a whole lot of place here, as i said i will try to no longer use existence as a predicate. instead of saying “x exists” explicitly in the proof, this restricts how we can say “x thinks”.

not using “exists” as a predicate severely limits the ability to prove that something exists. basically, it requires us to give that existant thing a property. i called it a “thinker”. so instead of saying “x exists”, you would say “for some x, x is a thinker”. i suppose that implies its existence, and doesn’t fall into the holes we wish to avoid by not using “exists” as a predicate.

so then, saying “there is a thought, so there is a thinker” is a sound argument. do you agree?

Quite. But looking at the passage I quoted, you use the word “generate” which I dare say does use cauality. I am not sure how to understand the word “generate” without causal relationships.

Ramanujan, sorry for responding to you so, uh, enthusiastically, but you didn’t seem to believe me when I told you that you were getting a bit creative with the formal logic. Y’see, logic’s got its rules like everything else, and what makes symbolic logic so useful is that, by rigid adherence to the rules and forms, the truth is automatically retained through the argument. But, the system only works if you follow the rules, rigidly. Really, just use english. We still know what you mean, and you don’t have to concern yourself with notation. 'Cause if you get the notation wrong, you get the proof wrong.

Uh, for example, I don’t know what you mean by Et(T(t)). Sorry.

But, I think we may be getting somewhere anyway. The process behind cogito ergo sum is, indeed, supposed to be taken more as a realization than a logical proof. I’ve actually been disturbed by the term ‘proof’ as a reference to Descartes’s argument. “I think, therefore I am” is not a formal logical argument, it’s a summary. The way we know that we exist is by noticing that we are unable to reasonably doubt the fact that we think. There’s no reason to get all technical about it; Descartes introduced the idea in about one sentence!
erislover, I’ll bite. Suppose we take is as assumed that a thinking mind is in fact the cause of the thougts that it is thinking. I’ll even go one better; suppose we define ‘a thinking mind’ as any source of thoughts. Now, the mind doesn’t always have to be thinking; necessarily; but if you should find a thought, then, if that thought has any source, that source shall be called a thinking mind.

Now, your turn. Why should this be a problem?

i think we finally are getting somewhere.

by Et(T(t)) i meant “for some t, t is a thinker”, or thereabouts.

and, as far as i know, erislover and i have objected not to the acceptance of “i am” as a reasonable axiom and decision, but to the idea that it can be proved logically.

that forces one to ask why “therefore” is in an axiom, as erislover did, but if we consider “the cogito” as a justification and an axiom, rather than solid proof of something, i think we can let it slide. what descartes meant by it, i think we could argue till death and never agree (he’s not here to settle it).

Well, some thought is required before accepting the axiom, and we’re hoping that that thought isn’t illogical. :slight_smile:

You’re not supposed to just take existence as an axiom without reason, though. The notion is, that by a bit of thought about your thought, you can convince yourself that your mind exists. You’re not supposed to take it on total faith.

Axioms are funny things; we probably shouldn’t be using the term. An axiom is assumed true at the beginning of a symbolic-logic argument, at least for the duration of its working. But, when you’re done, the truth of your answer is dependent on the truth of all of your premises. So, except in methematics, you’re not expected to take much of anything as an axiom, without sufficient reason to believe it on its own.

Descartes’s argument is supposed to demonstrate a way of seeing for yourself that you exist. Something better than, say, “Unicorns are imaginary, therefore I am.” :slight_smile:

“cogito ergo sum” is not an axiom, though after you’ve thought about it an accepted that it seems to be convincing, you can take the validity of it, and of what it implies, as axiomatic. If so, then you can use “I am” as an axiom in other arguments.

Depends on who it is to be a problem for. It isn’t a problem for me, but for Descartes, who wants to doubt everything he can. Whether the proposition you indicate is doubtable or not doesn’t interest me much, only that it is necessary to help complete the demonstration, which is part of my dichotomy mentioned earlier: either we didn’t doubt everything we could, or we didn’t mention everything else we couldn’t doubt (definitions, in this case, which are arguable but not doubtable).

As Ramanujan notes, were this just the justification for an axiom I should be rather content to let it slide. But I am quite sceptical that this is so as Descartes intended it.

Why do you suppose we couldn’t do that before? :slight_smile:

Probably because we hadn’t yet demonstrated a resaon for believeing it. There’s a difference between “I exist beause I say so” and “I exist because I’ve thought about it, and have come to the conclusion that the thoughts that I think I am manifesting are inconsistent with the idea that I might not exist.”

