I think I have some idea of what Corvus and Beverley are objecting to in the statement "I think, therefore I am." They are objecting to the "I," which is presupposed in the assertion. Perhaps Corvus and Beverley would endorse a proposition that did not include "I" such as the proposition "there is thinking happening." Perhaps they would even endorse the proposition : "there is thinking, therefore something exists." But then we can be certain of two things 1 there is thinking, and 2 something exists.

Despite appearances, I don't think Beverley and corvus reasoning is remotely similar to each other.

For one thing, Beverley rejects denying the Antecedent as a valid logical step, while corvus calls it "basic logic".

And another is, I'm not sure Beverley is aware that Corvus believes existence is required for thought.

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Maybe there is a distinction to be made between the capacity to doubt and the capacity to be certain. So I can doubt "I think therefore I am" and yet it is also a proposition I can have certain knowledge about (though not simultaneously both). Or, does certainty imply an impossibility to doubt?

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?

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. — Banno

The invalidity of the Cogito hasn't been a factor in my involvement in the discussion. My involvement has been out of curiosity as to whether Corvus could admit to having been a doofus.

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

...fallacy... — Lionino

What fallacy?

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

What I was hoping for, was that Corvus would recognize his lack of insight into logic, and engage in error correction with regard to his thinking. Unfortunately he doubled down on speaking as if he was some sort of expert on the subject, while repeatedly demonstrating that he didn't know what he was talking about.

: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?

And still you kick.

Even I give up after a page or two.

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.

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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.

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.

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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

, 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.

Lots of vodka drinking causes one to be drunk.
I am drinking lots of vodka, therefore, I am drunk.

“Therefore” causally joins drinking to subsequent drunkenness.

But there is no causation and subsequent effect or conclusion between “I think” and “I am.” When one realizes one is being, when one realizes one is, “I think” is already “I am thinking”, so already “I am”; not therefore I am.

But this is no small observation (despite how cleverly we can think small of the cogito syllogism).

Realizing that I am is an act of realizing - it’s an act. It’s not a thing. Realizing, like thinking, is an act. But when you realize you are realizing, then the thing realized is an act as well, and further, it is the same act that lead to the realization. This demonstrates self-evidence, or certainty. It combines cause and effect into something else, like a simple, momentary observation such as “I am thinking.”

Now you can introduce “therefore” again.

The causal relationship here is not between thinking and being (they are the same basically). The causal relationship is between an existing fact (“I am”) and subsequent knowledge of that fact (“therefore, here is what I still know despite all of the doubting.”)

Descartes was saying the fact that he is causes him to know something certain. The causal relationship and the “therefore” arises between the fact of his existence as cause, and him knowing certainty as effect. Fact causes knowledge; fact, therefore knowledge.

New cogito: “I can doubt everything and think I know nothing, but still, I am thinking, or more simply, I am being; and therefore, there is something I can know, namely, that I am.”

“I am” is one certain fact we can each stop and visit with whenever we want, like a security blanket for science.

you're not using the word "valid" correctly in that post. p implies q is a premise. It's not valid or invalid on its own, it's a premise.

You can disagree with the premise. "Invalid" wouldn't be the word you use to describe a premise you disagree with though. The word would be "false" - "this premise is false".

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.

That's not what invalid means. Invalid doesn't just mean "there's some way to make this premise false"

Validity is a property of a whole argument, not an individual premise.

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

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 really believe that all p implies q statements are inherently invalid, because to you p implies q is not a tautology, then you're absolutely in disagreement with the majority of users of symbolic logic, including professors who teach logic and writers of logic textbooks.

P implies q is a standard part of countless symbolic logic proofs, and its presence as a premise doesn't make an argument invalid to anybody except apparently you.

Modus ponens and modus Tollens are the most simple proofs in symbolic logic. Each one takes "p implies q" as a premise. If "p implies q" is generally invalid, then modus ponens and modus Tollens would be invalid.

Oh, Flannel.

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

I'll leave you to it.

So you really think all arguments that take p implies q as a premise are invalid?