 |
I knew I was in trouble when I was told I was too
logical.
"The brain works by pattern matching not logic." - Jonathan
Haidt
Due to the truthfulness of the preceding
statement it becomes imperative that those pattern matches be based on a logic
accurate assessment of objective reality which includes an accurate and
unbiased understanding of the world outside of personal first-hand
experience.
The
law of (non-)contradiction states
that no statement
(proposition, assertion, etc.) can be both true and not
true (false).
The
law of excluded middle is
generally given as "A is B or A is not B;"
object (A) either has or lacks a
given property (B).
An alternate formulation of this (with propositions
instead of objects) is "p or not p" - but not both.
"There is nothing
between asserting and denying." - Aristotle
The
law of identity states that A
equals A or "if any statement is true, then that statement is true."
The law of
rational inference monitors inferences between premises and conclusions.
If A equals B, and B equals C, then A equals C.
"The
law of rational inference teaches
that if premise A and B are valid, then, by what Martin Luther called
resistless logic, that conclusion C
follows." - C. Matthew McMahon
These
four primary laws of logic are
essential to all
coherent intelligible
communication.
Logic is defined as:
valid
reasoning
A mode of reasoning.
A system of reasoning.
Reasoned and
reasonable judgment.
The branch of
philosophy that
analyzes inference.
The formal, guiding
principles of a
discipline,
school, or
science.
The
principles that guide
reasoning within a given field or
situation.
The relationship between
elements and between an element
and the
whole in a set of
objects, individuals,
principles, or events.
The
nonarithmetic operations performed by a computer,
such as sorting, comparing, and matching, that involve yes-no
decisions.
A branch of philosophy and
mathematics that deals with the
formal principles, methods
and
criteria of validity of inference,
reasoning and knowledge.
The study
of the principles of
reasoning, especially of the
structure of
statements as
distinguished from
their content and of method and validity in
deductive
reasoning.
Concerned with what is
true and false. This involves
the representing statements and
logical connectives.
The
science or art
of exact reasoning, or of pure and formal thought, or of the laws
according to which the processes of pure
thinking should be conducted; the
science of the formation and
application of general notions; the science of generalization,
judgment, classification, reasoning, and systematic arrangement; correct
reasoning.
Symbolic
logic uses a meta-language concerned with truth, how we can
know whether something is true and the
formalization of logical arguments and proofs in
terms of symbols representing
statements and logical connectives which
may or may not have a corresponding expression in the
world of objects
called existence. The meanings of these
logical connectives
are expressed by a set of
rules or primitives which are assumed to be self
evident.
Boolian logic deals with the
basic operations of truth
values: AND, OR, NOT and combinations thereof.
Predicate logic extends this with existential and
universal quantifiers and symbols standing for
predicates which may depend on variables. The rules of
natural
deduction describe how
we may proceed from valid premises to valid
conclusions, where the premises and conclusions are
expressions in predicate
logic.
inference in logic is:
- the process of
deriving the strict logical
consequences of assumed premises.
-
the process of arriving at some conclusion that, though it is not logically
derivable from the assumed premises,
possesses some degree of probability relative to
the premises.
- a proposition reached by a process of
inference.
"It has been known for some years that we cannot
speak sense about man in the old language. Although Wittgenstein has proved
this point, he did not show us the way out. The way out is simple. We must form
a new vocabulary." - Alfred Korzybski
This text will be
understood only by someone who has himself already had the
thoughts that are
expressed in it.
This text deals with the
problems of philosophy - that the
logic of language
is misunderstood.
The whole sense of this text might be summed up in
the following words: what can be
said at all can be said clearly, and what we cannot talk about we must
pass over in silence.
Thus the aim of this text is to draw limits to the
expression of thoughts.
I do not wish to judge how far my efforts coincide
with those of other philosophers.
The thoughts that are
here communicated seems to me unassailable and definitive.
