You have a different understanding of the meaning of 'falsify' to me. I think it involves argument or evidence. Just contradicting something is not to demonstrate it to be false.You said 'A' didn't stand for anything. So, it's just a logical variable. How do you falsify a variable? Add a tilda~
But as I say, if that is what you understand by 'falsify' then there is nothing that cannot be falsified - therefore there is also nothing that can be verified.
And as I said, re the OP's question about '1 + 1 = 2', it would be 'falsified' by putting 'not' in front of the equals sign, but could be 're-verified' by adding a second 'not' to make a double negative, then 're-falsified' again with a further 'not'... Again, I do not think that process is what is normally understood by 'verification' and 'falsification'.
I do not see how this relates to the question in the OP. Roquentin is not Pythagoras, he does not see the world as number, but he can still add one and one. We are discussing what we mean by terms like 'one'.Especially this latter, an encounter with Being sans the particulars, sans the body of contingency that provides contextual sense in order for individual identity to announce itself. Roquentin experiences the world free of logical structure and the purpose of this bloated epiphany is to make a powerful point: the world is not logic; it has no categories, no Kantian synthetic concepts that divide and formalize. It is cognitively alien, amorphous, and entirely unspeakable.
It isn't about what might cause you to say 'the book is on the shelf'. Nor is 'the book is on the shelf' an argument, it is only a proposition that might be part of an argument.Sound arguments, which are supposed to be true about the world, are really about language and its rules for concatenation. I could say something "out there' causes me to say the book is on the shelf, but the equation of proposition rests with the rules and their principles of subsumption. And when I say "something causes" I am, as Wittgenstein will tell you, speaking nonsense.
If I wanted to know what you meant by 'the book is on the shelf' I might ask you what would falsify it. Would it be the location of the book? If the book was really on the floor, might the proposition 'the book is on the shelf' still be correct? I gather you think so. That the location of the book doesn't matter when it comes to the truth of 'the book is on the shelf'.
Rather you say it is a matter of whether 'the equation of proposition rests with the rules and their principles of subsumption'. (What is a 'principle of subsumption'? As far as I can see it that phrase refers to ideas in educational theory about how individuals learn from pictures or text, which I cannot see is relevant). So what then are 'the rules'? Is it more than the notion that 'the book is on the shelf' can be falsified with the addition of 'not'?
I don't think I should be diverted into discussing Wittgenstein, so I will just say that I do not think he was saying what you are saying.
A valid logical argument is one where the conclusions are consequent, or entailed, by its premise. That is to say the conclusion is already completely contained in the initial assumptions; it does not require anything external, for example empirical evidence.I don't really follow this. Logic expounds?
Pure maths is. 'Bachelors are unmarried men' is true because we have decided one term means the other. But there is no logic in it. 'X is X' is not logic. It is an axiom necessary in order for us to do logic, but it is not in itself something known through logic.My point has been, with some side steps, that 1+1=2 cannot be refuted because you can never get behind logic, and mathematics is a system of logic; that if you could refute the principle of addition (notwithstanding how you want to display it) you would be refuting a tautology (all mathematics is tautological. I think this is likely true.)
But if something cannot be refuted, then it can't be verified either. Thus we are back to the point I have been making all along, that '1 + 1 = 2' cannot be refuted or verified because it has no content - like a tautology it is circular.
That doesn't follow at all. Once again, I am not saying 'logic doesn't work'....and if you are fine with this, then you must be equally fine refuting any and all occasions of logicality, which would apply to the logic you employ to make your refutation and the bleeding affair is self-refuting.
I'm saying that a logical or mathematical formula in which the propositions do not relate to anything will produce conclusions that don't relate to anything either.
It is simply the ability to appreciate that pure maths is different to applied maths and that a logical argument being 'valid' does not make it 'sound' .
I think this exchange has run its course.