6. The general form of a truth function is [p, x, N(x)]
This is the general form of a proposition.
truth functional analysis is a propositional game
- -
-
with [p, x, N(x)] – what you have is a general rule for the
truth-function game
in propositional logic – as
distinct from propositional game playing –
the proposition is a proposal
– open to question – open to doubt – and uncertain
the form of a proposition is a proposed structure of
the proposition –
any such proposal is open to question – open to doubt – and
uncertain
as to a ‘general form’ – in the
sense of general structure – a structure common to all proposals
any such proposal –
is open to question – open to doubt – and is uncertain
6.001. What this says is just that every proposition is a
result of the successive
applications to elementary propositions of the
operation -
N(x)]
every proposition is a proposal
–
a proposition – a proposal
– is not a result of successive applications to elementary propositions
-
the successive application to
elementary propositions of the operation N(x)]
is a propositional game
-
N(x) – is the game
playing a truth-function game is not propositional
analysis
propositional analysis is the
logical activity of question – of doubt – and the exploration of propositional
uncertainty
6.002. If we are given the general form according to which
propositions are
constructed, then with it we are also given the general form
according to which one
proposition can be generated out of another by means of an
operation.
yes – this is how the game is constructed and played
-
6.01. Therefore the general form of an operation Ω‘(h) is
- -
- - - -
[x, N(x)’(h) (= (hxN(x)))
This is the most general form of transition from one
proposition to another.
what you have here is a game rule for the transition
of one game proposition to another –
it is a rule of play
6.02. And this is how we arrive at numbers. I give
the following definitions
x =
Ω°’ x Def.,
Ω’Ω ͮ
’x = Ω ͮ + ¹’ x Def.
So in accordance with these rules, which deal with signs, we
write the series
x, Ω’x,
Ω’ Ω’x, Ω’ Ω’ Ω’ x, ...,
in the following way
Ω’°'x,
Ω’°+¹'x, Ω’°+¹+¹'x, Ω’°+¹+¹+¹'x, .....
Therefore, instead of '[x, x,Ω'x]',
I write [Ω°’x,
'Ω ͮ ’x, Ω ͮ + ¹]'.
And I give the following definitions
0+1 = 1 Def.,
0+1+1 = 2 Def.,
0+1+1+1 = 3 Def.,
(and so on).
what we have here is game rules – transformation rules –
rules for transforming from one game to another
6.021. A number is the exponent of an operation.
an exponent of an operation? – yes – but this characterization
is rather woolly – rather imprecise
a number is a sign in a calculation game
‘calculation’ – is the game – is the operation
6.022. The concept of number is simply what is common to all
numbers, the general
form of a number.
The concept of the number is the variable number.
And the concept of numerical equality is the general form of
all particular cases of
numerical equality.
what is common to all numbers is that they are signs in a
calculation game
this notion of ‘general form’ – sounds impressive – but it
goes nowhere – and amounts to nothing
outside of a calculation game – there is no number
saying that the concept of number is the variable number –
is to say the concept of number – is the number
and in that case – the ‘concept of number ‘ is rendered –
superfluous – and irrelevant –
numerical equality – is a sign game – a substitution game
6.03. The general form of the integer is [0, x, x + 1].
[0, x, x + 1] – is a rule – a definition
6.031. The theory of classes is completely superfluous in
mathematics.
This is connected with the fact that the generality required
in mathematics is not
accidental generality.
the theory of classes functions as a game theory
and what is ‘general’ in mathematics – is the game –
the game – is rule
governed
6.1. The propositions of logic are tautologies.
the propositions of logic are rule governed – game
propositions
the tautology is a game proposition
6.11. Therefore the propositions of logic say nothing. (They
are the analytic
propositions.)
games – do not propose – games are played
6.111. All theories that make a proposition of logic appear
to have content are false.
One might think, for example, that the words 'true' and
'false' signified two properties
among other properties, and then it would seem to be a
remarkable fact that every
proposition possessed one of these properties. On this
theory it seems to be anything
but obvious, just as, for instance, 'All roses are either
yellow or red', would not sound
obvious even if it were true. Indeed, the logical
proposition acquires all characteristics
of a proposition of natural science and this is the sure
sign that it has been constructed
wrongly.
content is proposed –
games – logical games – sign-games – do not propose – they are
rule governed propositional actions
logical games – are played.
6.112. The correct explanation of the propositions of logic
must assign to them a
unique status among propositions.
the logical game – is
just another propositional game –
and as a game – it has no special status – among
propositional games
6.113. It is the peculiar mark of logical propositions that
one can recognize that they
are true from the symbol alone, and this fact contains in
itself the whole philosophy of
logic. And so too it is a very important fact that the truth
or falsity of non-logical
propositions cannot be recognized from propositions alone.
a ‘symbol alone’ without – interpretation – without context
– is simply a ‘mark’ –unknown
if however – a rule is introduced that symbols of a
particular game or set of games are true –
those who play these games in terms of that rule – will
recognise the symbols as true
according to Wittgenstein all logical propositions are
tautologies – and tautologies say nothing
the tautology is empty – its ‘truth’ amounts to nothing –
it is a game – a truth function game – where regardless of
the truth values assigned to the propositions – T or F – the result of the play
is T
logical propositions – are games – propositional games
such games can be fun to play – as any game can be – but to
suggest that they have any significance beyond the pleasure of play – is
entirely misconceived
it is plain rubbish
what Wittgenstein here calls ‘non-logical propositions’ –
are non-game propositions –
propositions that are not rule governed
‘non-logical propositions’ – are proposals –
a proposal is open to question – open to doubt – and
uncertain
a proposal – a non-game proposition – is true – if assented
to – false – if dissented from –
assent and dissent are propositional actions – open to
question – open to doubt – and uncertain
6.12. The fact that the propositions of logic are
tautologies shows the formal – logical –
properties of language and the world.
The fact that a tautology is yielded by this particular
way of connecting its
constituents characterizes the logic of its constituents.
If propositions are to yield a tautology when they are
connected in a certain way, they
must have certain structural properties. So their yielding a
tautology when combined
in this way shows that they posses these structural
properties.
the tautology is a propositional game – it is not
a proposal
in saying that tautologies show the formal – logical
properties of language and the world
Wittgenstein puts that the tautology is a proposal –
and in so doing – gets the tautology wrong – and –
gets the proposition wrong –
he confuses the two
the tautology game is a rule-governed propositional
construction
a proposition – is a proposal – open to question –
open to doubt – and uncertain
any proposal regarding the relation between language and the
world – is open to question – open to doubt – and is uncertain
‘The fact that a tautology is yielded by this particular
way of connecting its
constituents characterizes the logic of its constituents.’
