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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