We can define a sentential constant 'f' (read as 'falsum'):

s be the first sentential constant:

f <-> (s & ~s)

That is not "gibberish". — TonesInDeepFreeze

A month ago I was talking about the implications of interpreting (B∧¬B) as 'FALSE' and all I received were superficial objections from the very people who were interpreting it in this manner but had not yet recognized it. I'm guessing those posts will have a very long shelf life.

I was not a person who objected to defining falsum as 'B & ~B'.

There are some distinctions to be made however.

In the context of my post, falsum is a symbol, not a truth value. It is a sentential constant. The value 'false' is not a symbol.

But the truth value of falsum is false in all interpretations. Just as the truth value of 'B & ~B' is false in all interpretations.

In 's thread on Irad Kimhi some of the same issues that were present in this thread are coming up again. For example:

Hence, for example, understanding p as an expression of consciousness depends on understanding the use of p in negation. As such, from this point of view we come to see that no conscious act is displayed or specified by the proposition of the form (p and ~p) and therefore no judgment or assertion is displayed by ~(p and ~p). This means that ~(p and ~p) and (p and ~p) are not genuine propositions. Understanding OPNC [ontological principle of non-contradiction] consists in seeing that the repetition of p in these logical contexts is self-cancelling. — Kimhi, Thinking and Being, 31

This thread quickly turned into a discussion of (a→(b∧¬b)), and a few of us raised the question of whether (b∧¬b) is a "genuine proposition," to use Kimhi's language. First was Count Timothy:

Can anyone think up a real world example where you would point out that A implies both B and not-B — Count Timothy von Icarus

Then I argued <here>, that (b∧¬b) is not ontologically possible. Following Kimhi I would say that it is also not psychologically possible. The truth-functionalists trying to stick to their guns could only make sense of (b∧¬b) as FALSE (or falsum, which is the same thing). As I pointed out multiple times, false is different from contradictory/absurd/impossible. And as I also argued multiple times, sentences containing (b∧¬b) are not well-formed in the specific sense I laid out. In Kimhi's language (b∧¬b) is not a genuine proposition. It will not do to say, "Ah, Kimhi doesn't understand Fregean logic." The point is that if Fregean logic thinks (b∧¬b) is a genuine proposition, so much the worse for Fregean logic.

But I would say that even in propositional logic things like (b∧¬b) are never part of the object language (and again, RAA ferrets them out). They only represent a sort of second-order psychological act, and they can only be asserted by those who do not understand that they are asserting a contradiction. But when someone contradicts themselves, the sense of what is asserted is crucially different from the sense of what is objected to, for the person asserting does not recognize the contradiction within their claim.

IMO, the issue is the reduction of logic to "formal logic," the form of argument, without any concern for the matter of an argument (what Scholastics called "material logic).

As Aristotle says:

All syllogism, and a fortiori demonstration, is addressed not to the spoken word, but to the discourse within the soul, and though we can always raise objections to the spoken word, to the inward discourse we cannot always object.

And St. Thomas says something similar in the commentary on the Metaphysics

It is impossible for anyone to actually adopt or believe the view that one and the same thing both is and is not in a given respect, even though some have attributed this opinion to Heraclitus. For while it is true that Heraclitus said this, yet it was not possible for him to believe what he said.Nor is it necessary that everyone has in mind or really believes everything that they say.Nor is it necessary that everyone has in mind or really believes everything that they say.

But if "logic" means only the study of words, language games, and not discourse/argument, then contradiction plays a different role, for surely we can speak the assertion of a contradiction, even if we cannot believe it.

- Yes, I very much like the way you set this out. A contradictory word and a contradictory intention/meaning are two different things, and a capable thinker must be able to recognize when words and meanings separate.