A beginner question You are talking about every triangle in realationship to having four sides. — TheWillowOfDarkness
Yep. So we can talk about the intersection of sets - {triangles} and {four sided polygons} - that then result in empty sets. It fits one view of set logic. But then more realistic is the thought that triangles are a subset of the polygons. And the particular constraint is that they have just three sides. Or even more importantly - in being maximally generic - they are the least sides a polygon can have in a two dimensional plane.
So an apparently simple logical operation is in fact a flattening of the hierarchical complexity of an actual world (even the actuality represented by the idea of spaces enclosed by edges on a plane).
A subsumptive hierarchy notation would make the point plainer - {n-gon {3-gon}}. Or putting it the other way around, given the world of a plane - constraint in two dimensions - the minimum constraint that has to be added to close those two degrees of freedom is 1 further. Or a rotation of 180 degrees. The n-gon, effectively a circle or 360 degree rotation, is then the maximum number of sides that can be used to enclose a space.
So four sided triangles sound a logical nonsense because they are understood as a particular of set theoretic operation. But set theory is itself a metaphysically impoverished language for doing real metaphysics. Logical atomism's spectacular crash and burn was surely enough to demonstrate that. And perhaps you can forgive the survivors for walking away muttering, metaphysics, never again!
:)
Now one might point out the unrestricted "everything" is talking about possibilities, saying that our language may talk of anything. This is true, but what does it mean? Well, it isolates the specific possibility of what our language can say. In the sense that it talks about anything, it's restricted to a specific possibility. It not about an unrestricted "everything" at all. — TheWillowOfDarkness
Again yep. This is why a metaphysical strength logic wants to employ the further notion of vagueness, or the distinction between the radically indeterminate and the crisply individuated.
Vagueness can never be exhausted by inquiry. And the good thing about that is it means inquiry doesn't have to exhaust itself trying.
Theories of truth break themselves on the rocks because they believe the world is something definite and therefore every possible proposition has some true or false value. It's that AP disease. But as soon as you take the pragmatic view, everything changes. Truth only needs determining to the degree that a difference could make a difference.
So that is a real economising move. Truth is only in question to the degree it might actually matter in terms of a purpose or finality. We can lighten up. That was Witti's Peircean point.
On the other hand, we then need an objective model of finality - the purpose that determines what counts as meaningful. So that is the extra work that philosophy of language types never really got going on because they retreated into a commonsense realism about speech acts, thus completely avoiding the metaphysical issues which semiotics had already addressed.