‘the logic of it’s constituents’ – is rule determined
‘If propositions are to yield a tautology when they are
connected in a certain way, they
must have certain structural properties. So their yielding a
tautology when combined
in this way shows that they posses these structural
properties.’
if propositions yield a tautology – you are playing a
propositional game –
the structural properties of game propositions are
rule-governed
combining propositions in this way is game construction
6.1201. For example, the fact that the propositions 'p'
and '~p' in the combination
'~(p. -p)' yield a tautology shows
that they contradict one another. The fact that the
propositions 'p É q', 'p' and 'q', combined
with one another in the form
'(p É q) .(p): É (q)',
yield a tautology shows that q follows from p and p É q.
The fact that '(x). fx: É : fa' is a tautology shows
that fa follows from (x).fx. Etc. etc.
playing the tautology game
6.1202. It is clear that one could achieve the same purpose
by using contradictions
instead of tautologies.
yes – same game – same rules – different coloured tokens
6.1203. In order to recognize an expression as a tautology,
in cases where no
generality-sign occurs in it, one can employ the following
intuitive method: instead of
'p', 'q', 'r', etc. I write 'TpF',
'TqF', 'TrF', etc. Truth combinations I express by means of
brackets, e.g.
and I use lines to express the correlation of the truth or
falsity of the whole proposition
with the truth combinations of its truth-arguments, in the
following way
So this sign, for instance, would represent the proposition p
É
q. Now, by way of
example, I wish to examine the proposition ~(p.
~p)
(the law of contradiction) in order
to determine whether it is a tautology. In our notation the
form ‘~x’ is written as
and the form ‘x.h’ as
hence the proposition ~(p. ~p) reads as follows
If we here substitute ‘p’ for ‘q’ and examine
how the outermost T and F are connected with the innermost ones,
the result will be that the truth of the whole proposition is
correlated with all the truth values of its argument,
and its falsity with none of the
truth combinations.
what we have here in the above bracket presentation is an
explanation of the tautology game in illustration
6.121. The propositions of logic demonstrate the logical
properties of propositions by
combining them so as to form propositions that say nothing.
This method could be called a zero method. In a logical
proposition, propositions are
brought into equilibrium with one another, and the state of
the equilibrium then
indicates what the logical constitution of these
propositions must be.
propositions that say nothing – are game propositions
the game says nothing because the game proposes nothing –
the game is not a proposal
this ‘zero method’ – is nothing more than game construction
6.122. It follows from this that we can actually do without
logical propositions; for in
a suitable notation we can in fact recognize the formal
properties of propositions by
mere inspection of the propositions themselves.
yes – we can do without logical propositions – we can do
without propositional games –
but the reality is that we construct and play games
we can do without them – but we are not going to
a so called ‘suitable notation’ – will just be a game
notation – and recognised as such
the ‘formal properties’ of (game) propositions are rule
determined
you will only recognise a rule – if you recognise – a game
‘mere inspection of the propositions themselves’ – tells you
nothing –
the point is – you need to know if you are playing a game –
or not
rules – are the key –--
if you are not operating in a rule governed (game) context –
a proposition – of whatever form – is a proposal –
a proposal – open to question – open to doubt – and
uncertain
6.1221. If, for example, two propositions 'p' and 'q' in the combination 'p É q' yield a
tautology, then it is clear that q follows from p.
For example, we see from the two propositions themselves
that ‘q’ follows from
‘p É q. p’, but it is also
possible to show it in this way: we combine them to form
‘p É q. p:É :q’, and then show that this is a
tautology.
we are not ‘doing without’ logical / game
propositions here –
here we have a play of the tautology game
6.1222. This throws some light on the question why logical
propositions cannot be
confirmed by experience any more than they can be refuted by
it. Not only must a
proposition of logic be irrefutable by any possible
experience, but it must be
unconfirmable by any possible experience.
a game – is neither true nor false
you play games – you don’t confirm or refute them
6.1223. Now it becomes clear why people have often felt as
if it were for us to
‘postulate’ the ‘truths of logic’. The reason is that
we can postulate them in so far as we
can postulate an adequate notation.
the so called ‘truths of logic’ – are sign-games –
there are no truths of logic
you don’t affirm or deny a game –
you play it – or you don’t play it
‘adequate notation’ – is game language
6.1224. It also becomes clear now why logic was called the
theory of forms and of
inference.
‘logic’ – is a sign-game – a symbolic game – a rule-governed
propositional activity
the game is a propositional use –
there are two uses of the proposition – the critical use –
and the game use
inference in a game – is rule governed
inference in a critical context – is a proposal – open to
question – open to doubt – and uncertain
6.123. Clearly the laws of logic cannot in their turn be
subject to the laws of logic.
you set up rules for a game – and you play the game –
according to the rules –
it is as simple as that
6.1231. The mark of a logical proposition is not
general validity.
To be general means no more than to be accidentally valid
for things. An
ungeneralised proposition can be tautological just as well
as a generalized one.
the mark of a ‘logical proposition’ – is that it is rule
governed –
the mark of the ‘logical proposition’ – is the game
‘validity’ – is a game concept – a rule-governed concept
as to ‘accidental validity’ –
in a game – all actions are rule governed
the tautological game can be played with ungeneralised
propositions as well as generalized
6.1232. The general validity of logic might be called
essential, in contrast with the
accidental general validity of such propositions as 'All men
are mortal'. Propositions
like Russell's 'axiom of reducibility' are not logical
propositions, and this explains our
feeling that, even if they were true, their truth could only
be the result of a fortunate
accident.