L.W. Vienna,
1918
{Note: Although
what can be said may be stated clearly and succinctly many times it is in the
interests of the speaker or writer to not do so and in the case of
propaganda and
deception imperative.}
{NOTE:
THE FOLLOWING EXCERPT HAS A LOGICAL THREAD RUNNING THROUGH IT.
All numbering
and thoughts by Ludwig Wittgenstein}
4
|
A
thought is a statement with a
sense.
|
4.001
|
The totality of
statements is language.
|
4.022
|
Man possesses the ability to
construct languages capable of
expressing materially related thoughts, without having any idea how each word has meaning
or what its meaning is – just as people speak without
knowing how the individual sounds are produced.
Everyday language is a part of the human
organism and is no less complicated than it. It is not humanly possible to
gather immediately what the logic of language is.
Language disguises
thought.
So much so, that from
its outward form of language it is impossible
to infer the form of the thought beneath it,
because its outward form is not designed to reveal the form of the
thought, but for entirely different purposes. The
tacit conventions on which the
understanding of everyday
language depends are enormously complicated.
|
4.003
|
Most of the
statements and
questions of philosophers arise when a society experiences
a
cultural wide failure to
understand the logic of their own
language.
|
4.01
|
A statement is an
image of reality - a model
of reality as we imagine it.
|
4.014
|
A gramophone record, the musical
idea, the written notes, and the sound-waves, all
stand to one another in the same internal relation
of depicting knowledge that holds between
language and culture. They are all constructed according to a common
logical pattern.
|
4.0141
|
There is a general
rule, a common logical pattern, by means of which the musician can
obtain the symphony from the score, and which makes it possible to derive the
symphony from the groove on the gramophone record, and, using this first
rule, to derive the score again. The common
logical pattern is the general
rule that creates the inner similarity between a
musical score, a symphony and a gramophone record - things which are
constructed in such entirely different ways but which produce identical
results.
|
4.015
|
The possibility of all
imagery, of all our pictorial modes of
expression, is contained in the
logic of depiction.
|
4.02
|
We understand the sense of a
statement without it having been explained in detail through a commonly held
logic of depiction.
|
4.021
|
A statement is a
image of reality: if I
understand a statement, I know the situation that
it represents without having had its details explained to me.
|
4.022
|
A statement shows its sense. A
statement shows how things stand if the statement is true.
|
4.023
|
A statement restricts
reality to two alternatives:
true or false. In
order to do that, it must describe reality
completely. A statement is a description of a
state of affairs. Just as a
description of an object describes it by
its properties, so a statement describes reality by
its properties. A statement constructs a reality
with the help of a logical scaffolding, so that
one can actually see from the statement how
everything stands logically if the statement is
true.
|
4.024
|
To recognize the
truth of a true
statement is to logically understand actual
reality.
|
4.025
|
When translating one
language into another,
translators do not proceed by
translating each statement of the one into a
statement of the other, but merely by translating the constituents of
statements. (And the dictionary
translates not only substantives, but also
verbs, adjectives, and conjunctions, etc.; and it treats them all in the same
way.) Therefore all translations will be
corrupt.
|
4.026
|
The meanings of simple
symbols (words) must be
explained to us or defined for us if we are to fully understand them. With
statements, however, we communicate a
state of affairs.
|
4.027
|
It belongs to the
essence of a statement that it should be able to
communicate a state of affairs
or a situation.
|
4.03
|
A statement must use old
expressions (symbolic imagery) to
communicate a situation.
