I am not disputing what you said. There are lots of examples of things I know e.g. I know my name, date of birth, place of birth, which school I went to, etc. The same goes for you and billions of other people.

How can you be 100% certain of your place of birth? You can't imagine any circumstance where that's a lie? You probably don't remember it yourself. You're trusting other people to be telling you the truth, how are you 100% certain?

If there is any use in the term “certainty” there must be something taken to be 100% certain. Otherwise, the term wouldn’t work at all, at any percentage.

I don't really know what you mean by this. Something? There must be something?

We are here distinguishing “certainty” as a term.

In order to move from one sentence to the next using this term, we must make, we must take something distinguished in this term in our minds, hold it as something, and then build the next statement.

Following this process you can reply to Truth Seeker “how can you be 100% certain of the place of your birth?” And you can mention “lie” or show place of birth can’t be 100%, etc, and make all of the context, but still hovering around this term “certainty”. You can’t be hovering around certainty (or focus on any single thing) without taking something as certain. Or you would not be able to form your question.

Now I can make something of your statement and say, we wouldn’t still be using the term “certainty” in this discussion unless there was something still clear, still fixed, a center of gravity - something is there we are getting at.

We are each taking this “something there” as the currently fixed idea “100% certainty.”

This means to me the same three things I said before: certainty is exemplified in the tautologous; certainty itself is therefore certain (clear, a useful term); and certainty in a practical sense, in complex scenarios, is rare and best thought of as a tool or method used to seek out further clarifications in the complex.

If there is any use in the term “certainty” there must be something taken to be 100% certain — Fire Ologist

"If there is any use in the term «extraterrestrial», there must be something that is extraterrestrial."

I am 100% certain that you know of some difference between “certainty” and any other term. Or this conversation wouldn’t work.

If there is any use in the term «extraterrestrial», there must be something that is extraterrestrial. — Lionino

That’s not quite parallel to what I said. To make your example parallel to mine, you would have to say “If there is any use in the term “extraterrestrial” there must be something taken to be extraterrestrial.” Besides there is the moon, which I’m some percentage certain is extraterrestrial. So even without some real distinction between the extraterrestrial and any other term, you’ve managed to use the term functionally well to describe the moon, creating the real distinction, taking something distinct up.

I am 100% certain that you know of some difference between “certainty” and any other term. Or this conversation wouldn’t work. — Fire Ologist

Well certainly there are a few terms that I can think of that are different than "certainty".

Besides there is the moon, which I’m some percentage certain is extraterrestrial — Fire Ologist

You know what I meant with "extraterrestrial". The point is that for a term to be useful it does not need to be instantiated in the real world or in our minds.

Extraterrestrial refers to a physical thing or many physical things. You will not get to any use of the term extraterrestrial until you place the earth and some space beyond it. Now you can introduce a distinction between a term and its instantiation in a physical world. You had to take the earth as a fixed jump off point to go extraterrestrial and sharpen a distinction between instantiated terms and non instantiated terms.

Instantiation of certainty is found in tautology (instantiated in the mind, instantiated in the brain if you will…). If you are saying certainty has no instantiation, is not distinct, then how are we still talking about it?

In symbolic classic logic, the contents don't matter. It works purely on the format.
So if you say,
P-> Q
Not P
Then it must be Not Q

There is no way Not P, and it is still Q. — Corvus

Corvus' argument here is of course invalid - tragic that this should need saying.

But Corvus is correct that the Cogito is not valid, at least in its usual form. "I think, therefore I am", rendered as "p⊃q", is invalid.

One needs to get inside the existential quantification if one is going to show validity. That is not an easy task.

Try it for yourself, see if you can avoid circularity.

Hence the common reading of the Cogito as an intuition rather than as an inference.

Corvus' argument here is of course invalid - tragic that this should need saying. — Banno

Your formula seems incorrect. This is the correct one.

I simply fed what you said in the quote above into the tree proof generator, verbatim.

But go ahead and bite the hand that feeds you. I am agreeing with your more general point that the validity of the cogito is questionable - indeed, it is questionable if the cogito is an inference. Your interlocutors seem to think that it is logically undeniable. Let them show us how.

Just was suggesting a would-be better formula. Not biting your hands at all.
My point was the content of Not Q was FALSE, therefore the original assumption P -> Q is False.
The 3 dualists have been havering with their muddled examples which didn't make any sense at all.
I agree cogito is not a logical statement, and it looks doubtful if it is even an inference.

You wrote

(I think, therefore I exist) or (I don't think, therefore I don't exist)

All your friends need do is deny the right of the disjunct - which they have done.

No… in plain English:

p implies q.
But if p is false, that doesn’t always mean that q is false. q could have another cause

Like saying it’s sunny and so it is warm. Hey if it isn’t sunny then it isn’t warm.

It is a standard fallacy - can’t remember what it is called, been too long, but the concept is sound.

The standard with 3 facticities (not quite the same thing but another implication fallacy)

P -> q
Q > T
So p implies T. Obviously not sound. Plain English: I’m hungry so I eat. Eating makes you feel good. Being hungry makes you feel good.

Obviously not sound. — Metaphyzik

:chin:

p⊃q, q⊃t ⊢ p⊃t. is the Hypothetical Syllogism.