‘the general validity of logic’ –
‘logic’ – is a class of rule governed propositional
sign-games
‘All men are mortal’ –
is a proposal –
open to question – open to doubt – and uncertain
as to Russell’s axiom of reducibility – it has the form of a
rule –
it was introduced by Russell in an attempt to deal with
contradictions he discovered in his analysis of set theory
it is a rule in Russell’s set theory game
6.1233. It is possible to imagine a world in which the axiom
of reducibility is not
valid. It is clear, however, that logic has nothing to do
with the question whether our
world really is like that or not.
the axiom of reducibility is a game rule Russell
devised to deal with contradictions he found in his analysis of set theory
and Wittgenstein is right it has nothing to do with the
question of how the world is –
games – and game-rules – are not proposals –
they are not open to question – open to doubt – or uncertain
rules determine games – and games are played
6.124. The propositions of logic describe the scaffolding of
the world, or rather they
represent it. They have no 'subject-matter'. They presuppose
that names have meaning
and elementary propositions have sense; and that is their
connection with the world. It
is clear that something about the world must be indicated by
the fact that certain
combinations of symbols – whose essence involves the
possession of a determinate
character – are tautologies. This contains the decisive
point. We have said that some
things are arbitrary in the symbols that we use and that
some things are not. In logic it
is only the latter that express: but that means that logic
is not a field in which we
express what we wish with the help of signs, but rather one
in which the nature of the
absolutely necessary signs speaks for itself. If we know the
logical syntax of any sign-
language, then we have already been given all the
propositions of logic.
the propositions of logic are game propositions
the ‘scaffolding of the world’ – is a metaphysical proposal
in saying that the propositions of logic describe the
scaffolding of the world – or that they represent it –
Wittgenstein is taking the logic game – and presenting it as
a descriptive proposal
the logic game describes nothing – nothing but itself
pretending that it has descriptive significance is to
completely confuse the two modes of propositional activity
it is to confuse the critical mode and the game playing mode
and perhaps it is to suggest that one is the other – that
the logic game – describes the world?
in any case this ‘argument’ – destructive and hopeless as it
is – is indeed the central argument of the Tractatus
any proposal regarding the ‘scaffolding of the world’ – is
not a rule-governed propositional game – it is a proposal – a proposal open to
question – open to doubt – and uncertain
the propositions of logic – have no bearing – on any
metaphysical question –
unless they are misapplied
and in philosophy there is a rich and deep history of this
misapplication –
and Wittgenstein’s misapplication here – is one of the most
influential
these presuppositions that names have meaning and that
elementary propositions have sense – are entirely irrelevant to the logic game
the logic game is a rule governed sign game – it has nothing
to do with names – meaning – or sense
names – meaning – sense – are irrelevant to the game
construction – its rules – and its play –
here – logic or game theory – has been hijacked by
philosophers – to give a foundation to their philosophical theories
this is the decisive point
this has happened because they don’t understand the nature
of the proposition
if they understood that the proposition is a proposal – open
to question – open to doubt – and uncertain – they would have no reason to
pretend that logical games provide a foundation to their descriptive theories
‘We have said that some things are arbitrary in the symbols
that we use and that some things are not.’
in a properly constructed propositional game the symbols are
rule governed
what is ‘indicated’ by tautologies – is rule governed
propositional behaviour
signs do not speak for themselves –
signs in propositional games express the rules of the game –
express the play of the game
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
propositions.
all language games are rule governed constructions
6.1251. Hence there can never be surprises in logic.
there are no surprises in rule governed – propositional
games
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 by 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.
there is no mystery as to whether a proposition belongs to
‘logic’ as Wittgenstein is using the word –
a proposition ‘belongs to logic’ if it is a game proposition
–
that is rule governed
proof is a game – a propositional game
using only rules that deal with signs is a definition
of the game
‘successively applying certain operations that generate
further tautologies’ – is the application of a rule – i.e. only tautologies
follow from a tautology
the tautology is a propositional game – and here
Wittgenstein employs the tautology as the ground of the proof game
games within games
6.1261. In logic process and result are equivalent. (Hence
the absence of surprise).
in logic – process and result – are rule governed
6.1262. Proof in logic is merely a mechanical expedient to
facilitate the recognition of
tautologies in complicated cases.
proof is a rule governed propositional game – with or
without the incorporation of the tautology game
6.1263. Indeed, it would be altogether too remarkable if a
proposition that had sense
could be proved logically from others, and so too
could be a logical proposition. It is
clear from the start that a logical proof of a proposition
that has sense and a proof in
logic must be two entirely different things.
the proof game is a rule-governed propositional action
as regards propositions that ‘have sense’ – such
propositions are not game propositions –
proof – the proof-game – is irrelevant to propositions ‘that
have sense’ –
and if the proof game is placed in this propositional
context – it is misplaced
‘propositions that have sense’ – are proposals – open
to question – open to doubt – and uncertain
6.1264. A proposition that has sense states something, which
is shown by its proof to
be so. In logic every proposition is the form of a proof.
Every proposition of logic is a modus ponens represented in
signs. (And one cannot
express modus ponens by means of a proposition.)
‘a proposition that has sense’ – is a proposal – open to
question – open to doubt – and uncertain
whether a proposition is ‘to be so’ – depends on whether it
is put – on whether it is proposed – the matter is entirely contingent
the existence of a proposal – has nothing to do with
proof
‘proof’ is a propositional game – a rule governed
propositional action
Wittgenstein’s ‘logic’ – is a game – a propositional game –
and a proof game
modus ponens – is a rule – a game rule – the rule of
affirming the antecedent – ‘if p then q . p – therefore q
it is a formulation of the proof game
6.1265. It is always possible to construe logic in such a
way that every proposition is
its own proof.
a game is determined by its rules
a rule that every proposition is its own proof – is just
another rule
6.127. All propositions of logic are of equal status: it is
not the case that some of them
are essentially primitive propositions and others
essentially derived propositions.
Every tautology shows itself that it is a tautology
all ‘propositions of logic – are game propositions – are
rule governed
the tautology is a propositional game
6.1271. It is clear that the number of the 'primitive
propositions of logic' is arbitrary,
since one could derive logic from a single primitive
proposition, e.g. by simply
constructing the logical product of Frege's primitive
propositions. (Frege would
perhaps say then we should then no longer have an
immediately self-evident primitive
proposition. But it is remarkable that a thinker as rigorous
as Frege appealed to the
degree of self evidence as the criterion of a logical
proposition.)
a ‘primitive’ is some basis on which to begin
Wittgenstein is right here – the starting point is arbitrary
and he puts that you construct the game by constructing the
logical product of the primitive proposition
what you have here is a theory of game construction
no proposition is ‘self-evident’ – any proposition – any
proposal – is open to question – open to doubt – and is uncertain –
this notion of the
‘self-evident’ in propositional logic is pretentious
in game theory – game propositions – are not open to
question – not open to doubt – or not
uncertain –
game-propositions – are tokens of play –
calling them ‘self-evident’ – is still pretentious – and
misleading – but in the end
no real harm is done
6.13. Logic is not a body of doctrine, but a mirror image of
the world.