For a statement to communicate a situation it must
be essentially connected
to the situation.
|
4.032
|
It is only in so far as a
statement is logically articulated that it is an
image of a situation.
|
4.06
|
A
statement can be
true or false only in
virtue of being an image of
reality.
|
4.1
|
Statements represent the
existence and non-existence of actual
states of
affairs.
|
4.11
|
The totality of
true statements is the whole of
natural science (or the whole corpus of
the natural sciences).
|
4.112
|
Philosophy aims at the logical clarification of thoughts. Philosophy
is not a body of doctrine but an activity. A philosophical work consists essentially of elucidations. Philosophy does not result in 'philosophical statements', but rather in the clarification
of actual statements. Without
philosophy thoughts
are cloudy and indistinct: Sophia's task is to
make them clear and to give them sharp boundaries.
|
4.113
|
Philosophy defines the limits to the much disputed
sphere of natural
science.
|
4.114
|
Philosophy defines the limits to
what can be thought; and, in doing so, to what
cannot be thought. Philosophy defines the
limits to what cannot be thought by working
outwards through what can be thought.
|
4.115
|
Philosophy will verify what cannot be said, by
presenting clearly what can be said.
|
4.116
|
Everything that can be
thought at all can be thought clearly. Everything that can be put into
words can be put clearly into words. (Clarity is many times not an intent of the speaker
or author.)
|
4.12
|
Statements can represent
reality, but they cannot represent what they must
have in common with reality in order to be able to
represent it - the logical form of
reality. In order to be able to represent the
logical form of reality with statements,
we have to be able to station
ourselves as observers somewhere outside logic, outside
reality.
|
4.121
|
Statements do not represent the
logical form of reality: the logical form
of reality is mirrored in them.
Statements reveal the
logical form of reality.
|
4.125
|
The existence of an internal relation between possible situations
expresses itself in
language by means of an internal
relation between the
statements representing those possible
situations.
|
4.21
|
The simplest kind of statement,
an elementary statement, asserts the
existence of a
state of
affairs.
|
4.211
|
If a statement's is elementary
there can be no elementary statement
contradicting
it.
|
4.22
|
An elementary statement consists of names. It is a
nexus, a concatenation, of names.
|
4.23
|
It is only in the nexus of an
elementary statement that a name occurs in a
statement.
|
4.25
|
If an elementary statement is true, the
state of affairs
exists: if an elementary
statement is false, the
state of affairs does not
exist.
|
4.026
|
If all
true elementary
statements are given, the result is a complete description of
reality.
|
4.411
|
It immediately strikes one as
probable that the introduction of elementary
statements provides the basis for
understanding all other
kinds of statement. Indeed the
understanding of
general statements palpably depends on the
understanding of
elementary statements. (If elementary statements
are misunderstood then a false understanding of reality will be
created.)
|
4.46
|
Among the possible groups of
truth-conditions there are two extreme cases. In one of these cases the
statement is true for all the truth-possibilities
of the elementary statements. We say that the
truth-conditions are tautological. In the second case the statement is
false for all the truth-possibilities: the
truth-conditions are contradictory . In the first case
we call the statement a tautology; in the second, a
contradiction.
|
4.461
|
Statements 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.(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 of language, much as '0' is part of the
symbolism of arithmetic.
|
4.462
|
Tautologies and
contradictions are not
images 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
reality – 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
statement determine the range that it leaves open. 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 in
logical space for reality. Tautologies and
contradictions are thus unable
to determine reality in any way.
|
4.464
|
A tautology's
truth is certain, a statement's possible, a
contradiction's impossible.
(Certain, possible, impossible: the first indication of a scale to be used in
the theory of probability.)
|
4.465
|
The logical product of a tautology and a statement says
the same thing as the statement. This product, therefore, is identical with the
statement. It is impossible to alter what is essential to a symbol without
altering its essence.
|
4.5
|
It now seems possible to give
the most general propositional form: that is, to give a description of the
statements of any
language whatsoever in such a way that every
possible sense can be expressed by a
symbol satisfying the description, and every
symbol satisfying the description can
express a sense, provided that the
meanings of the names are suitably chosen. It is clear that only what is
essential to the most general propositional form may
be included in its description - for otherwise it would not be the most general
form. The existence of a general propositional
form is proved by the fact that there cannot be a statement whose form could
not have been foreseen (i.e. constructed). The general form of a statement is:
This is how things stand.
|
4.51
|
If I am in possession of a
basic truthful understanding of all elementary
statements then I can intuitively deduct from that library of
elementary statements the actual conditions of
reality. Out of that knowledge I can construct a structural definition of the
limits of the common logical language pattern's
ability to define reality
accurately.
|
5
|
A statement is a
truth-function of elementary
statements.
