Meaning, Logic, Depth

 

For classical logic to work, terms must have clear borders. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Thus Aristotle with his "essential" definitions. For propositional logic to work (and connect to reality) statements must refer to states of affairs. The cat is on the mat is true if and only if the cat is on the mat, which presupposes the existence of cats and mats. Thus Wittgenstein of the Tractatus. Both, I think, involve metaphysical assumptions, but ones that fall well short of the richness of the ideas I have been exploring. Wittgenstein of the Philosophical Investigations seems to be working at a pre-logical level. i.e. doing something different.

 

Logical systems are not metaphysically neutral. The two I just referred to offer two versions of what “fit” with reality means. Classical logic works with terms (man, mortal, Socrates) that require stable boundaries. It must be clear which referents are covered by the term and which aren’t; otherwise, no inferences can be validly made. All tall men are strong. Socrates is tall. Therefore, Socrates is strong. If in one premise, “tall” means over 180 cm and in another, it means over 170 cm, then the term does not pick out a stable set. Thus the syllogism appears formally valid but the inference is unsound or unreliable, because the term shifts, the point being that if the boundary of the term is unclear or unstable, we do not know what set we are talking about. Another example. All students must pay the fee. Anna is a student. Hence, Anna must pay the fee. Now suppose in the first premise, “student” means full-time enrolled student but in the second Anna is a student in the sense of a guest auditor. Now the inference breaks down. Why? Because “student” does not refer to the same set in both premises. Again, the point is that valid inference requires that the term pick out the same class throughout. Philosophy, to the extent it depends on arguments and thus logic, requires terms with fixed boundaries. Geometry (with its precise terms) seems a paradigm and indeed Plato thought that geometry was the way into philosophy.

    It follows that if logic has anything to do with the real world, it depends on something like essences (in the narrow sense) or kinds. Thus seen through the lens of classical logic, reality is structured into kinds that can be stably identified. All blue whales are mammals. All mammals are animals. Therefore, all blue whales are animals. For this to fit, to be true, the terms must refer to closed sets of objects, which must be real. Most of us common sense folk and most scientists would affirm the reality of blue whales, mammals, and animals. Nominalism gets no foothold here.

 

      Propositional logic, however, works with propositions. Propositions picture states of affairs. Truth is the correspondence between proposition and fact. The cat is on the mat corresponds to a specific arrangement in reality. Here the metaphysical assumption is that reality consists of facts (states of affairs) that can be represented.

 

    Even when both present themselves as “pure logic,” both frameworks presuppose a structured world; a fit between thought and reality; a stability that allows language to latch on. Aristotle assumes natures/kinds; early Wittgenstein assumes facts/structures. These are not neutral; they are ontological commitments.

 

      Still, both are “thin” compared to what I was exploring in the last two entries. Both systems require clear, well-defined units. But they operate at a level where richness is bracketed and depth is flattened for the sake of precision. Thus they capture what must be true for inference to work and not the full richness of how reality is disclosed, as discussed previously.

 

     I wrote that the later Wittgenstein was working at a pre-logical level. He is exploring how terms get their boundaries in the first place, or how propositions come to have sense, or what makes reference possible at all. So instead of building logical systems, as he did in the Tractatus, he explores

the conditions under which logic can even get started.

      Thus I would distinguish between three levels.

 

 

 

1) The pre-logical (Wittgenstein, later) realm of practices, forms of life, shared criteria, “knowing how to go on,” etc. Here meaning is established, boundaries are negotiated.

 

 

2) The logical realm (Aristotle / Tractatus Wittgenstein) of clear terms or propositions and stable reference – both required for valid inference. This is where reasoning happens and truth can be formally tested.

 

3) And then there is the metaphysical (my project), which is about what things are, building on that what Being is, and how both are intelligible. This is the level where depth appears and different modes (science, poetry, etc.) come into play.

 

 I do not reject any of these, just trying to order them. Without the first level,  logic floats free (no grounded meaning). Without the second level, there can be no disciplined reasoning. Without the third level, there can be no depth, no real understanding of reality, which is why, I suppose, Bertrand Russell found the work of the later Wittgenstein to be trivial – he resists moving from the first to the third. He shows how meaning emerges but remains agnostic or skeptical about how the reality has to be to make meaning possible. Anyway, logic depends on pre-logical practices, and both presuppose a deeper intelligibility of being.

 

So to summarize this line of thought, classical and propositional logic presuppose a world already structured and accessible to thought; the later Wittgenstein investigates the practices that make such access possible; but neither fully accounts for the deeper intelligibility of reality that these practices and logical systems presuppose.