Logic is transcendental.
logic is a game – a language-game – or a series of
language-games –
a language-game is a rule-governed propositional action
a language-game is not a mirror image of anything – a
language-game is a play with signs and symbols
logic is not transcendental – logic – ‘logical games’ – are
contingent – human creations
6.2. Mathematics is logical method.
The propositions of mathematics are equations, and therefore
pseudo-propositions.
mathematics is a language-game – a game of signs and symbols
equations are rule-governed sign-games – substitution games
the propositions of mathematics are rule governed
propositions
a game is not a proposal – is not a proposition –
a game (as played) is not open to question – not open to
doubt – and not – uncertain
a game is a play – not a proposal
6.21. A proposition of mathematics does not express a
thought.
a proposition of mathematics – is a sign-game
a proposition that expresses a thought is a proposal
– open to question – open to doubt – and uncertain
a game – is not a proposal –
a game – a language-game – is a play – a play with
signs and symbols
6.211. Indeed in real life a mathematical proposition is
never what we want. Rather
we make use of mathematical propositions only in
inferences from propositions 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 proposition
for?' repeatedly leads to valuable insights.)
mathematical games can be played in any propositional
context
6.22. The logic of the world, which is shown in tautologies
by propositions of logic, is
shown in equations by mathematics.
logical games – mathematical games –
the tautology game – the equation game – are different
games
the logic of the world – is the logic of the proposal – of
the proposition
the proposal – the proposition – is open to question – open
to doubt – and uncertain
propositional reality is uncertain –
the world is uncertain
6.23. If two expressions are combined by means of the sign
of equality, that means
that they can be substituted for one another. But it must be
manifest in the two
expressions themselves whether this is the case or not.
When two expressions can be substituted for one another,
that characterizes their
logical form.
it is the equality sign that determines that the two
expressions can be substituted
there is no substitution without the equality sign
so to say that the substitution must be manifest in the two
signs themselves – in the absence of the equality sign – is meaningless
when two expressions are substituted for one another
– they are tokens in a substitution game
when two expressions can be substituted for each other –
this characterizes the structure of the game
6.231. It is a property of affirmation that it can be
construed as double negation.
It is a property of '1+1+1+1' that it can be construed as
'(1+1) + (1+1)'.
that an affirmation can be constructed as a double negation
– is a play – in the
‘affirmation game’
that '1+1+1+1' can be constructed as '(1+1) + (1+1)' – is a
numbers game
6.232. Frege says that the two expressions have the same
meaning but different
senses.
But the essential point about an equation is that it is not
necessary in order to show
that the two expressions connected by the sign of equality
have the same meaning,
since this can be seen from the two expressions themselves.
meaning and sense are irrelevant when it comes to sign games
an equation is a sign game – a substitution game
the ‘=’ sign signifies that one sign can be substituted for
the other
it is the ‘=’ sign – not the ‘two expressions themselves’ –
that signifies – substitution
substitution is a play of tokens
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.
proving the propositions of mathematics – is playing the
proof-game –
‘facts’ – are irrelevant to the proof game
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.
identity is a substitution game
the question of meaning is a critical issue –
the meaning of an expression – is open to question – open to doubt – and
uncertain
6.2323. An equation merely marks the point of view from
which I consider the two
expressions: it marks their equivalence in meaning.
the substitution game – avoids the whole question of – the
propositional issue of – meaning –
the equation – the substitution game – as it were –‘jumps’ – the question of
meaning altogether – and declares equivalence –
it is a rule governed declaration
the game is rule governed – it is a separate propositional
mode to logical assessment –
logical assessment is the critical the mode of question – of
doubt – and of dealing with uncertainty
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.
the solution of mathematical problems is in the art of the
game
which games apply to this problem – and which rules apply?
and indeed it may well involve the construction of new games
and new rules
a well versed mathematician will have at his or her
fingertips – games already developed and played –
are we to say a new discovery is a result of intuition or
the result of being deeply engaged in the mathematical experience?
could it come down to a lucky guess?
who knows?
6.2331. The process of calculating serves to bring
about the intuition.
Calculation is not an experiment.
calculation is a rule governed operational game
6.234. Mathematics is a method of logic.
mathematics is a sign-game
logic is a sign-game –
mathematics and logic are different games
6.2341. It is the essential characteristic of mathematical
method that it employs
equations. For it is because of this method that every
proposition of mathematics must
go without saying.
the equations game – is mathematics – is the mathematics
game
every ‘proposition’ of mathematics – is rule governed
nothing goes without saying –
no game goes without playing
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.
that is the game
6.241. Thus the proof of the proposition 2 x 2 = 4 runs as
follows:
(Ω²) ͧ ’x
= ͮ
ͯ ͧ x Def.,
Ω² ˟ ² = (Ω²)²’ x = (Ω²)¹+¹'x
= Ω²’ Ω²’x =
Ω¹+¹ Ω¹+¹x = (Ω’Ω)’ (Ω’Ω)’ x
= (Ω’Ω)’ (Ω’Ω)’ x = Ω¹+¹ Ω¹+¹+¹+¹’x = Ω⁴x.
if you understand the substitution game – and it has been
constructed correctly –
the proof is unnecessary and irrelevant
proof is really just a parallel game
6.3. The exploration of logic means the exploration of everything
that is subject to
law. And outside logic everything is accidental.
logic is a rule governed language game
‘outside’ of propositional game-playing is the critical
evaluation of proposals –
critical evaluation is not rule-governed –
critical evaluation is the putting of propositions –
proposals – to question – to doubt
critical evaluation – is the exploration of propositional
uncertainty
6.31. The so-called law of induction cannot possibly be a
law of logic, since it is
obviously a proposition with sense. – Nor therefore, can it
be a priori.
the so called law of induction – is a proposal – open to
question – open to doubt –
and uncertain
6.32. The law of causality is not a law but the form of a
law.
the law of causality – is a proposal –
a proposal – open to question – open to doubt – uncertain
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.