(An elementary statement is a truth-function of
itself.)
|
5.01
|
Elementary statements are the truth-arguments of
statements.
|
5.1
|
Truth-functions arranged in
series is the foundation of the theory of
probability.
|
5.123
|
If God
created a reality in which
certain elementary statements were
true, then by that very act God would have also created a
reality in which all the
statements that follow from those
elementary statements are
true.
|
5.124
|
A statement affirms every
statement that follows from it.
|
5.13
|
The truth of one statement following from the
truth of others can be seen in the structure of the
statement.
|
5.131
|
The truth of one statement following from the
truth of others, finds
expression in the structural
relation of the forms of the
statements to one another. These
relations exist independently of definitions, the
relations are internal and their
existence is an immediate result of the
existence of the statements.
|
5.143
|
Contradiction is that common
factor of statements which no statement
has in common with another. Tautology is the common factor of all
statements that have nothing in common
with one another. Contradiction, one might say,
vanishes outside all statements:
tautology vanishes inside them. Contradiction is the outer limit
of statements: tautology is the
unsubstantial point at their center
|
5.153
|
In itself, a statement is
neither probable nor improbable.
Either an event occurs or it does not:
there is no middle way.
|
5.154
|
Suppose that an urn contains
black and white balls in equal numbers (and none of any other kind). I draw one
ball after another, putting them back into the urn. By this experiment I can
establish that the number of black balls drawn and the number of white balls
drawn approximate one another as the draw continues. Now, if I say, 'The
probability of my drawing a white
ball is equal to the probability of
my drawing a black one', this means that all the circumstances that I
know of (including the laws of nature assumed as
hypotheses) give no more probability
to the occurrence of the one event than to that of the other. What I confirm by
the experiment is that the occurrence of the two events is independent of the
circumstances of which I have no more detailed knowledge.
|
5.155
|
The minimal unit for a
probability statement is this: The
circumstances – of which I have no further knowledge – give such and such a degree of
probability to the occurrence of a
particular event.
|
5.156
|
It is in this way that
probability is a generalization. It
involves a general description of a propositional form. We use
probability only in default of
certainty – if our knowledge is not indeed
complete. (A statement may well be an incomplete image
of a certain situation, but it is always a complete image of a conceptualized situation.) A
probability statement is derived
from other statements.
|
5.3
|
All
statements are results of
truth-operations on elementary statements. A
truth-operation is the way in which a truth-function is produced out of
elementary statements. It is of the
essence of truth-operations that, just as
elementary statements yield a truth-function of
themselves, so too in the same way truth-functions yield further truth-
functions. When a truth-operation is applied to truth-functions of
elementary statements, it always generates
another truth-function of elementary statements.
When a truth-operation is applied to the results of truth-operations on
elementary statements, there is always a single
operation on elementary statements that has the
same result. Every statement is the result of truth-operations on
elementary statements.
|
5.32
|
All truth-functions are results
of successive applications to elementary
statements of a finite number of truth-operations.
|
5.45
|
If there are primitive
logical archetypical truths,
then any logic pattern that fails to show clearly how those logical archetypical truths
are placed relatively to one another to justify their existence will be incorrect.
|
5.451
|
If logic has primitive logical archetypical truths,
they must be independent of one another.
|
5.4541
|
The solutions of the problems of logic must be simple, since they set the standard of
simplicity. Men have always had a presentiment that there must be a realm in
which the answers to
questions are symmetrically combined
– a priori – to form a self-contained system. A realm subject to the
law: Simplex sigillum veri.
