It doesn't seem very serious to me. — flannel jesus

Walk away, then.

The question is, what can I know with 100% certainty? You seem to be claiming the Cogito as the source of your certainty. I'm asking how that works. What you have said in the last few posts does not appear coherent.

That this poem is stated as concisely at possible for aesthetic purposes, but implies a more complete argument within? — flannel jesus

So it's a poem and an argument? In your own words, it's not

a complete thought — flannel jesus

You were convinced by an incomplete thought?

My thoughts grant certainty to me. — flannel jesus

All of them, or just the incomplete ones?

...develop outputs that are *about* the input. — wonderer1

How's that, then? Can you set it out?

So you think of the Cogito as a poem, and are not convinced by it, but by the argument you find in it?

I don't follow that.

The poem doesn't grant certainty, the poem is just a poem. — flannel jesus

So what grants certainty? Is "I must exist in order to think" an inference? Or an intuition?

It's not the poem that gives certainty. — flannel jesus

Then what?

This is quite the broad statement, describing the essence of all Abrahamic religions, from Shia Muslims, to Mormons, to Church of Christ, to Reconstructionist Jews and so on. — Hanover

Yep. It sits in the foundational story of Abraham, who would sacrifice his son because god wills it, glorifying doing what one is told to do over taking personal responsibility.

Personally, I feel like it's better to think of the cogito as a poem — flannel jesus

Is the poem sufficient to give you 100% certainty?

Here's a list of your replies to me.

SO, if we go back to the beginning, I gather you were being ironic.

Again, I find myself puzzling as to what we might be disagreeing about.

Is that enough for the first premise? — Lionino

Is that it is an intuition enough for it to be 100% certain? Folk are 100% certain about all sorts of things.

Is it enough for it to be known with 100% certainty? Well, what justification is there for this intuition?

Thanks for your patience.

This is the first time you ask for a demonstration of that specific premise. — Lionino

Well, no, but I won't do chapter and verse. See, you took over an argument from someone else - where they were claiming that to be the whole of the Cogito. And so I at first presumed you were also claiming it to be the whole thing.

I hope we are now agreed that

Whatever thinks, exists.
I think.
I exist

is a furphy.

Let's look at "Whatever thinks, exists".

I'm making the point that it does not parse validly (is not a tautology) in first order logic anymore than in propositional logic.

Do you agree?

Thanks - Hegel as a case in point.

...there is an error in your logic. — Banno

From a related thread...

Think of free logic as an attempt to make explicit the logical structure of such existential arguments by making explicit the first order existential predicate E!a - "a exists", where a is a proper name; so an example would be "MadFool Exists".

And what this explication found is that it cannot deduce that MadFool exists. All it can do is presuppose it, by assuming that MadFool is a part of the domain of E!x.

Put anther way, in trying to show the validity of "I think therefore I exist" it instead shows that it is circular, that "I think" already supposes that "I exist".

Descartes' argument is valid, but circular. — Banno

The Madfool was a now-banned individual.

It might be better to say that If Descartes' argument is valid, then it is circular.

A good rule of thumb might be that if your logic appears to demonstrate that some particular individual thing must exist, then there is an error in your logic.

There is a reason 90% of all people 10 years old or more think “I think therefore I am” is a stupid argument. It’s not because of the logic; it’s because what it is trying to argue is so obvious. Everyone already knows “I am” - and they rightly think that if you needed a proof to conclude you exist you might be an idiot. — Fire Ologist

Quite right.

In so far as I have a purpose here, it is to show how silly it is to rely on "I think, therefore I am".

To that end, I have been at pains to show that a certain syllogism does not show that "I think, therefore I am" is true; and that "I think, therefore I am" is not the result of an inference but is rather closer to an intuition.

It would be extraordinary if mere logic were to conclude that this or that thing exists. That is not the sort of thing logic is capable of.

"I am" does not need "I think" as a preamble.

On Tuesdays and Thursdays...

It seems like it:

But this just says that if some individual has a property, then there is an individual. It works not just for thinking but for being pink. For all x, if x is pink then there is something that is pink.
— Banno — Lionino

There is a difference between concluding that a particular individual is pink - "Fred is pink" - and concluding that something is pink - "x is pink" .

That's why we differentiate Px and Pa in first order logic.

The crux is that we may doubt that anything is pink, but we cannot doubt that we think, because when we doubt that we doubt, we are doubting, and doubting is a type of thinking — and that is self-evident aka clear and distinct. — Lionino

This is more to the case. But there is a problem here, in the move from a variable to an individual...

U(x)(Px ⊃ ∃(y)(x=y))

to

Pa

For clarity, let's move to free logic, adopting the definition ∃!a = ∃(x)(x=a).
What Descartes wanted was

U(x)(Px ⊃ ∃!x)
Pa
⊢∃!a

(edited) But again, this is invalid. It needs the additional deduction Pa ⊃ ∃!a, which requires ∃!a.