‘laws of the causal form’ – are causal proposals in
different propositional contexts
6.3211. Indeed people even surmised that there must be a
'law of least action', before
they knew exactly how it went. (There as always, what is
certain a priori proves to be
something purely logical.)
a ‘law of least action’ is proposal – open to
question – open to doubt – and uncertain
we don’t know exactly how any proposal will function – until
we put it to use –
until we put it to question – to doubt – and we explore its
uncertainty
‘purely logical’ propositions – are rule governed propositions – in propositional
games
if by a priori propositions is meant – propositions that are
certain – there are no a priori propositions –
a proposition – is a proposal – open to question – open to
doubt – and uncertain
a proposition not held open to question – not held open to
doubt – and regarded as certain
is a proposition held as a prejudice
6.33. We do not have a priori belief in a law of
conservation, but rather a priori
knowledge of the possibility of a logical form.
what we have is a proposal – the proposal of a law of
conservation –
a proposal – open to question – open to doubt – and as with
any proposal – uncertain
‘the possibility of a logical form’ – is not knowledge –
it is not actually anything
Wittgenstein once again abandons logic and embraces
mysticism
logical form is a proposal of propositional structure
there is no logical form – that is a proposal of
propositional structure – unless there is a proposal –
our knowledge is actual proposal – cash on the
barrelhead
not some other-world possibility
6.34. All such propositions including the principle of
sufficient reason, the laws of
continuity in nature and of least effort in nature, etc.
etc. – all these are a priori insights
about the forms in which the propositions of science can be
cast.
all propositions including the proposal of sufficient reason
– the proposals of continuity in nature and of least effort in nature etc. etc.
– are proposals – open to question – open to doubt – and uncertain
the ‘forms’ in which the propositions of science can be cast
– are proposals – proposals of propositional structure –
proposals – open to question – open to doubt – and uncertain
6.341. Newtonian mechanics, for example, imposes a unified
form on the descriptions
of the world. Let us imagine a white surface with irregular
black spots on it. We then
say whatever kind of picture 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. In this way shall I
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 net
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 course triangular mesh than with a fine
square mesh (or conversely)
and so on. The different nets correspond to different
systems for describing the world.
Mechanics determines one form of description of the world by
saying that all
propositions used in the description of the world must be
obtained in a given way
from a set of propositions – the axioms of mechanics. It
thus supplies the bricks for
building the edifice of science, and it says, 'Any building
that you want to erect,
whatever it may be, must somehow be constructed with these
bricks, and with these
alone.'
(Just 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 proposition of
physics that we wish.)
‘The different nets correspond to different systems for
describing the world.’
different systems for describing the world – different proposals
for describing the world
‘Mechanics determines one form of description of the world
by saying that all
propositions used in the description of the world must be
obtained in a given way
from a set of propositions – the axioms of mechanics.’
yes – Newtonian mechanics is one descriptive proposal
the axioms of mechanics – are proposals –
proposals – open to question – open to doubt – and from a logical point of view – uncertain
'Any building that
you want to erect, whatever it may be, must somehow be constructed with these
bricks, and with these alone.'
Newtonian mechanics
is a comprehensive proposal –
and if you are going with the proposal that is Newtonian
mechanics – then any building you construct will be described in its terms
however logically speaking Newtonian mechanics is a proposal
open to question – open to doubt – and uncertain
and it is this uncertainty – which accounts for the
development of alternative descriptions
‘(Just 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 proposition of
physics that we wish.)’
any number we wish – must be a number of the proposed number
system –
if you somehow or another – have in mind a number not
compatible with the number system –
you need to find or develop a number system that
accommodates it –
or forget about it
yes – if Newtonian mechanics is to function as a
comprehensive account of the physical world – it must accommodate any proposed
proposition of physics
where a proposed proposition of physics does not fit with
the Newtonian system –
or where an alternative system is proposed –
the adequacy of Newtonian mechanics – is brought into
question
any proposed description – whether enjoying acceptance – or
not – is open to question – open to doubt – and is uncertain
6.342. And now we can see the relative position of logic and
mechanics. (The net may
also consist of more than one kind of mesh: e.g. we could
use both triangles and
hexagons.) The possibility of describing a picture like the
one mentioned above with
the net of a given form tells us nothing about the picture.
(For that is true of all such
pictures). But what does characterize the picture is that it
can be described completely
by a particular net with a particular size of mesh.
Similarly the possibility of describing the world by means
of Newtonian mechanics
tells us nothing about the world: but what does tell us
something about it is the precise
way in which it is possible to describe it by these means.
We are also told something
about the world by the fact that it can be described more
simply with one system of
mechanics than with another.
‘(The net may also consist of more than one kind of mesh:
e.g. we could use both triangles and hexagons.)’
this is just to say that the proposal – ‘the world’ – is
open to question – open to doubt and is uncertain
and therefore different proposals are valid
‘The possibility of describing a picture like the one
mentioned above with the net of a given form tells us nothing about the
picture.’ –
‘the picture’ – is the
description proposed
in the absence of description – in the absence of proposal –
‘the picture’ – is an unknown
‘But what does characterize the picture is that it can be
described completely by a particular net with a particular size of mesh.’
what characterizes the picture – is the description proposed
and any such description – any such proposal – is open to
question – open to doubt – and uncertain
and thus – logically speaking – incomplete
‘Similarly the possibility of describing the world by means
of Newtonian mechanics
tells us nothing about the world: but what does tell us
something about it is the precise
way in which it is possible to describe it by these means.’
the world as proposed – as described – is the world
and yes – of course the Newtonian description tells us that
the world can be described in the precise terms – of the Newtonian description
‘We are also told something about the world by the fact that
it can be described more simply with one system of mechanics than with another.’
different descriptions ‘tell us’ that we can describe differently
– that we can put – different proposals
and simplicity is in the eye of the beholder
6.343. Mechanics is an attempt to construct according to a
single plan all the true
propositions that we need for the description of the world.
yes – a complex proposal – or set of proposals –
open to question – open to doubt – and uncertain
6.3431. The laws of physics, with all their logical
apparatus, still speak, however
indirectly, about the objects of the world.
the objects of the world are proposals
the ‘laws’ of physics are proposals in relation to these
object / proposals
and any such proposal – is direct
6.3432. We ought not to forget that any description of the
world by means of
mechanics will be of the completely general kind. For
example, it will never mention
particular point-masses; it will only talk about any
point masses whatsoever.