|
5.47
|
It is
clear that whatever we can say
in advance about the form of all statements, we must be able to say all at
once . An elementary statement really contains
all logical operations within itself.
|
5.471
|
The general propositional form
is the essence of a statement.
|
5.4711
|
To give the
essence of a statement means to give the
essence of all description, and thus the
essence of reality.
|
5.472
|
The description of the most
general propositional form is the description of the one and only general
primitive archetypical
truth in logic.
|
5.473
|
Logic must look after itself. If a
archetypical truth is possible , then it is also capable of
signifying. Whatever is possible in logic is also
permitted.
|
5.47321
|
Occam's Razor is, of course, not an
arbitrary rule,
nor one that is justified by its success in practice: its point is that
unnecessary units in a language mean nothing.
Symbols that serve one purpose are logically
equivalent, and symbols that serve none are logically
meaningless.
|
5.476
|
It is
clear that this is not a
question of a number of primitive
archetypical truths that have to be signified, but rather of the
expression of underlying
rule.
|
5.511
|
How can
logic – all-embracing
logic, which mirrors reality – use such peculiar crotchets and
contrivances?
Only because they are all connected with one another in an
infinitely fine network, the great mirror.
|
5.526
|
We can describe
reality completely by means of fully generalized
statements
without first correlating
any name with a particular object.
|
5.5261
|
A fully generalized statement,
like every other statement, is composite.
The mark of a composite
symbol is that it has something in common with other
symbols.
|
5.5262
|
The truth or falsity of every statement does make some
alteration in the general conceptual construction of reality. The range that the totality of
elementary statements leaves open for the
construction of reality is exactly the same as that
which is delimited by entirely general
statements.
|
5.5301
|
It is self-evident that
identity is not a relation between
objects.
|
5.5423
|
To perceive a
complex statement means to
perceive that its
constituents are related to one another in such and such a way. Contradictions
arise when constituent elementary statements have been improperly
conceptualized which explains the existence of apparent
contradictions.
|
5.552
|
The 'experience' that we need in
order to correctly understand logic is not that
something or other is the state of
affairs, but that something actually exists.
|
5.555
|
Clearly we have some concept of
elementary statements quite apart from their
particular logical forms. When there is a system
by which we can create symbols, the system is what is
important for logic and not the individual
symbols. We need to understand what makes it possible
for us to create those symbols.
|
5.556
|
There cannot be a hierarchy of
the forms of elementary statements. We can
foresee only what we ourselves can construct.
|
5.5561
|
Empirical
reality is limited by the totality of
objects. The limit also makes itself
manifest in the totality of elementary
statements. Hierarchies are and must be independent of
reality.
|
5.5563
|
In fact, all the
statements of our everyday
language, just as they stand, are in perfect
logical order. – That utterly simple thing,
which we have to formulate here, is not a likeness of the truth, but the truth itself in
its entirety. (Our problems are not abstract, but perhaps the most concrete
that there are.)
|
5.6
|
The limits of my
language set the limits of my
reality.
|
5.61
|
Logic pervades reality:
the limits of reality are also the limits of
logic. We cannot think what we cannot think; so
what we cannot think we cannot say either.
|
5.62
|
Reality is my world: this is manifest in that the
limits of language are the limits of my
world.
|
5.621
|
My world and my reality are
one.
|
5.641
|
Thus there really is a sense in
which philosophy can talk about the
self in a non-psychological
way. What brings the self into philosophy is the
fact that 'reality is my world'. The philosophical self is not
the human being,
not the human body, or the human
soul, with which
psychology deals, but rather
the metaphysical subject, the limit of reality
– not a part of it.
|
6.1
|
The
statements of logic are tautologies.
|
6.112
|
Statements of logic must be assigned a unique status among all
statements.