That is, the argument does not lead to the conclusion that I think - that individual. All it concludes is that something thinks - whatever is the referent of the variable x.

This is I take it the point Russell makes, probably set out a bit more formally than he was able to do with the state of logic in his time.

You have: — Lionino

You keep doing this. I ask for a demonstration that "Whatever thinks, exists", and you reply with a demonstration that if "Whatever thinks, exists" then I exist:

Whatever thinks, exists.
I think.
I exist. — Lionino

I am after a proof of the first line. The syllogism is not a proof of the first line of the syllogism.

I seem to have to keep making this point, and I am not enjoying doing so.

But then the claim "it is not the case that this proof-path pre-exists our construction of it", the syntax being the proof-path, and in our case being the FOL that we see in things such as ZFC, did we really construe relations such as ∧ and →? If so, it would then bring up "how did we"? — Lionino

I'm not following what you say here.

It seems more reasonable to me than the inverse that mathematics was/is invented and that applications for it were/are discovered. — 180 Proof

Same here.

When he says proof-path, is he referring to the syntax which we use to prove theorems? — Lionino

Pretty much. So mathematical expressions are true only if there is a proof-path that shows it to be true. There are, one concludes, mathematical expressions that are neither true nor false. This is opposed to Platonism, in which mathematical expressions are either true or false regardless of our having a proof.

Arguably this approach is not subject to Benacerraf's problem because there need not be a thing to which each number refers.

Wittgenstein's own approach place restrictions on the creativity mathematicians.

But this topic requires a far more formal approach than is doable here.

From the Second Meditation:

Thinking? At last I have discovered it—thought; this alone is inseparable from me. I am, I exist—that is certain. But for how long? For as long as I am thinking. For it could be that were I totally to cease from thinking, I should totally cease to exist.

Descartes might have had more sympathy for @Corvus' argument than folk hereabouts suppose.

The shape p→q is invalid under a broad definition of invalid, yes. — Lionino

Thank you.

That is, and this is the point being made, "I think therefore I am", if parsed as "p⊃q", is not a tautology, is invalid, and need not, at least on that account, be accepted as 100% certain. It appears that this point is missed by some of our brethren, although not by you. The error to which I wish to draw attention was of supposing that the following argument is valid, therefore "I think ⊃ I exist" is true.

1. I think ⊃ I exist. (Cogito, assumption)
2. I think. (assumption)
3. ⊢ I exist. (1.2, MPP)

I will concede that is not Descartes' argument. — Lionino

Thank you.

Just to be clear then, this is an argument for one's existence, and not an argument for Cogito ergo sum; if it where considered an argument for Cogito ergo sum then it presumes its conclusion.

Descartes' argument itself is not an intuition, it is a full-fledged argument as I have shown and as can be verified in the books. — Lionino

The argument is often taken from here:

I have convinced myself that there is absolutely nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist? No: if I convinced myself of something then I certainly existed. But there is a deceiver of supreme power and cunning who is deliberately and constantly deceiving me. In that case I too undoubtedly exist, if he is deceiving me; and let him deceive me as much as he can, he will never bring it about that I am nothing so long as I think that I am something. So after considering everything very thoroughly, I must finally conclude that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind — Second Meditation

Now what I have asked is for someone to present the structure of the argument. If you have indeed done so, then I've missed it.

For example, it might be tempting to pars the argument into a first-order logic, with "a exists" understood as ∃(x)(x=a); That might give "I think therefore I am" as

U(x)(Tx ⊃ ∃(y)(x=y))

Which is valid. But this just says that if some individual has a property, then there is an individual. It works not just for thinking but for being pink. For all x, if x is pink then there is something that is pink. This seems not to capture the quality of the Cogito.

Now I do not think there is any clear and distinct way (see what I did there?) to set out a logical structure for the argument given in the Second Meditation. In that regard, I do not see that it is an inference.

More can also be said concerning hyperbolic doubt. In On Certainty Wittgenstein shows that doubt is a language game, and so presupposes the features of language. To doubt some statement is to take other statements as undoubted. Here I will side with Gassendi, suggesting that Descartes has gone much further than he needed, and as a result concluded much less than he might have.

Goodness.

A wonderful topic, but I suspect that there is too much here for a single thread - it might have been better to choose one part of the issue at a time to deal with. The juggler will have. a hard time working out which ball is which.

Despite that, I'd throw another ball to the juggler: Wittgenstein’s Philosophy of Mathematics

On Wittgenstein’s view, we invent mathematical calculi and we expand mathematics by calculation and proof, and though we learn from a proof that a theorem can be derived from axioms by means of certain rules in a particular way, it is not the case that this proof-path pre-exists our construction of it.