‘any point-mass’ covers ‘particular point masses’
6.35. Although the spots in our picture 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 give a priori.
Laws like the principle of sufficient reason, etc. are about
the net and not about what
the net describes.
geometry is a rule governed propositional game –
a game – whether ‘geometrical’ or not is not a proposal –
a game says nothing
propositions of form / structure – and propositions of
position – are proposals –
proposals open to question – open to doubt – and uncertain
geometry is a propositional game – its properties are not a
priori – they are rule governed
any description of the net – or any so called law like the
principle of sufficient reason – is a proposal – open to question – open to
doubt – and uncertain
and what the net describes – is a different proposal
– to a proposed description of the net
6.36. If there were a law of causality, it might be put in
the following way: There are
laws of nature.
But of course this cannot be said; it makes itself manifest.
well of course it can be said – because it is
said – because it is proposed – and proposed here
– by Wittgenstein
‘laws of nature’ – are
proposals –
proposals – open to question – open to doubt – and uncertain
6.361. One might say using Hertz's terminology, that only
connections that are subject
to law are thinkable.
so called ‘laws’ – are well established propositions –
‘well established’ – because they are generally accepted and
used
as to what is ‘thinkable’ –
the short answer is that what is thinkable is what is
proposed
a thought is a proposal –
it can remain private – or it can be made public
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
their is nothing to cause
the one to occur rather than the other, it is really a
matter of 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.
to compare a process with the passage of time – yes you need
a definition of the passage of time – and a chronometer functions as such a
definition
likewise with the lapse of time – it is a calculation
in either case you construct a game – a rule governed
propositional game
‘something analogous applies to space’ –
the idea is that ‘neither of two events (which exclude one
another) can occur because their is nothing to cause the one to occur
rather than the other’ –
here we are unable to describe one of the two events – ‘unless
there is some sort of asymmetry to be found’ –
that is to say – unless a rule is put that there is ‘some
sort of asymmetry’ –
and then you have a
rule – a game – an asymmetry game
so yes – there is ‘something’ of an analogy – here – you end up with two games – two
different propositional games
6.36111. 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
- - - - o------x - - x------o - - - -
a b
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 around in four
dimensional space.
‘left and right’ here
is a propositional game –
a rule governed propositional game
the left token and the right token in this game are
congruent –
they are distinguished by their positions relative to a
nominated centre point
one side of the centre point is termed ‘left’ – the other
‘right’ –
‘a’ and ‘b’ – would do just as well
that they cannot be made to coincide is the game-rule
if a ‘right token’ was played to coincide with the ‘left token’ – or visa
versa –
you have a different game
6.362. What can be described can happen too: and what the
law of causality is meant
to exclude cannot even be described.
what can be described / proposed – may or may not happen
presumably what the law of causality excludes – is un-caused
events
uncaused events – will not be described by a law of
causality
the notion of the uncaused event – causa sui – is a proposal
– one that has a long history in philosophy – and one that is central to the
philosophical system of Spinoza
a proposal – that as with the causal proposal – is open to
question – open to doubt – and uncertain
6.363. The procedure for induction consists in accepting as
true the simplest law that
can be reconciled with our experiences.
what is to count as the ‘simplest law’ – the simplest
proposal – that can be reconciled with our experiences?
any proposed ‘simplest law’ – will be open to question –
open to doubt – and uncertain
and any affirmation of a proposal here – will likewise be
open to question –
so where does this
leave ‘induction’?
6.3631. The 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.
a proposal – described as ‘logical’ – or described as
‘psychological’ – is open to question – open to doubt – and uncertain
logically speaking – there is no ‘justification’ for any proposal
– if by justification is meant the end of questioning – the end of doubt – and
an end to uncertainty
if we proceed with a proposal – and we proceed logically –
we proceed with uncertainty – in
uncertainty
‘there are no grounds for believing that the simplest eventuality will in fact be realized’ –
any so called grounds for any proposal – are open to
question – open to doubt – and uncertain
6.36311. It is an hypothesis that the sun will rise
tomorrow; and this means that we do
not know that it will rise.
our knowledge is what we propose – whatever we propose
and what we propose – is open to question – open to doubt –
and uncertain
6.37. There is no compulsion making one thing happen because
another has happened.
the only necessity that exists is logical necessity.
any proposal regarding the relation between events is open
to question – open to doubt – and uncertain
if by logical necessity is meant – a proposition that is
true by definition – i.e. – ‘no unmarried man is married’ – then all logical
necessity amounts to is a language game –
and here we are
talking about a language game that goes nowhere –
if by logical necessity is meant that the proposal is true –
because it could not be otherwise – i.e. it is certain –
then there is no logical necessity
a proposal – a proposition – is open to question – open to
doubt – and is uncertain
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.
the ‘so-called laws of nature’ – are proposed as
explanations of proposed natural phenomena –
and they function as explanations of proposed natural
phenomena
however from a logical point of view – these proposals – as
with any proposal of any kind – are open to question – open to doubt – and
uncertain
there is nothing illusory here
a proposal is open to question – open to doubt – and uncertain
6.372. Thus people today stop at the laws of nature,
treating them as something
inviolable, just as God and Fate were treated in past ages.
And in fact both are right and wrong: though the view of the
ancients is clearer in so
far as they have a clear terminus, while the modern system
tries to make it look as if
everything were explained.
the idea that the laws of nature are inviolable – is
illogical
any proposed explanation of proposed natural events – is
open to question – open to doubt and uncertain
6.373. The world is independent of my will.
‘my will’ – is a proposal –
a proposal – open to question – open to doubt – and
uncertain
likewise any proposed relation between ‘my will’ and the
‘the world’ – whatever that is supposed to mean – is open to question – open to
doubt – and uncertain
6.374. Even if all we wish for were to happen, still this
would only be a favour
granted by fate, so to speak: for there is no logical
connection between the will and the
world, which would guarantee it, and the supposed physical
connection is surely not
something that we could will.
proposed connections of any kind – are proposed relations – between
propositions
any proposed relation between propositions – is open to question – open to doubt – and uncertain
6.375. Just as the only necessity that exists is logical necessity, so too the only impossibility
that exists is logical impossibility.
logical necessity – as in the proposition – ‘no unmarried
man is married’ – is a language game
likewise – logical impossibility – as in ‘it is raining and
it is not raining’ – is a language game
language games – signifying nothing
if by logical necessity is meant – the proposal is true –
because it could not be otherwise – i.e. it is certain –
then there is no logical certainty –
a proposal is open to question – open to doubt – and uncertain
–
if by logical impossibility is meant the proposal is false –
because it could not be otherwise – i.e. it is certainly false
there is no logical impossibility –
a proposal is open to question – open to doubt – and is
uncertain
these notions of ‘logical necessity’ and ‘logical impossibility’
– are really just pretentious covers for
ignorance and prejudice
at the root of this –
is fear of uncertainty
6.3751. For example, the simultaneous presence of two
colours at the same place in
the visual field is impossible, in fact logically
impossible, since it is ruled out by the
logical structure of colour.
