Education as an institution like all things has a dark side. The presumption of the "blank slate" of mind is to blame for the failure of the necessary transference of evidence for truth as evidence of truth. Not unlike a Modus Ponens syllogism;
Facts are true.
Truth is facts.
Therefore, facts are truth.
No, not so. Facts are facts. Truth is truth.
Looking for the facts of the truth, I lost the truth for the facts.
Looking for the truth, I found the facts.
I have knowledge of facts, but truth remains to be determined.
2.22 What a picture represents it represents independently of its truth or
falsity, by means of its pictorial form.
2.221 What a picture represents is its sense.
2.222 The agreement or disagreement or its sense with reality constitutes
its truth or falsity.
2.224 It is impossible to tell from the picture alone whether it is true or
false.
3.031 It used to be said that God could create anything except what would
be contrary to the laws of logic. The truth is that we could not say what an
'illogical' world would look like.
4.46 Among the possible groups of truth-conditions there are two
extreme cases. In one of these cases the proposition is true for all
the truth-possibilities of the elementary propositions. We say that
the truth-conditions are tautological. In the second case the
proposition is false for all the truth-possibilities: the
truth-conditions are contradictory . In the first case we call the
proposition a tautology; in the second, a contradiction.
4.461 Propositions show what they say; tautologies and contradictions show
that they say nothing. A tautology has no truth-conditions, since it is
unconditionally true: and a contradiction is true on no condition.
Tautologies and contradictions lack sense. (Like a point from which two
arrows go out in opposite directions to one another.) (For example, I know
nothing about the weather when I know that it is either raining or not
raining.)
4.46211 Tautologies and contradictions are not, however, nonsensical. They
are part of the symbolism, much as '0' is part of the symbolism of
arithmetic.
4.462 Tautologies and contradictions are not pictures of reality. They do
not represent any possible situations. For the former admit all possible
situations, and latter none. In a tautology the conditions of agreement
with the world--the representational relations--cancel one another, so that
it does not stand in any representational relation to reality.
4.463 The truth-conditions of a proposition determine the range that it
leaves open to the facts. (A proposition, a picture, or a model is, in the
negative sense, like a solid body that restricts the freedom of movement of
others, and in the positive sense, like a space bounded by solid substance
in which there is room for a body.) A tautology leaves open to reality the
whole--the infinite whole--of logical space: a contradiction fills the
whole of logical space leaving no point of it for reality. Thus neither of
them can determine reality in any way.
4.464 A tautology's truth is certain, a proposition's possible, a
contradiction's impossible. (Certain, possible, impossible: here we have
the first indication of the scale that we need in the theory of
probability.)
4.465 The logical product of a tautology and a proposition says the same
thing as the proposition. This product, therefore, is identical with the
proposition. For it is impossible to alter what is essential to a symbol
without altering its sense.
4.466 What corresponds to a determinate logical combination of signs is a
determinate logical combination of their meanings. It is only to the
uncombined signs that absolutely any combination corresponds. In other
words, propositions that are true for every situation cannot be
combinations of signs at all, since, if they were, only determinate
combinations of objects could correspond to them. (And what is not a
logical combination has no combination of objects corresponding to it.)
Tautology and contradiction are the limiting cases--indeed the
disintegration--of the combination of signs.
6.2321 And the possibility of proving the propositions of mathematics means
simply that their correctness can be perceived without its being necessary
that what they express should itself be compared with the facts in order to
determine its correctness.
6.2322 It is impossible to assert the identity of meaning of two
expressions. For in order to be able to assert anything about their
meaning, I must know their meaning, and I cannot know their meaning without
knowing whether what they mean is the same or different.
6.43 If the good or bad exercise of the will does alter the world, it can
alter only the limits of the world, not the facts--not what can be
expressed by means of language. In short the effect must be that it becomes
an altogether different world. It must, so to speak, wax and wane as a
whole. The world of the happy man is a different one from that of the
unhappy man.
6.1251 Hence there can never be surprises in logic.
6.126 One can calculate whether a proposition belongs to logic, by
calculating the logical properties of the symbol. And this is what we do
when we 'prove' a logical proposition. For, without bothering about sense
or meaning, we construct the logical proposition out of others using only
rules that deal with signs . The proof of logical propositions consists in
the following process: we produce them out of other logical propositions by
successively applying certain operations that always generate further
tautologies out of the initial ones. (And in fact only tautologies follow
from a tautology.) Of course this way of showing that the propositions of
logic are tautologies is not at all essential to logic, if only because the
propositions from which the proof starts must show without any proof that
they are tautologies.
6.1261 In logic process and result are equivalent. (Hence the absence of
surprise.)
6.24 The method by which mathematics arrives at its equations is the method
of substitution. For equations express the substitutability of two
expressions and, starting from a number of equations, we advance to new
equations by substituting different expressions in accordance with the
equations.
6.362 What can be described can happen too: and what the law of causality
is meant to exclude cannot even be described.
6.363 The procedure of induction consists in accepting as true the simplest
law that can be reconciled with our experiences.
6.3631 This procedure, however, has no logical justification but only a
psychological one. It is clear that there are no grounds for believing that
the simplest eventuality will in fact be realized.
6.36311 It is an hypothesis that the sun will rise tomorrow: and this means
that we do not know whether it will rise.
6.37 There is no compulsion making one thing happen because another has
happened. The only necessity that exists is logical necessity.
6.371 The whole modern conception of the world is founded on the illusion
that the so-called laws of nature are the explanations of natural
phenomena.
6.4312 Not only is there no guarantee of the temporal immortality of the
human soul, that is to say of its eternal survival after death; but, in any
case, this assumption completely fails to accomplish the purpose for which
it has always been intended. Or is some riddle solved by my surviving for
ever? Is not this eternal life itself as much of a riddle as our present
life? The solution of the riddle of life in space and time lies outside
space and time. (It is certainly not the solution of any problems of
natural science that is required.)
-Tractatus Logico-Philosophicus
by Ludwig Wittgenstein
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment