I think therefore i am.....

Great Debates
121

erislover, unfortunately, I have doubts that I’ll have time to keep my end of the debate any longer, but I didn’t want to leave this hanging:

The foundation of mathematics is axiomatic set theory (the axiom of choice is also often included, but not listed here). It’s not really ever “defined” what a set is, the axioms just state what properties our collection of sets must satisfy. One of the axioms (the second one listed) basically states, “The empty set exists”, so if I’m understanding what you mean by “presuppose”, one of the axioms of set theory presupposes that a set exists–namely, the empty set.

The other axioms basically provide ways of constructing other sets, in addition to the given empty set. The union of a collection of sets exists, the power set of a set exists, given a particular set, you can construct a subset of elements that satisfy a particular property, and so forth.

Actually, there is one other axiom that “presupposes” the existence of a set–the axiom of infinity, which basically says, “There is an infinite set”.

From these axioms, you can construct numbers (the natural numbers, the rational numbers, real numbers, whatever numbers you want). For example, the natural numbers, in terms of sets:

0 = {} (the empty set)

1 = {0}

2 = {0, 1}

3 = {0, 1, 2}

and so forth. You can then prove that this construction satisfies the Peano axioms for the natural numbers.

Back to the axioms, again, the axioms are really only a list of properties the collection (proper class, actually) of sets must satisfy. In fact, here you may have one collection of sets satisfying the axioms, while there you may have a different collection of sets, also satisfying the axioms. In the first collection, maybe the set of real numbers has cardinality aleph-one, while in the second collection, the set of real numbers has cardinality aleph-ten million. There’s nothing in the axioms strong enough to tell you, “This is the true collection of sets”–one collection of sets satisfying the axioms is just as good as any other collection satisfying the axioms, as far as the axioms go. And that’s why we have those undecidable propositions, such as the continuum hypothesis, that Goedel warned us about.

Anyway, I got carried away there, sorry for the hijack. Carry on. :smiley:

122

Like so:
I don’t actually exist in a theoretical void; I seem to have senses, which seem to be percieving the real world; I seem to have memories about previously existing in the real world, and I seem to have thoughts about my memories and observations from the real world. These perceptions, memories, and thoughts are what constitute my existence; they can reasonably be called mine, because I percieve them to be so.

Because I can think about my own thoughts, it occurs to me that I might not exist, and be percieving only illusions. So, I doubt my perceptions: I mentally decide that they are false. This is easy to do; in dreams we experience differing workds; they cannot all be real, can they? Rregardless, I can assume that all that I sense, that I percieve, is a trick presented to me, which I cannot depend upon.

If my senses are false, then all my memories of them are false, invalidating memories of past events. Still worse, perhaps I have been fed my memories like some kind of script, and nothing that I recall is true.

My sphere of reliable existence is now much reduced. I now can turn my attentions to my thoughts; perhaps those don’t exist either. So I can imagine that I don’t actually have any thoughts in my head… but reason betrays me. That imagination is in fact a thought; I needed to give one thought credence to invalidate the rest. Fine, then I can imagine that that imagining is, uh, false. In fact, the more I think about how to disbelieve in my thoughts, the more of them there are to disavaow. I must yield; by my thoughts I cannot deny my thoughts.

It is easy to imagine a universe that does not contain me; yet, those imaginings exist somewhere. I find it bizarre that you can reasonably say that your thoughts do not exist. How can you deny them, without using them to do so?

And erislover, as I say here, I cannot evade the fact that I cannot successfully deny my thought. And my thought does imply the existence of something to be thinking it. I know nothing else about that source of cognition but that it must exist, because the resulting thoughts are irrefutable.

Oh, and Iamthat? You are putting forth some fairly obtuse stuff there, with which I have one problem:

I did ask the question! So there’s a little more going on than nothing.

123

posted by begbert2

In some posts you appear to see the problem and in others you don’t .

The I is just another thought. It’s a thought claiming to have thoughts. If I can’t find anything that is this " I " except a thought then that’s all it is. How can a thought have thoughts?

These thoughts don’t know where these thoughts come from, in fact these thoughts don’t know anything. They just happen.