You might say I just pulled a fast one; I took what looked like an implication and restated it as a definition. This isn’t terribly evil; I’m just explicitly abandoning any preconceptions about the idea of ‘mind’, defining it as nothing but the source of thoughts.

To present an idea, or to even think about it clearly, you have to state it in meaningful terms. While constructing an argument, even a metaphysical one, it is alright to define what you’re thinking about. Descartes’ argument is basically an outgrowth on the realization that non-existence, as understood, and thought, as can be observed, are incompatible.

Yes, the difference is that one of them is circular.

Actually, they are both circular… I don’t exist because I say so. I exist. That’s it. There’s no motivation, no justification, no reasoning behind it.

With no motivation, justification, or reasoning, how can you claim that you exist? That doesn’t seem reasonable. How do you know?

I know because it is part of the axiomatic foundation of my system of knowledge. Any attempt by me to justify my existence is necessarily circular reasoning.

I literally have no reason to say I exist… any attempt at reasoning it out begs the question.

Correct me when I’m wrong:

So, what you’re saying is:

  1. You have accepted, without reason, that you exist.
  2. This being the case, “I exist” is in the axiom set of any argument you consider, be it mathematical, physical, or metaphysical.
  3. Because “I exist” is in the axiom set for all arguments you consider, all arguments that have it as the conclusion are then begging the question, because you could have referred to the axiom, and thus skipped the argument.

Uhh, just beause an argument supports a conclusion that you have already decided is axiomatic, does not make the argument circular.

I make the argument that proves I exist to myself. What part of this circle seems open to you, begbert2?

1) You have accepted, without reason, that you exist.

Yes.

2) This being the case, “I exist” is in the axiom set of any argument you consider, be it mathematical, physical, or metaphysical.

Yes.

3) Because “I exist” is in the axiom set for all arguments you consider, all arguments that have it as the conclusion are then begging the question, because you could have referred to the axiom, and thus skipped the argument.

Because you cannot prove axioms, if you could, they’d be theorems, or theories, or laws, or what have you. You especially cannot prove axioms by assuming them in the first place; that is circular. It is not a question of me thinking that there is no motivation behind such an axiom, I think it is very motivated, but that is a far cry from saying I can prove it. I can prove it, but every proof I give of my identity is going to be circular: I am the subject and the predicate. The very definition of a circular justification.

Uhh, just beause an argument supports a conclusion that you have already decided is axiomatic, does not make the argument circular.

It doesn’t matter whether I, erislover of the SDMB, assume it axiomatically or not. It matters that I have never seen a proof, including Descartes’s cogito proof, of the self that didn’t assume a self in the first place. I am not sure what I would gain by achieving it, so I simply shrug it off and make up a fiction: a consistent subject “I”.

Let us consider the following case: proof by contradiction. This is what Descartes was more or less heading towards by doubting everything that can be doubted and finding that he couldn’t doubt his own existence. What is important to note here is that in a more general sense we would like to assume non-existence and arrive at a contradiction… but Descartes, unfortunately, didn’t do that. His second meditation is just that: second. And up to the second meditation, and in it, he assumes a subject that is being deceived. So when he then comes to the “conclusion” that there must be a subject, I am not surprised. Nor impressed.

How about this: I make the argument; that proves: I exist (to myself). Hello Descartes!

erislover, you have already intuitively exersized the proof, and therefore know that you exist. You’re so clever that you didn’t need Descartes to tell you how to do it.

Oh, and as to your most recent post:

Descartes didn’t come at this like a formal proof; he didn’t list all his assumptions at the beginning, for example. For the entire proof leading up to this sentence, he does indeed assume that he exists. Here, though, he drops that and momentarily entertains the notion that he might not exist as well. He might not actually go all the way and declare himself nonexistent, but the way he does it, etnertaining the notion is logically equivalent. See below: (begbert2 translation)

We start with the ‘assumed fact’ 1, below, which is readily observable:

  1. I appear to be be percieving a lot of stuff, etc.
  2. If I am correct in this assumption, then I exist. (Goes without saying.)

