5. A proposition is a truth function of elementary propositions.
(An elementary proposition is a truth function of itself.)
OK - a proposition is a truth function - either of elementary propositions - or in the case of an elementary proposition - of itself -
a literal reading of this could result in the view that a proposition is just a truth value
we might normally say -'its' truth value - but if truth value is all there is to it -that's it
this is a literal reading - but it is one that gives - potentially the greatest scope
if e.g. we were to say a proposition's truth value is it assent or dissent - that this is finally all truth comes to - then on such a view a proposition is just that which is assented to or dissented from -
I like such an idea
what it does is leave the question of the nature of proposition - really up to experience
we could in this connection ask - what in fact do people give there assent to or not?
undoubtedly sentences would figure in this - but what else?
that's the interesting question
a work of art - a sunrise - a thought - a symphony - a good act?
I guess what I think is the real power of such a view is that it leaves the question of substance (if you like) of propositions entirely open -
open that is in a positive way -
5.01. Elementary propositions are the truth arguments of propositions.
yes for the life of me I really can't see that Wittgenstein has any other theory of the proposition - but the elemental proposition
I entirely agree that elementary propositions placed together - put together - are an
argument - and if proposition - 'the' proposition is to mean anything - this is all it can mean - it is an argument
an argument here is - the internal (logical) relations of the elementary propositions
this if anything - is what the proposition is
but it is not really anything
it is a possible argument - and when it is actual - actualized - it can be an argument about anything - and then it is gone
whereas the elementary proposition - the initial statements do have or can have some
continued currency
the elementary proposition can be placed in an infinite number of propositional
arguments
let us say for example the world is such and such
propositional arguments will have no necessary connection to how the world is
are they not simply - the placing of elemental propositions in argument?
perhaps I was right a proposition is a ghost
albeit a necessary one - a logical one
what I suppose I am getting is the question of the form of such
what do we say of the nature of logical argument?
does it have any necessary expression?
does it indeed have to have any expression at all?
an argument in thought - manifests itself how?
the point being it may or may not
the proposition here is truly an open entity
it has to be - if it is to be a genuine argument
for any genuine argument must also hold itself in argument
that is its own status is an open question
and this does not mean that it has no value - or no utility
you don't need to know the nature of something in order to use it
and in fact I suggest that the openness of the argument or the proposition is just what indeed guarantees the possibility of its utility
what this amounts to is that the essence of the proposition is an internal relation
(between elements)
the external form of the proposition is an accidental property
p.s.
so how are we to understand propositional elements?
I will put that a propositional element is a focus of consciousness
how that focus is expressed is optional
the optional possibilities here begin with the senses
that is sight hearing smell taste and touch
the senses function as portals for focus
so the elements we begin with are sensual
a proposition though is more than a reflection in the senses
a proposition is a proposal based on the elements given
it is thus always a reflection on
and is expressed in whatever form (language) as a proposal
what is given is the ground of description
how we describe this (i.e. I have put that it is elemental and sensual) is a question of metaphysical decision
what we have before us prior to description is unknown
we do however have a relationship with it
a relationship that is enhanced with proposal
p.p.s.
the mind and the body - dimensions of the unity
the unity is represented in the proposition
it is the representation that cannot be described
its elements are the description
5.02. The arguments of functions are readily confused with the affixes of names. For
both arguments and affixes enable me to recognize the meaning of the signs
containing them.
For example, when Russell writes '+c', the 'c' is an affix which indicates that the sign as a whole is the addition-sign for cardinal numbers. But the use of this sign is the result of arbitrary convention and it would be quite possible to choose a simple sign instead of '+c'; in '~p', however, 'p' is not an affix but an argument: the sense of '~p' cannot be understood unless the sense of 'p' has been understood already. (In the name Julius Caesar 'Julius' is an affix. An affix is already part of a description of the object to whose name we attach it: e.g. the Caesar of the Julien gens.)
If I am not mistaken, Frege's theory about the meaning of propositions and functions
is based on the confusion between an argument and its affix. Frege regarded the
propositions of logic as names, and their arguments as the affixes of those names.
the propositions of logic - of propositional logic - are functions
the elementary propositions are the function of the proposition
names are essentially irrelevant to the question of function
I would say propositional signs signify rather than name
naming as I see it is the proposal of logical point
5.1. Truth functions can be arranged in series.
That is the foundation of the theory of probability.
the idea being that truth function possibilities are the foundation on which probability theory begins or is launched
5.101. The truth functions of a given number of elementary propositions can always
be set out in a schema of the following kind:
(TTTT) (p,q) Tautology (If p then p and if q then q.) (p q. q q)
(FTTT) (p,q) In words: Not both p and q. (~(p.q)
(TFTT) (p,q) " " : If q then p. (q p)
(TTFT) (p,q) " " : If p then q. (p q)
(TTTF) (p,q) " " : p or q. (p v q)
(FFTT) (p,q) " " : Not q. (~q)
(FTFT) (p,q) " " : Not p. (~p)
(FTTF) (p,q) " " : p or q, but not both. (p. ~q: v : q. ~p)
(TFFT) (p,q) " " : If p then q, and if q then p. (p = q)
(TFTF) (p,q) " " : p
(TTFF) (p,q) " " : q
(FFFT) (p,q) " " : Neither p nor q. (~p. -q or p/q)
(FFTF) (p,q) " " : p and not q. (p. ~q)
(FTFF) (p,q) " " : q and not p. (q. ~p)
(TFFF) (p,q) " " : q and p. (q . p)
(FFFF) (p,q) Contradiction (p and not p, and q and not q.) (p. ~p . q. ~q)
I will give the name truth-grounds of a proposition to those truth-possibilities of its truth-arguments that make it true.