Unfortunately you’re not an entity, an " I ", you’re just another percept/idea. And your question/answers are just other thought/ideas. If I can’t prove, or don’t know if I exist your existence fairs even worse. :slight_smile:

124

i’ve read my descartes. i followed his reasoning. i also saw the flaw.

as i said before, you can’t prove the existence of something, because you must first assume that something exists, in order to imply the existence of the other thing.

you don’t have to imagine a universe in which you don’t exist, you don’t have to use thoughts to say you don’t exist. just realize that your existence can’t be proved in this manner.

you can’t show that you can think something without assuming you exist first with a series of sentences that start with “i think” or “i seem to” or “it seems that i”. it’s clear that those also assume that “i” exists.

in order to say anything about yourself, you must first assume that you exist. unless you phrase it like:

E(I) -> T(I, y).

that is, if I exist, then I think y.

but with that substituted for your premise, your logic doesn’t prove E(I).

125

Iamthat:

Yeah, I know that my assertions aren’t relevant, but I can’t exactly assert your thoughts, now can I? :smiley:

As usual, there are a few things we don’t agree upon. I think we’ve shed the logical argument, and are strictly considering wether the fact that we think (or think we think, or think we think we think, whatever) constitutes sufficient proof for necessary existence. I think it is (with disclaimers against further assumptions) and you seem to think it isn’t.

If I am interpreting you correctly, you are defining the ‘self’ as a thought, and then dismissing a thought’s validity as an existing thing.

I find this a bit difficult to understand, since thought, the noun, is merely the manifestation of the verb, thinking, which implies another noun, thinker, as the agent of thought. Are you saying that, after moving around all the furniture and lifting up the edges of the carpet, we still cannot find anything in out mind that does not resemble a thought, like the other thoughts?

A reasonable observation; but consider your own comment: How can a thought have thoughts? There doesn’t seem to be a normal of heirarchy of thoughts in my mind, at least; I don’t have a main thought which has other thoughts, each of which has other thoughts, and so on. All thoughts seem to be about equal, give or take the attention I’m paying them.

I maintain that a thought cannot be had by a thought; there must be something cognizant behind it. That thing is not withing out capability to observe; the only evidence of it is our thought itself. Consider a computer program: though it runs on a computer, and is in a sense like a thought of that computer, the program itself has no way to percieve the computer, other than the fact that the program is actively being run at all (which kind of self-awareness is not, to my knowledge, actually found in programs as yet.) Dunno if you write programs, but it’s kinda an interesting metaphor of existence.

Anyway, I leave with you the thought, ‘By its works shall you know it’: The only evidence for this thinking entity is the thoughts is spawns, the consciousness which we use for ourself.

Ramanujan, of course swapping out my premise wrecks the proof. Also, I’m not sure that I like that premise anyway, even on its own. It seems to make thoughts a symptom of existence. :confused:

I don’t know what to tell you. You demand a demonstrable cause before you permit the existence of the effect, your own observations of the inside of your mind notwithstanding. (I’m assuming you have thoughts in there… just kidding. :)) When you see smoke, do you deny its existence, and the possibility of fire, until you are actually shown the fire? When you hear thunder, do you wait to see the lightning before you believe it happened? I can’t trot out the cognition behind your thoughts as an axiom; it is only discernible by the existence of your thoughts. If your thoughts don’t indicate a thinker to you, then you’re just going to have to find another avenue to prove your existence, or not, as you please.

But please, leave my premises alone. If you can’t accept them, just back away slowly, but fiddling with them won’t help anything.

126

i do not deny that i exist. simply, i deny that “cogito ergo sum” is a valid logical proof of that fact.

you simply can’t assume in one breath that thoughts require a thinker, and then in the next assume that there are thoughts without assuming there is a thinker. you can’t think or observe your thoughts if you don’t assume you exist.

127

let me rephrase myself, more simply.

any sentence in which “I” is a referent or an actor implicitly assumes “I” exists.

128

Sorry about the frequent long delays, everyone; I haven’t yet fully proven that ‘free time’ exists. :frowning:

Ramanujan, here are two restatements of the argument, which might help show when the ‘I’ gets tagged in.

Arg 1:

1: I seem to have found some thoughts lying around.
2: The existence of thoughts imply a thinker.
:. Something exists.

Arg 2:

1: I seem to have found some thoughts lying around (and they are the ones I consider ‘mine’).
2: The existence of thoughts imply a thinker.
:. Something exists (and I might as well consider it ‘me’).

The “I” in “I think” serves as a shorthand explanation for where I found the thought, not an assumption of the conclusion. And depending on where you stand on what constitutes ‘I’-ness, proving the existence of the force behind your cognition might be enough to definitively say “I am”. Even if it’s not, though, the proof is stull useful as a demonstrator of something’s necessary existence.