Let us think how this contradiction appears in physics: more
or less as follows – a
particle cannot have two velocities at the same time; that
is to say, it cannot be in two
places at the same time; that is to say particles that are
in different places at the same
time cannot be identical.
(It is clear that the logical product of two elementary
propositions can neither be a
tautology nor a contradiction. The statement that a point in
the visual field has two
different colours at the same time is a contradiction.)
the presence of two colours at the same place in the visual
field –
will depend on how the ‘one colour’ is described –
i.e. – the one colour could be described as a combination of
different colours – and in that case – there is no ‘one’ colour in the visual
field –
but different colours in the same place
there is no logical impossibility – there is only
propositional / logical uncertainty
and how the proposal of colour and the proposal of the
visual field are interpreted provides a good example of propositional
uncertainty – and therefore of propositional options
and again – the structure of colour – is a matter – open to
question
a particle cannot have two velocities at the same time?
isn’t this a question of reference points and theories of
measurement?
with different reference points – and different theories of
measurement – it may well be proposed that one particle has different
velocities
as to different places at the same time?
with different set of spacial co-ordinates there will be
different positions at the same time
as to identity – the question is – can one proposed set of
co-ordinates – be substituted for the other?
that will depend on the theory or theories being tested at
the time
the propositions of physics are not game propositions – they
are proposals –
open to question – open to doubt – and uncertain
6.4. All propositions are of equal value.
all propositions are proposals – open to question – open to
doubt – and uncertain
6.41. The sense of the world must lie outside the world. In
the world everything is as
it is, and everything happens as it does happen: in it no value exists – and if it did
exist, it would have no value.
If there is any value that does have value, it must lie
outside the whole sphere of what
happens and is the case. For all that happens and is the
case is accidental.
What makes it non-accidental cannot lie within the world, since if it did it would not be accidental.
It must lie outside the world.
our world is propositional
sense is proposed –
what happens – is what is proposed
value is a proposal
proposals of value are open to question – open to doubt –
and uncertain
our world is
uncertain
‘outside’ of our proposals
– is the unknown
we propose to make
known
6.42. So too it is impossible for there to be propositions
of ethics.
Propositions can express nothing that is higher.
well there are propositions of ethics – to suggest
otherwise – is just plain ridiculous
propositions of ethics are an empirical fact –
and propositions of ethics are central to our propositional
lives
and as with any proposal – any proposition – the
propositions of ethics are – open to question – open to doubt and – and
uncertain
‘propositions of ethics can express nothing that is higher’
–
our reality is propositional –
there is no ‘non-propositional reality’ – unless by that is
meant – the unknown
if by ‘higher’ – is meant – something like a
non-propositional realm of morality –
there is no such realm –
this idea of ‘higher’ – is more in the realm of poetic
imagery – i.e. Dante’s Divine Comedy –
it has no logical significance –
it is just plain rubbish
6.421. It is clear that ethics cannot be put into words.
Ethics is transcendental.
(Ethics and aesthetics are one in the same.)
the plain fact is that ethics is put into words
if by ‘transcendental’ – is meant that a non-propositional
reality – there is no such reality
and the idea that ethics – a propositional activity –
transcends propositional activity – is absurd
as to the relation of ethics to aesthetics – that is a
matter – open to question – open to doubt – and uncertain
6.422. When an ethical law of the form, 'Thou shalt....', is
laid down, one's first
thought is, 'And what if I do not do it?' It is clear,
however that ethics has nothing to
do with punishment and reward in the usual sense of the
terms. So our question about
the consequences of an action must be unimportant – At least
those consequences
should not be events. There must indeed be some kind of
ethical reward and ethical
punishment, but they must reside in the action itself.
(And it is also clear that reward must be something pleasant
and the punishment
something unpleasant)
‘when an ethical law
…is laid down’ – by whom?
logically speaking –
there are no ethical laws – and there are no ethical authorities –
though there is
ethical prejudice – and ethical pretension
from a logical point
of view – the only ‘authority’ is authorship –
authorship of a
proposal –
you may decide – as
Wittgenstein has – that the consequences of an action are not ethically
relevant
however the question
of the ethical relevance of the consequences of an action – is not
unimportant
and why must
there be some kind of ethical reward and ethical punishment?
our ethical
proposals – like any other – are our responses to the question of how to
understand the world and how to live in the world
and these proposals
– like any other – are open to question – open to doubt – and uncertain
we operate with
uncertain proposals – in an uncertain world
6.423. It is impossible to speak of the will in so far as it
is the subject of ethical
attributes.
And the will as a phenomenon is of interest only to
psychology.
well – it’s not ‘impossible’ to propose that the will is the
subject of ‘ethical attributes’ –
it is just another proposal
any proposition – be it described as ‘psychological’ or not
– is open to question – open to doubt – and uncertain
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 a happy man is a different one from that of a
unhappy man.
how the world is – and how we affect it – is open to
question – open to doubt – and is uncertain
perhaps it is best to speak of different propositional
worlds –
different propositional realities – the focus of which is
the unknown
the world of one man is different to that of another –
the propositional life of one man is different to that of
another
6.431. So too at death the world does not alter, but comes
to an end.
what happens at death – is open to question – open to doubt
– and uncertain
logically speaking it is no different to what happens in
life
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.
