Russell’s Paradox (a version of the liar’s paradox), is not a paradox, it’s an ill formed statement (Grammatical error) because it failed the test of continuously recursive ambiguity – which is what ‘grammar’ means: rules of continuous recursive disambiguation. Nearly all seemingly challenging philosophical questions play on some variation of the verb to be. In the case of the liar’s paradox in all its forms, it’s not a paradox it’s constructed ambiguity. Words don’t mean things. People mean things. They use language well or not well to state their meaning – or their deceit.
A number is the name of a position, and beyond the base (glyphs) we use ‘Positional Naming’. We can name anything we choose with a position in an order just like we can name anything else. All that matters is that we all rely on the same names in the same order. Numbers exist as names. That’s it. Nothing else.
Mathematics is ill-grounded (vulnerable to grammatical errors) because of sets (platonic, ideal, verbal) rather than operations (gears and geometry). If you explain all mathematics using positional names, gears, and geometry (as it was invented) you do not expose yourself to grammatical errors.
The same is true of philosophical (verbal) statements. If you state all statements as promises, in operational prose, in complete sentences, without the ‘cheat’ (or lie) of the verb to be, you will have a very difficult time make grammatical errors.
So the entire analytic program (sets) was a failure. So was the attempt to discover a via-positiva scientific method. This is because all epistemology is falsificationary and adversarial, with surviving truth propositions competing in networks of paradigms themselves in falsificationary and adversarial competition.
Most of philosophy is little more than sophistry. (really)
Everything that isn’t sophistry is in the domain of science including that science we call ‘grammar’.
17Serg Gio, Stephen Thoma