129

No one I have ever known has considered your “arg 1” to be the case we are dealing with. Even Descartes.

130

That’s fine, erislover, I’m presenting the thing to try and refute Ramanujan’s statement that

THink of “arg 1” as a warmup for “arg 2”, which I think does bear some similarity to Descartes’ argument.

Yes, I know I could have just offered “I don’t exist” as an example of a sentence in which “I” is a referent or an actor and which doesn’t implicitly assume “I” exists, but I thought that such a counterexample would have merely sounded like I was jumping on technicalities.

131

And, to add to the confusion, Descartes never assumed that he didn’t exist. Think of it as a bunch of stacked statements: I Am -> I Think -> I recall ->I perceive. Descartes started at the top and removed as many as he could, before he ran up against one that he could remove, which turned out to be ‘I think’. Because he never got as far as removing ‘I am’, it is perfectly valid to state the argument in terms of ‘I’.

If you wish to start with a clean slate, in which you don’t yet have an assertion of ‘I am’ on the playing field, then you are correct, you cannot assert ‘I think’ without first or simultaneously asserting ‘I am’. But that isn’t how Descartes approached the problem.

132

I don’t think it adds to the confusion at all. It explains it.

I don’t wish to start with a clean state. But I don’t see the power behind: “Let’s assume I exist. :. I exist.” And that’s pretty much my participation in this thread, explained.

133

Descartes plan for the day was: I’m going to sit down within the world as I know it, and see how many of the things around me I can disbelieve. If everything was doubtable, then nothing could be asserted, and he would not be able to assert “I am”. It’s as if the universe had been offering him an argument in favor of existence, and his perceptions, being real, and Descartes was going to try and refute their argument, and thus disprove his reality. Being unable to (completely) do so, he announced at what point the universe withstood his attempts to doubt it.

So, you might say that Descartes never assumed that he existed. The universe, (or his own perceptions, or self-awareness, or whatever) put forth that assumption, and Descartes, though he was unable to dismiss the other assumptions, was never able to disprove the assumption of his own existence.

134

:confused: :wink:

135

You’re right, I mistyped. It should have been, "So, you might say that Descartes never assumed that he existed. The universe, (or his own perceptions, or self-awareness, or whatever) put forth that assumption, and Descartes, though he was able to dismiss the other assumptions, was never able to disprove the assumption of his own existence.

Why am I not optomistic that this will allay any confusion? (I’m not actually sure what you really find confusing.)

136

I emphasized the key parts that confused me.

137

Since you have teh means to communicate on this message board, I assume that you recognise ‘the real world’ as an environment in which to operate. Descartes was questioning the assumption that the real world, and all that it implies, is really real. You might say that ‘the real world’ is the thing that presents the argument of itself. Reality *presents us with the xiom of our own existence; in fact, it assumes that all things that we percieve exist. Descartes made his arguments in response to the arguments, the assumptions presented by reality, and considered wether it was reasonable to doubt what reality presented. He was able to doubt most, but not all, that he saw.

138

Yes, Descartes was unable to doubt that he was doubting. But we are now asking, Who’s doing the doubting?

Russell argued that Descartes concluded more then he was entitled to from his data and method. Accordingly the only certainty(?) is thinking not that there is a thinker doing the thinking.

There is no one asserting, “I think”, or “I am”

139

But you don’t deny that the assertions “I think” and “I am” exist?

I don’t recall Russell. What was his argument? And how can there be ‘thinking’ (a verb) without a thinker??

And as for the identity of the doubter, it was ‘I’ (Descartes), on the strength of the assertion that those doubts were perceived to be his own.

140

Clarification of last concept, before I depart for (the bulk of) the day:

When I’m laying claim to my thoughts, it’s like me sticking a flag in the ground and claiming this continent to be ‘mine’. I don’t have any dinifinitive proof that these are not a subset of somebody else’s thoughts, or that somebody else doesn’t claim to have exactly the same set of thoughts as I do. I am claiming these thoughts as mine.

It provides a convenient, and actually meaningful label. After all, wouldn’t it be fair to say that the holder of my thoughts is me? Even if ‘I’ turn out to be nothing more than the left half of The Great Slug’s brain, ‘I’ (the slug) still exist, and am still spending at least part of ‘my’ time acting as the cognition that I percieve as myself.