Ah yes…

I agree cogito is not a logical statement, and it looks doubtful if it is even an inference. — Corvus

I agree too.
I think = I am thinking.
So “I am thinking, therefore I am” isn’t much of an argument. It’s a tautology. Descartes pre-loads being as thinking in order to pull content out as “certain knowledge” of a thinking being.

I mean I see how he got to there, and that he was at a pivotal moment in his exercise of doubting.

Parmenides said “It is the same thing to think and to be.” He captured the Cartesian moment better. The cogito moment is an ontological moment, not a logical one; it highlights the “am” most of all in the words “I am.” You no longer really need any words so there is no argument to be constructed. You’re not at a conclusion.

If I say “am” out loud, there is no need to cloud this assertion by saying “I” first. Saying “am” is self-assertion. The “I” or any other self is redundant. More tautology. Saying is as good as thinking where you are trying to conclude “being”, as in “therefore, I am being.”

With all of this tautology and self-evident assertion at play, Descartes found “certainty” close by, which makes sense.

But the logic and certain knowledge comes after, or around, or just separately from the ontological observation here. “I am” is a premise, not a conclusion. I think.

I agree too. — Fire Ologist

Do you agree with him for the same reasons he thinks?

He thinks that if someone accepts "I think therefore I am", they must also accept "I don't think, therefore I am not". In other words, and in his own words:

P-> Q
Not P
Then it must be Not Q

Is this good reasoning?

You wrote
(I think, therefore I exist) or (I don't think, therefore I don't exist)
All your friends need do is deny the right of the disjunct - which they have done. — Banno

Sure, good point.  They disputed that Not P -> Not Q doesn't make sense. But the logic checker says it is valid.

(p→q)∨(¬p→¬q)
(P -> Q) = -P or Q (P. Bogart)

We know and they even admit that Not Q = False
So it must be P -> Q = Not P or Not Q
P-> Q = False (proves I think therefore I am, is false).

Because Cogito is a psychological statement or intuition, it is very awkward to prove its validity using first order logic.

It is like a psychological statement, I feel happy, therefore I dance.
The statement is an obscurity itself.  Who is "I"? And what does "I" feel happy about? We don't know.

The same goes with Cogito ergo sum. I think therefore I am. Who is the "I"? and What is the content and object of "think" in there. It is unclear. The only "I" know, is my "I", but I think I am doesn't warrant I am. Rather, what I see, feel, sense, remember and reason is a warrant for my existence. And it is absolute a private state of mentality.

We would never know anything about the state or nature of Cogito, who it belongs to or what the Cogito was about.

Perhaps for this type of purely psychological statement logical analysis, it would be better to use Kripke frame,  Epistemic or Intentional Logic, and check for its validity.  It would turn out to be invalid for sure.

But the logic checker says it is valid. — Corvus

You haven't quite grokked what the logic checker is actually doing. Guess what else the logic checker says is valid:

(p→q) ∨ (¬p→q) is valid.

Also

(p→q) ∨ (p→¬q) is valid.

You don't seem to know what valid means. Valid just means conclusion was derived from the premises. It doesn't mean conclusion is true.
A statement can be valid, but it could still be false. P -> Q is FALSE.

This is why I advised you to read some basic Logic books. It is not about the symbols.
The basic concepts on Logic seem lacking in your writings.

so are you agreeing that "(p→q)∨(¬p→¬q) is valid according to this logic checker" doesn't prove anything?

If not, what do you think it proves?

What does "(p→q)∨(¬p→¬q) is valid according to this logic checker" prove in the context of this conversation?

It is just to show that Not P then Not was validly drawn from P -> Q. That is all.

if that were true, then this:

(p→q) ∨ (¬p→q) is valid.

Shows that "Not P then Q" is validly drawn from P →Q.

I'm using the same reasoning as you.

The thing you're getting confused by is thinking v can mean "the right side is validly drawn from the left side". That's not what v means.

I am telling you this again mate. Logic will only show you whether the propositions were derived correctly or not from the assumptions, and that's all. Nothing more.

The truths must be checked out with the reality in the world i.e. the events, objects and situations.
I think therefore I am is a psychological statement. How do you check "I" think of someone else apart from your "I"? It is a contradiction.

Almost none of what you said is pertinent to any conversations being had here. Not the "I think therefore I am" conversation. Not the "is denying the Antecedent a logical fallacy?" conversation.

"I think therefore I am" is not meant to be applied to someone else, it's meant to be applied to yourself only. Every person can only apply it to themselves.

You aren't using the logic checker correctly. You've misunderstood what v means.

You are back to your nonsense sophistry again. Bye~

You have chickened out of every disagreement once it's starts looking like you might be wrong. Be brave. Look at the possibility that you might be wrong in the face. I dare you.

If you want to use the logic checker correctly, here's how you do it. First I will demonstrate a valid argument, Modus Tollens

https://www.umsu.de/trees/#(p~5q)~5(~3q~5~3p)

Then, if we slightly modify it to your argument, which is that if you have p implies q, you can get not p implies not q, look at what happens

https://www.umsu.de/trees/#(p~5q)~5(~3p~5~3q)

Modus Tollens is a valid argument format. It is generalisable and applicable to any p implies q situation.

Denying the Antecedent is invalid. It is not generally true, it is not applicable to all p implies q situations. It is trivially easy for anybody to think of situations where it doesn't apply.