|
6.113
|
Logical statements can be recognized as
true immedialtely from the symbols alone, and this fact contains in itself the
whole philosophy of logic. The truth or
falsity of non-logical
statements cannot be recognized from the
statements alone. .
|
6.12
|
The fact that the
statements of logic are tautologies shows the formal –
logical – properties of
language and reality. The fact that a tautology is yielded by this
particular way of connecting its constituents characterizes the
logic of its constituents. If
statements are to yield a tautology when
they are connected in a certain way, they must have certain structural
properties. Their yielding a tautology when combined in this shows that they
possess these structural properties.
|
6.1202
|
It is
clear that one could achieve
the same purpose by using contradictions instead of
tautologies.
|
6.121
|
The
statements of logic demonstrate the logical properties of
statements by combining them so as to
form statements that say nothing. In a
logical statement,
statements are brought into equilibrium
with one another, and the state of equilibrium then indicates what the
logical constitution of these
statements must be.
|
6.122
|
It follows from this that we can
actually do without logical
statements; for in a suitable notation we
can in fact recognize the formal properties of
statements by mere inspection of the
statements themselves.
|
6.1222
|
This throws some light on the
question why logical statements cannot be confirmed by experience
any more than they can be refuted by it. Not only must a statement of
logic be irrefutable by any possible experience,
but it must also be unconfirmable by any possible experience.
|
6.1232
|
The general validity of
logic might be called essential, in contrast with the
accidental
general validity of such statements as
'All men are mortal'.
|
6.124
|
The
statements of logic describe the scaffolding of
reality, or rather they represent it.
If
we know the logical
syntax of any language, then we have already
been given all the statements of
logic.
|
6.125
|
It is possible – indeed
possible even according to the old conception of logic – to give in advance a description of all
'true' logical
statements.
|
6.1251
|
Thus there can be no surprises
in logic.
|
6.1261
|
In logic process and result are equivalent. (Hence the
absence of surprise.)
|
6.1262
|
Proof in
logic is merely a mechanical expedient to
facilitate the recognition of tautologies in complicated cases.
|
6.127
|
All the
statements of logic are of equal status: it is not the case that
some of them are essentially derived
statements. Every tautology itself shows
that it is a tautology.
|
6.1271
|
It is
clear that the number of the
'primitive statements of
logic' is arbitrary, since one could derive
logic from a single primitive
statement.
|
6.13
|
Logic is not a body of doctrine,
but a
mirror-image of reality.
Logic is transcendental.
|
6.2
|
Mathematics is a
logical method. The
statements of mathematics are equations,
and therefore pseudo-statements.
|
6.211
|
We make use of
mathematical statements as
inferences from statements that do not
belong to mathematics to others that likewise do not belong to mathematics.
|
|
(In
philosophy the
question,
'What do we actually use
this word or this statement for?'
repeatedly leads
to valuable insights.)
|
6.22
|
The logic of reality, shown
in tautologies by the statements of
logic, is shown in equations by mathematics.
|
6.23
|
If two
expressions are combined by means of
the sign of equality, that means that they can be substituted for one another.
When two expressions can be substituted
for one another, that characterizes their logical
form.
|
6.233
|
The
question whether
intuition is needed for the
solution of mathematical problems must be given the
answer that in this case
language itself provides the necessary
intuition.
|
6.2331
|
The process of calculating
serves to bring about that intuition.
|
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.
|
6.3
|
The exploration of
logic means the exploration of everything that is
subject to law . Outside logic everything is accidental.
|
6.31
|
The mathematical
law of induction cannot possibly be a law of logic, since it is
obviously a statement with sense. - Nor, therefore, can it be an a priori
law.
|
6.32
|
The law
of causality is not a law but the form of a
law.
{"All actions are caused by
entities. The nature of an action is caused and determined by the nature of the
entities that act; a thing cannot act in contradiction to its nature."- Ayn
Rand
"If one thing the same in nature at different times, or two
things the same in nature, are to act in situations the same in their nature,
they must act on both occasions in the same way."- H. W. B.