Our life has no end in just the way in which our visual
field has no limits.
death is an event in life –
outside of life – in the absence of life – it would make no
sense to speak of death
I would say we have no experience after death –
and therefore there is no way of knowing if we have an
experience of death or not
however whether we have experience after death – or not – is
really a matter open to question – open to doubt – and uncertain
there are people who have been declared medically dead and
have ‘come back to life’ to report an experience of death –
i.e. – some have reported an experience of nothingness –
others have reported a bright light – outer body experiences – bliss – peace – beatific visions – etc. –
etc. –
whether these reports – and any others – count as reports of
death – or indeed of experience –
is open to question – open to doubt – and uncertain
perhaps death – like so many physical / biological changes
in the body – is not experienced – but just happens?
all this begs the question – what is death? –
and Wittgenstein has nothing to say here
living in the present – is not timelessness –
the past – the present – the future – are categories
of time –
to live in the present – is to question – is to doubt – and
is to explore propositional uncertainty
that we cannot see an end to our own lives – does not
mean there is no end
experience tells us that human beings die –
whether death is the end of life or not – is open to
question – open to doubt – and is uncertain
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
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.)
and is not ‘outside of space and time’ – ‘as much of a
riddle’ as ‘eternal life’ and ‘our present life’?
a riddle is a game – and yes – you can regard ‘our present
life’ – as a riddle – as a game –
this however is not to deal with any of the critical matters
we face in life –
and is therefore quite a superficial view of life
any so called ‘solution’ to the ‘problems’ of life – is a
proposal – or proposals – open to question – open to doubt – and uncertain
we live in and with and through propositional uncertainty
6.432. How things are in the world is a matter of
complete indifference for what is higher. God does not reveal himself in
the world.
‘God’ is a proposal –
open to question – open to doubt – and uncertain
6.4321. The facts all contribute to the setting of the
problem, not its solution.
‘facts’ – are proposals – open to question – open to doubt –
and uncertain –
as are ‘problems’ and ‘solutions’
6.44. It is not how things are in the world that is
mystical, but that it exists.
once you step into mysticism – you turn your back on
propositional reality – (or at least try to) – and pretend – a superiority – a
‘higher’ understanding
it is really just a retreat into ignorance and prejudice –
and one that is bound to come unstuck – if you have a brain
6.45. To view the world sub specie aeterni is to view it as
a whole – a limited whole.
Feeling the world as a limited whole – it is this that is
mystical.
the world – our world – is what is proposed –
we can only ‘view’ what we propose – and what is put to us –
and yes – that is limited
our feelings – are proposals
what we feel is what we propose – and that is propositional
– not mystical
6.5. When the answer cannot be put into words, neither can
the question be put into
words.
The riddle does not exist.
If a question can be framed at all, it is also possible to
answer it.
it is not a matter of question and answer –
a proposal – a proposition is put – and put to question –
put to doubt – its uncertainty –
explored
and any propositional responses to the initial proposal –
are put to question – put to doubt – their uncertainty explored –
a riddle can exist – it’s a propositional game – a rule-governed propositional
game
in a critical
propositional process – there is no riddle – just proposal – question – doubt –
uncertainty
a proposal – a
proposition – can be put to question
and any response – any
so called ‘answer’ – is open to question – open to doubt – and is uncertain
6.51. Scepticism is not irrefutable, but obviously
nonsensical, when it tries to raise
doubts where no questions can be asked.
For doubt can only exist where a question exists, and an
answer only where something
can be said..
scepticism – as with any other proposal – is open to
question – open to doubt – and is uncertain
what is ‘nonsensical’ is that there are proposals
that are not open to question – not open to doubt – and are certain
where no question is asked – is where no proposition has
been put
when ‘something is said’ – that is – when a proposal is put
– it can be doubted – questions can be raised – and its uncertainty explored
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 no questions left,
and this itself is the answer.
any and all scientific propositions – are open to question –
open to doubt – and uncertain
our lives are propositional – we deal with proposals –
propositions – and we put them to question – put them to doubt – and we proceed
– with and in uncertainty
there are no questions if there are no proposals –
and any ‘answer’ – is open to question
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?)
life is not a problem
life – human experience – is a propositional exploration –
our logical tools are question and doubt – and with question
and doubt – we explore propositional uncertainty
with a bit of luck – what ‘vanishes’ – is ignorance
prejudice and stupidity – in short –
mysticism
‘(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?)’
the reason they have nothing to say – is because they have
stopped proposing – stopped
questioning – stopped doubting – and have fallen into the
delusion of certainty –
they have become dead-heads
6.522. There are indeed, things that cannot be put into
words. They make themselves
manifest. They are what is mystical.
‘There are indeed things that cannot be put into words.’ –
like what?
if it can’t be proposed – it’s not there
‘They make themselves manifest’
what is ‘manifest’ – is what human beings propose
‘They are what is mystical.’ –
‘they’ are what is not there –
the point is Wittgenstein cannot avoid referring to what he
says can’t be referred to
his ‘mysticism’ – is a self-refuting argument –
and his ‘logic’ ends up – in a contradictory mess –
his mysticism – is his failure – and it’s a deep failure
6.53.The correct method in philosophy would really be the
following: to say nothing
except what can be said, i.e. the propositions of natural
science – i.e. something that
has nothing to do with philosophy – and then, whenever
someone else wanted to say
something metaphysical, to demonstrate to him that he had
failed to give a meaning to
certain signs in his propositions. Although it would not be
satisfying to the other
person – he would not have the feeling that we were teaching
him philosophy – this
method would be the only strictly correct one.
‘to say nothing except what can be said’ – says nothing –
and tells us nothing
the propositions of natural science – and metaphysical
propositions – are proposals
and as with any proposal – they are open to question – open
to doubt – and uncertain
logically speaking – philosophy is no different from any
other propositional activity
and any method adopted – in any propositional endeavour – is
open to question – open to doubt – and is uncertain
6.54. My propositions serve as elucidations in the following
way: anyone who
understands me eventually recognizes them as nonsensical,
when he has used them –
as steps – to climb up beyond them. (He must, so to speak,
throw away the ladder after
he has climbed up it.)
He must transcend these propositions, and then he will see
the world aright.
Wittgenstein’s propositions are open to question – open to
doubt – and uncertain
anyone who understands them – can put them to question – put
them doubt – and explore their uncertainty
as to throwing away the ladder after it has been climbed –
of course you can stop questioning – you can put an end to
doubt – and you can close your mind to propositional uncertainty –
or at least you can try to do this – but if you have an
ounce of intelligence – your attempt
to withdraw to ignorance – will fail
if we are to live intelligently in this world –
we have to question – we have to doubt – we have to explore
uncertainty
ignorance and prejudice and pretension – are not sustainable
options
we don’t ‘transcend’ propositional reality – we can’t – our
reality is propositional
there is no actual transcendence – the idea is delusional
if seeing the world ‘aright’ – means seeing the world
without question – without doubt – and as a certainty –
then you will not see the world –
for you will be blinded by ignorance – prejudice and
pretension
(c) greg t. charlton. 2018.
(c) greg t. charlton. 2018.
