Question

Hello,
I’m currently studying René Descartes’ Meditations, and our teacher claimed in class that, among other things, Descartes also casts doubt on logic, and that the cogito argument does not depend on logic.
That reminded me of your claim about the inability to make valid arguments without logic, and it raised a question for me.
As I understand it, one can challenge classical logic in four ways –

1. Challenge the idea that truth and falsehood are the only truth-values for every proposition (I won’t address that challenge here)
2. Challenge the way the logical connectives work (for example, to claim that false and true is true)
3. Challenge the way one determines the validity of an argument (and propose a different way instead of: when the premises are true, the conclusion must necessarily be true).
4. Challenge the very idea that there are such things as logical connectives and a way to infer validity at all (and I’d like to suggest that perhaps in this way it would be possible to make meaningful claims about the world).

As for someone who challenges the way logical connectives work and the way validity is determined, I understand your claim that his arguments are worthless. For example, a person who claims that P and not-P is true is asserting everything and asserting nothing. But such a person is not challenging the existence of logic, only what the truth table of negation or conjunction looks like (and perhaps the truth tables of additional logical connectives as well).
But what about a person who does not believe at all in the existence of logical connectives and the validity of arguments, and all of his claims are intuitions/independent observations unrelated to any other claims.
Such a person, for example, would say that the truth-value of “the sun is green” is false. And if you ask him: if so, then is the truth-value of “the sun is not green” also true? he will ask you what “and” means, and what “not” means, because he does not use logical connectives at all. He is not claiming P and not-P; this person’s argument is indeed more limited, but there is no contradiction in it and his argument is not nonsense — he simply does not use logic at all (not changing it, but not using it).
If so, one could argue that Descartes’ argument in his Meditations — “I (the thinker) exist” — really is devoid of logic. It is simply an intuition/observation that he, the thinker, exists. That is, when you completely give up logic (and do not merely alter it), is it possible to make claims about the world without them being nonsense?
I hope I was clear,
and many thanks in advance 🙂