Sunday, 27 August 2017

Kant, Implication and Conceptual Containment

On an old reading, the statement

A implies B

is taken to be true (or false) because

B “contains” or “involves” something that is also “in” A.

This is the standard Kantian view of implication (or, later, synonym-based analyticity). However, B can be the consequence of A without it “containing” or “involving” something that's common to A. How, then, would B be a consequence of A? In physical nature, A can cause B without sharing anything with B. Non physically, B can also be deduced from A without sharing anything with A. If all that's so, how does this deduction or implication actually come about?

(All this hints at both “relevance logic” and “material implication”; as well as at the sharing of “propositional parameters”.)

In terms of statemental implication, to imply something means that there's actually something about the statement which somehow contains the implication. That doesn't really explain the relation between the implication and the implied. Can there be causal implication, for instance? In what sense is the implied actually in the implication?

We can also ask what it means to say that “B is contained within A”? Quine accused Kant of speaking at a metaphorical level when talking about “containment”. Thus what non-metaphorical way have we of describing what's at issue here? (If A is simply an inscription or “syntactic form”, then of course it can’t contain B – it can’t really contain anything except itself.)

So A will demand content if it's to imply B. In that case, it all depends on what the symbol A stands for. Is it a concept, sentence, statement or a proposition? All these possibilities have content.

If the symbol A stands for the concept [politician], then what content would it have? Can we say that contained within the concept [politician] are the macro-concepts [human being] and [person]; as well as the micro-concepts [professional] and [Member of Parliament]? However, in a certain sense it's quite arbitrary to categorise certain concepts as micro-concepts and others as macro-concepts because that distinction will depend on the context.

However, we can ask within which context we can categorise [politician] as a micro-concept. There's a simple way to decide what is what. We can ask this question.

Is it necessary for a politician to be a person or a human being?

The answer is no. It's not logically necessary; though what's been said is empirically the case. (A robot, computer or alien could be a politician.)

Is it necessary for a human being or person to be a politician?

The answer is: Of course not! In this simple sense the macro-concepts encompass the micro-concepts. Of course there are yet higher levels of concept. For example, [biped] and [animal]. This would include the concepts [human being] and [person]. And there are yet higher-order concepts than that. For example, [living thing] and [organism]. This could go on until we reach the concepts [object], [thing], [entity], [spatiotemporal slice] and so on.

If A is taken to be a concept, then it may well have a huge amount of implicit and explicit content. It could imply all sorts of things. However, it's a strange thing to take A as simply something standing for a single concept. It's hard to make sense of a concept all on its own (as it were). We need to fill in the dots ourselves.

If A is a sentence, then things become a little clearer and not as broad-ranging. The sentence may of course include concepts; though such concepts - within a sentential framework - will be more finely delineated and circumscribed. Something will be said about the concepts contained and they may be contextualised.

To say that the concept [politician] implies the concepts [human being] and [person] just sounds strange. In a sense, the bare concept [politician] isn't actually saying anything. The idea of containment must be taken less literally in the case of A standing for a concept than when if A stands for statements, sentences, etc.  This parallels, to a small extent, Frege's “context principle”.

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