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.

And still you kick.

Even I give up after a page or two.

:roll:

Here's the Cogito:

Cogito: I think ⊃ I exist

Here is a mooted proof that I exist, from various corespondents...
1. I think ⊃ I exist. (Cogito, assumption)
2. I think. (assumption)
3. ⊢ I exist. (1.2, MPP)

This proof is not the Cogito, although it makes use of the Cogito. It does not show that the cogito is true, because it assumes the Cogito. — Banno

What fallacy did you mean?

Oh, I see - you just wanted to join in the kick fest.

...fallacy... — Lionino

What fallacy?

Here's the Cogito:

Cogito: I think ⊃ I exist

Here is a mooted proof that I exist, from various corespondents...
1. I think ⊃ I exist. (Cogito, assumption)
2. I think. (assumption)
3. ⊢ I exist. (1.2, MPP)

This proof is not the Cogito, although it makes use of the Cogito. It does not show that the cogito is true, because it assumes the Cogito.

It is a valid argument that I exist. It is not a proof of the Cogito.

Now @Corvus attempted to show that the Cogito is invalid, with the following:

1. I think ⊃ I exist. (Cogito, assumption)
2. I don't think (assumption)
3. ⊢ I don't exist. (1.2, ?)

This has the form (p⊃q, ~p) ⊃ ~q. This argument is invalid. It will remain invalid even if, as points out, everyone is entitled to their opinion. Corvus has not demonstrated that the Cogito is invalid.

Here's a seperate point, made by Corvus, Beverly and myself, and pretty much unaddressed by others: It has not been shown that the Cogito is valid.

Indeed, in propositional logic, the Cogito would be rendered
1. p ⊃ q
Which is invalid.

So, is the Cogito is a valid inference?

Yep. True, but invalid.

Are there assignments of true and false for which it is false? Yes. Hence it is invalid.

https://www.umsu.de/trees/#p

I now sincerely regret having become involved in this discussion.

A formula is valid only if it is true for all assignments to its terms.

Here's the truth table for implication:


p⊃q is false for the assignment p=t and q=f; therefor it is not true for all values of its terms, therefore it is not valid.

Banno, I am not convinced by the website/program you are citing. That program considers "If P then Q" an invalid argument, so maybe there is some problem with the way the arguments are being inputted? — NotAristotle

But p⊃q is invalid. From p it does not follow that q.

Are you sure you understand validity?

So...

(((p⊃q) ⊃ (~p⊃~q))∧q)⊃~(p⊃q)
or
(((p⊃q)∧(¬p⊃¬q))∧q)⊃¬(p⊃q)

Still invalid.

The inference is invalid. logic does not show that if 'I think therefore I am' is true, then 'I do not think, therefore I do not exist' must also be true.

Things may exist and yet not think.

That is, letting p="I think" and q="I exist", the syllogism would be
(p⊃q) ⊃ (~p⊃~q)
But this is, as has been explained many times, invalid.

Any 1 line argument is invalid because it is not an argument! — NotAristotle

((p⊃q)&p)⊃q is valid, and on one line.

But if one denies p, then the argument does not bind one to q.

And I ought correct myself, or at least finesse the point; line 1 is valid in S5.

Go on, set out your reductio.

Line 1 is invalid (edit: it is valid in S5). Again, you presume your conclusion.

if I don't exist, then possibly I think. — NotAristotle

Is that what you wanted to show? That's not the cogito.

It means "get on with it".

:roll:

It is valid.

Mind your p's and q's. What are they?

Yes, I can doubt everything except that I am doubting (which already includes that I am, which is the point of cogito). — Fire Ologist

Well, it seems from the length of this thread, that one can doubt that, too.

Consider this: we know things despite not being "100% certain".

"I exist" is an inference. — flannel jesus

Ok, so from what is it to be inferred? And if the answer is "I think", then how is the inference valid?

I've set out my view. The project here, to find something indubitable, is the source of the problem. Just as we can require reasons to believe, we can require reasons to doubt.

Or not.

A better account than others have provided.

Can you doubt that you are now reading my reply?

Point being, at the level you want to work, there are quite a few things besides the Cogito that are evident.

All, can you see that the Cogito does not provide the certainty you crave?

...the idea that you wouldn't be able to think if you didn't exist? — flannel jesus

Notice the presumption in that? Consider again Russell's objection - There is thinking occurring, but what is the "I"?

The other reading, which you might be groping towards, is to take the Cogito as a definition of "I"; that "I" am the thing that thinks - well, strictly, doubts.

You insist I answer your question when you have not answered mine - inference or intuition? Admit it is an intuition, not an inference.

For one to think, one must exist. — flannel jesus

Why?

p⊃q is not a valid argument.

Move past attacking Corvus ad nauseam, we agree that he does not show the Cogito to be invalid. But can you show it to be valid?

Or is it something else? If so, what?

See

(1) If I think, then I exist. — NotAristotle

Isn't that exactly what it was you were trying to prove, NotAristotle?

Can you show that the Cogito is a valid inference? Can you set out it's logical structure, so that we can see why we ought accept it's conclusion, if we accept it's assumption?

And if not, why should we accept it?

The catchphrase is not a syllogism, the complete argument is. — Lionino

What you call "the complete argument" is obviously circular. Hardly convincing.

...the complete argument is:
Thinking → existing
I think
Therefore I exist — Lionino

You assume your conclusion in the first line of your argument.

You yourself said earlier "you must start somewhere". A start is a foundation, if you agree that we need a solid one, you side with Descartes, if you are of the side that we don't need a solid one, you are a skeptic and a pragmatist. Pick your poison. — Lionino

You are playing on "solid" here, on the he misapprehension that we can only know stuff if we are certain of it, if our belief is indubitable.

If existence is required for thought, then "I think therefore I am" makes immediate sense, don't you think? If someone agrees that "I must exist in order to think", then the cogito becomes an obvious consequence. — flannel jesus

So it's an intuition.

Is that sufficient for the foundation of knowledge? No. If someone has an intuition that folk born under Pisces are natural leaders, you'd throw it out offhand. If you want the Cogito to be the foundation of your enterprise, you will need more than intuition.

Sure, @Corvus has it wrong. That doesn't make you right.