Joseph}
|
6.321
|
'Law of
causality' - that is a general name. And just as in mechanics, for example,
there are 'minimum-principles', such as the law of least
action, so too in physics there are causal laws,
laws of the causal form.
|
6.3211
|
Indeed people even surmised
that there must be a 'law of least action' before they
knew exactly how it went. (Here, as always, what is certain a priori proves to
be something purely logical.)
|
6.33
|
We do not have an a priori
belief in a law of conservation, but rather a priori
knowledge of the possibility of a
logical form.
|
6.34
|
All such
statements, including the principle of
sufficient reason, the laws of continuity in
nature and of least effort in nature, etc. - all these are a priori
insights about the forms in which the statements of science can be
cast.
|
6.341
|
Newtonian mechanics, for
example, imposes a unified form on the description of reality. Let us imagine a white surface with irregular
black spots on it. We then say that whatever kind of image these make, I can always approximate as closely as
I wish to the description of it by covering the surface with a sufficiently
fine square mesh, and then saying of every square whether it is black or white
(pixelated). In this way I shall have imposed a unified form on the description
of the surface. The form is optional, since I could have achieved the same
result by using a mesh with a triangular or hexagonal mesh. Possibly the use of
a triangular mesh would have made the description simpler: that is to say, it
might be that we could describe the surface more accurately with a coarse
triangular mesh than with a fine square mesh (or conversely), and so on. The
different meshes correspond to different systems for describing
reality. Mechanics determines one form of
description of reality by saying that all
statements used in the description of
reality must be obtained in a given way from a given
set of statements – the axioms of
mechanics. As with the number-system we must be able to write down any number
we wish, so with the system of mechanics we must be able to write down any
statement of physics that we wish.
|
6.342
|
And now we can see the relative
position of logic and mechanics. The possibility
of describing an image like the one mentioned above
with a mesh of a given form tells us nothing about the image which is true of all
such images. But what does characterize the
image is that it can be described completely by a
particular size of white mesh with a particular arrangement of black spots.
Similarly the possibility of describing reality by
means of Newtonian mechanics tells us nothing about reality: what does tell us something about
reality is the precise way in which it is possible
to describe reality by these means. We are also told
something about reality by the fact that it can be
described more simply with one system of mechanics than with
another.
|
6.343
|
Mechanics is an attempt to
construct according to a single plan all the true
statements that we need for the
description of reality.
|
6.3431
|
The laws of physics with all
their logical apparatus speak about the
objects of reality.
|
6.3432
|
We ought not to forget that any
description of reality by means of mechanics will be
of the completely general kind.
|
6.35
|
Although the spots in our
image are geometrical figures, nevertheless geometry
can obviously say nothing at all about their actual form and position. The
network, however, is purely geometrical; all its properties can be given a
priori. Laws like the principle of sufficient reason, etc. are about the mesh
and not about what the mesh describes. (The principle of sufficient reason
states that anything that happens does so for a definite
reason.)
|
6.36
|
If there were a
law of causality, it might be put in the following way:
There are laws of nature.
|
6.3611
|
We cannot compare a process with
'the passage of time' – there is no such thing – but only with
another process (such as the working of a chronometer). Hence we can describe
the lapse of time only by relying on some other process. Something exactly
analogous applies to space: e.g. when people say that neither of two events
(which exclude one another) can occur, because there is nothing to cause the
one to occur rather than the other, it is really a matter of our being unable
to describe one of the two events unless there is some sort of asymmetry to be
found. And if such an asymmetry is to be found, we can regard it as the cause
of the occurrence of the one and the non-occurrence of the other.