Me? I would have you to question the very notion of needing an absolute foundation for what you know.

I think you know plenty of things, like that I'm a bit of a twat, that this is a post on at best a second-rate forum, that you are reading this sentence - and all without the need for an absolutely firm foundation.

So to that end, I've been arguing that the Cogito is not as firm as folk otherwise suppose.

That'll do. We can leave Wittgenstein and Ordinary Language for another time.

That was an honest answer: I don't know.

So help me - show me that "I think, therefore I am" is 100% certain.

With something more than your intuition.

Do you think it's possible to think without existing? — flannel jesus

I do not think the Cogito convincing, on Tuesdays and Thursdays. Monday, and Wednesday, I'm quite convinced. Friday and Saturday, I take an agnostic position. Sundays, I rest.

Now, you think the Cogito is grounds for being 100% certain of your existence, on the basis of an intuition... is that right?

And do you Know, as a result of this intuition, that you exist? Is that a justified true belief? What justifies it?

I've answered that. Again, it is a loaded question.

If you are going to claim that the Cogito is 100% certain, then you presumably are able to set out why.

As it stands, it seems it is only because you are convinced by what you describe as "Descartes flowery language"...

Do you think it's possible for you to think if you don't exist? — flannel jesus

Can you show me that it isn't?

Can you make the Cogito the result of an argument, rather than a mere presumption?

You are going to need something more than propositional logic.

So the basis for 100% certainty in the Cogito is... your intuition?

Are you happy with that?

Try to stay on topic.

What is the basis for claiming that "I think, therefore I am" is indubitable?

Good. So you agree that, since for you it is not an argument, then it is not a valid argument.

Now, if it is not a valid argument, then it cannot be an inference.

So what is it?

How does it command 100% certainty?

If it is a premise, is your claim that it is just presumed?

Here's the point: "I think, therefore I am" is not a valid argument if it is understood as p⊃q.

Even you must see that.

↪Banno So you really think all arguments that take p implies q as a premise are invalid? — flannel jesus

No. That is not what I said.

Oh, Flannel.

https://www.umsu.de/trees/#p~5q

I'll leave you to it.

Think about truth tables. A tautology will be true, regardless of the values assigned to the propositional variables. That is, tautologies are valid; and only tautologies are valid.

If you won't accept such basic stuff, there's not a lot of point in discussing logic with you.

Validity is more formerly defined together with satisfaction and contradiction. An expression is satisfiable if at least one interpretation makes the expression true, and valid if the expression is true in every interpretation. It is unsatisfiable, or contradictory, if for every assignment the expression is false.

So (p v~p) is valid, since whether p is true or false, the expression will be true. (p⊃q) is satisfiable, but invalid, since if we assign true to p and false to q, the expression is false. (p & ~p) is contradictory, since for every assignment of true or false the expression will be false.

I'd surmise that an advantage of working this way is precisely so that every expression is either valid or invalid. Also this treatment applies to other logics - predicate and modal logic define validity in this way, with some modification.

, continuing...

If we agree that the argument quoted is not the Cogito, then do we agree that it is also not a proof of the Cogito? That as such, it would be circular?

And it seems we agree that the Cogito is

...an intuition. — Lionino

Then, returning to the topic, do we have some basis for thinking that this intuition counts as part of the 100% certain knowledge that the OP seeks?

If so, it seems odd that such a mere intuition should count as knowledge; if no, then Descart seems to have been of no help in answering the OP.

Well, yes, you are repeating yourself.

But if you think that "p⊃q" is not invalid, then let that be an end to the discussion.

So, do we agree that "p⊃q" is invalid?

If no, I'm done.

If yes, then do we agree that the Cogito is "I think, therefore I am"?

If no, then what is the Cogito? And if yes, then do we agree that the following is not the Cogito?

1. I think ⊃ I exist. (Cogito, assumption)
2. I think. (assumption)
3. ⊢ I exist. (1.2, MPP) — Banno

Any time now, one of you can mention that Descartes held that issues clearly and distinctly perceived are indubitable.

That'd at least move the topic along a smidge.

So are you, in a somewhat constipated fashion, saying that the cogito is not an inference, but an intuition?

Fine.

But it is not clear why an intuition must be seen as indubitable. And it seems odd to count a mere intuition as certain knowledge.

Just to be sure, this:

1. I think ⊃ I exist. (Cogito, assumption)
2. I think. (assumption)
3. ⊢ I exist. (1.2, MPP) — Banno

...is not a proof of the Cogito. As has been pointed out, it can't be, because it assumes the Cogito on line one.

Nor is it the Cogito.