Half done. Now, next case, which assumes 2 not to be the case. (This half is proven by an application of modus tolens, which is like a proof by contradiction but you don’t actually assume the falsehood to be true, you just entertain the idea):

  1. If I am not correct in this assumption, these apparent perceptions that I am observing still must be accounted for. Call the source of these false perceptions ‘the Deciever’.
  2. If I do not exist, then there is nothing to be the observer of these perceptions from the Deciever.
  3. If I do not exist, then 1 would not be the case.
  4. As 1 is the case, ‘I did not exist’ is false. (modus tolens :slight_smile: )

For it to have been a proof by condradiction, he would have made the assumption ‘I do not exist’ explicitly, put it through through the implication in 4 to get ‘there would be nothing to be the observer of these perceptions from the Deciever’, which would have directly contradicted with 1.

So both cases (1-2) and (1, 3-6) result in the same conclusion: I exist.
Entertainingly, his next sentence comes completely out of the blue:

This, unlike his previous argument, claims ‘I think therefore I am’. (I’m doing all this on the passage you posted aeons past; I haven’t got the text myself. If I misrepresent the proportions of time he gives to each argument, correct me.) This is a rather sudden comment; the method he just described for being aware of his own existence has nothing to do with his cognition about it. :smack: Not that “cogito ergo sum” is unprovable, but the moron could have provided the proof and saved a few years of confusion.

I’ll even give it to you in the form of a proof by contradiction! :smiley:

  1. Assume you don’t exist.
  2. From that, we can conclude that you do not think, perceive, appear to yourself like you are thinking, or appear to yourself to be perceiving.
  3. However, you do appear to yourself like you are thinking, and appear to yourself to be perceiving.
  4. contradiction!

Even if he is incorrect in this it goes without saying. Note the subject of (1).

I should hope so, he assumed a much.

3 reads: “however, you do exist”. So of course there’s a contradiction.

Nope. Use of an object as the object of a sentence does not imply that object’s existence.

“All Unicorns have one horn and cloven hooves” is a statement that has ‘unicorns’ as its subject, and incidentally is true*, but which certainly doesn’t imply that unicorns exist.

All of your refutations are based on the obviously false assumption that referring to the self as the subject of a sentence implies the existence of the self. You haven’t given me anything to reply to; keep up the good work.

*Ax.( U(x) -> 1H(x) & CH(x) ): true by common definition of “unicorn”

the difference is, in your case, it is the “i” that is doing the referring.

it would be equivalent to saying:

"a unicorn said ‘i have one horn and cloven hooves.’ "

that, it seems to me, does in fact imply the unicorn’s existence.

Oh, really? Says who? The phrases were

(Note that erislover’s claim that "3 reads: “however, you do exist” is rather obviously not true.)

Neither of these statements are written “I said 'I appear to myself like I am percieving things”. They take note of observed conditions, the same way we would note ‘Socrates was a man’ or ‘All men are mortal’. I grant that it’s a tiny step from noticing that you have various properties to the knowledge of your own existence, but it is a step nonetheless. You do not just assume that you exist; you have long ago deduced it from the percievable evidence, and have apparently forgotten that you did so.

Not that it matters wether you accept this.

So you say that, “I appear to have thoughts” implies ‘I exist’. (Yeah, and ‘My TV appears to have small people in it.’ implies that the TV exists.) Suppose that I grant that, by explicitly taking the definition of existence and thinking about it, it’s a short step.So what? At what point does that invalidate the observation? You realize that saying “the argument is obvious the minute I see your first premise” does not in any way invalidate my argument?

Not that it matters wether you accept this.

Even if you claim that Descartes’s axioms ‘beg the question’, that does not invalidate his reasoning.

Suppose I intend to show that rainbows are light effects. I first go through the complicated explanation, citing observations and scientific thoughts on the matter. I conclude with the statements: “And so it can be concluded by observing the facts that light rays through water droplets give the illusion of rainbows. Thus, rainbows are optical effects.” The expected resonse is NOT some kid in the back jumping up and saying, “But, since light rays through water are optical effects, your arguemnt begs the question!”

Remember, the interesting bit of Descartes’s meditations is the realization that one cannot by analysis explain away their thoughts. Not word games about the “pemises” and the “logic”.

Who wants to invalidate circular reasoning? It’s always true! How do you invalidate something that is always true?! But throughout human history of developing arguments, circular arguments have not been very motivating.

That is a fascinating thing to meditate upon, I don’t disagree. But it is not a sound argument proving existence beyond all doubt.

This is Descartes argument: “I can convince myself that that needn’t exist, I can convince myself that that other thing needn’t exist. But I can’t convince myself that I don’t exist because I’ve been convincing myself all this time! I am a necessary subject if I am going to be doubting!” Well, whoopie. Of course “I” is if “I” is.