|
3.36111
|
Kant's problem about the right
hand and the left hand, which cannot be made to coincide,
exists even in two dimensions. Indeed, it
exists in one-dimensional space in which the two
congruent figures, a and b, cannot be made to coincide unless they are moved
out of this space. The right hand and the left hand are in fact completely
congruent. It is quite irrelevant that they cannot be made to coincide. A
right-hand glove could be put on the left hand, if it could be turned round in
four-dimensional space.
|
6.363
|
The procedure of induction
consists in accepting as true the simplest
law that can be reconciled with our
experiences. Occam's Razor suggests this.
|
6.3631
|
Using
Occam's Razor rentlessly has no
logical justification, only a
psychological one. It is
clear that there are no grounds
for believing that the simplest eventuality will in fact be realized as a
belief does not declare actuality.
|
6.36311
|
It is an hypothesis that we will
see the sun will rise tomorrow: we do not know
whether we will see it rise. (From past experience we can expect the sun to
rise and when we understand the actual motion of the planets in
relation to the sun we have faith that, yes indeed,
the sun will rise tomorrow but we have no guarantee that we ourselves will be
standing there alive to witness the sun emerging over the
horizon.)
|
6.373
|
Reality is independent of human
will.
|
6.374
|
Even if all that we wish for
were to happen, still this would only be a favor granted by fate. The human
will's desire to modify reality has no
actuality.
|
6.375
|
Just as the only necessity that
exists is logical
necessity, so too the only impossibility that exists is logical
impossibility.
|
6.3751
|
For example, the simultaneous
presence of two colors at the same place in the visual field is impossible, in
fact logically impossible, since it is ruled out by the
logical structure of color. It is
clear that the
logical product of two elementary statements can neither be a tautology nor
a contradiction. The statement
that a point in the visual field has two different colors at the same time is a
contradiction.
|
6.4
|
All
statements are of equal
value.
|
6.41
|
An understanding of reality must lie
outside reality. In reality everything is as it
is, and everything happens as it does happen.
Only by understanding that human
will fails to have any material effect whatsoever on reality are we
freed.
|
6.421
|
Ethics
cannot be put clearly into
words. Ethics is
transcendental.
|
6.422
|
There must be some kind of
ethical reward and ethical punishment, but they must reside
in the action itself.
|
6.43
|
The reality of the happy man is
a different one from the reality of the unhappy man.
|
6.4311
|
Death is not an event in life: we do not live to experience death. If
we take eternity to mean not
infinite temporal duration but
timelessness, then eternal
life belongs
to those who live in the present.
|
6.44
|
It is not how things are in reality
that is mystical, but that reality actually exists.
|
6.5
|
When the
answer cannot be put into
words, neither can the
question be put into words.
|
6.51
|
Scepticism is not irrefutable, but obviously
nonsensical, when it tries to raise doubts where no
questions can be asked. For doubt can
exist only where a
question exists, a question only where an
answer exists, and an answer only where something can be said.
|
6.52
|
We feel that even when all
possible scientific questions have been
answered, the problems of
life remain completely untouched. Of course there are
then no questions left, and this itself
is the answer.
|
6.521
|
The solution of the problem of life is seen in the vanishing of the problem. Is not this
the reason why those who have found after a long period of doubt that the sense
of life became
clear to them have then been
unable to say what constituted that sense?
|
6.522
|
There are, indeed, things that
cannot be put into words.
They make themselves
manifest. They are what is mystical.
|
7
|
What we cannot
speak about we must pass over in silence.
|
|
adapted from Tractatus Logico-Philosophicus
by Ludwig Wittgenstein |
Weltanschauung is the conceptualization that all ideology, beliefs and
political movements is both limited and defined by
the schemata of common linguistic
understanding.
"There is no such thing as absolute
truth in logic and
mathmatics. The best that one can do is talk of the truth of statements
given a set of rules of reasoning. It is quite possible to have
statements that are
true in one logical
system but false in
another." - John D.
Barrow |
|
back to stacks
contents
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