the truth grounds of a proposition are the grounds on which it is true
its 'false grounds' the conditions under which it is false
5.11. If all the truth grounds that are common to a number of propositions are at the
same time truth-grounds of a certain proposition, then we say that the truth of that
proposition follows from the truth of the others.
yes truth follows from truth
5.12. In particular, the truth of a proposition 'p' follows from the truth of another proposition q if all the truth-grounds of the latter are truth grounds of the former.
latter and former?
what determines what follows from what?
not truth -
if p follows from q
then p is contained in q
if q is true
then p is true
5.121. The truth grounds of one are contained in the other: p follows form q
yes exactly
5.122. If p follows from q, the sense of 'p' is contained in the sense of 'q'
yes this puts it nicely
5.123. If a god creates a world in which certain propositions are true, then by that very act he also creates a world in which all the propositions that follow from them come true. And similarly he could not create a world in which the proposition 'p' was true without creating all its objects.
in the beginning was the word
5.124. A proposition affirms every proposition that follows from it.
we need to avoid logical mysticism here
what follows from a proposition is given in the proposition - once it is seen to follow from it
that is - what follows from a proposition follows an act upon the proposition - a
definitive use of it
strictly speaking nothing follows from anything - unless it is made to - unless that is there is reason for it
and once 'p' is seen to follow from 'q' - we are not talking a proposition per se - rather a propositional argument.
out of the argument the proposition is dead wood
though in practice - the proposition does not exist outside of the propositional
argument - though you could get this impression listening to logicians
mysticism and logic a fine line
5.1241. 'p . q' is one of the propositions that affirm 'p' and at the same time one of the propositions that affirms q.
The two propositions are opposed to each other if there is no propositions with a
sense, that affirms them both.
Every proposition that contradicts another negates it.
a proposition that contradicts another is a proposal against the first proposition
the proposing of it puts the negating proposition into the argument -
the resolution of the argument is a decision on the truth values of the proposals
either p or ~p
if -p in fact negates p then -p is held to be true
which is to say the world does not contain p - there is no such state of affairs
so there are two phases of the argument here - the proposal and the resolution
the proposal sets up the argument - the resolution is the decision regarding truth
values
5.13 When the truth of one proposition follows from the truth of others we can see
this from the structure of the propositions.
what we see here is propositional structure
truth is really no more than a proposal in such a scheme
if p is true then all that follows from p is true
the question of the truth of p is separate from the setting out of p and its possibilities
the setting out of p is it's display - its demonstration
the truth or not of p and its progeny is its reality -
i.e. p refers to a state of affairs or it does not
in the event that it does not ~p has no positive value -
that is it has no use
p.s.
(a)
my impression is that Wittgenstein wants to say that truth is a function of structure
that is that truth can only apply given a propositional structure - and the propositional theory and structure outlined in the 'Tractatus'
what I am suggesting is that there is no necessary connection
that truth is a proposal of resolution
that can indeed apply to propositions as outlined in the 'Tractatus' - but perhaps in
other forms also - other forms that is of propositions
the general idea being that there is more to propositions than Wittgenstein would
allow
and yes truth can be a function of elemental propositions - of strings of propositions in the sense that it can be a calculation of values
but all this is only made possible if the values of the elements are already determined
logic can determine possible values and combinations
I think we would say reality decides the issue
and the criterion of this I would say is utility or fruitfulness
but be that as it may reality decides the matter
(or is it we decide reality and reality determines the value?)
(b)
as I have been putting it a proposition is a proposal - it may or may not take the form of a sentence - a statement - it could be in the form of a musical notation - an image painted or represented in another form - i.e. sculpture or some other form yet to be seen - the possibilities are open
truth value is a response to the proposition - it is the response of assent or denial
what I am suggesting is that what truth value is ascribed to is an open matter
this is to say if you like that logical form is an open question
we have various expressions of it - various formulations - but the form is never
exhausted by any formulation
where in fact people do assent or dissent (deny) there you have logical form
there is no confusion it is simply a matter of understanding different formulation and with that different criteria -
criteria I would suggest are form dependent and that forms are expressions of
perspectives - ways of viewing the world
(this of course will not make sense to anyone who thinks there is or should be just one way of seeing things)
(c)
the idea of the proposition as picture can still work in this conception - here we would speaking about different kinds of picture
still I prefer proposal - picture has too much of a visual association to it - and some propositional forms are expressed in the terms of the non-visual senses
the other advantage of 'proposal' is that it avoids Wittgenstein's problem of logical
form -
logical form is the proposal of the proposition - or more correctly the ground of the
proposal - but this ground too is proposed
that is the relation between the proposition and the world is itself proposed
and thus logical form is the meta dimension of any proposition - or the meta
proposition
the meta dimension of any proposition - its meta statement - is not obvious - it is in a sense hidden
it can though be expressed on reflection as a meta proposition
that is the logic of the proposition can be expressed as a different or another mode of the proposition
5.131. If the truth of one proposition follows from the truth of others, this finds
expression in relations in which the forms of the propositions stand to one another;
nor is it necessary for us to set up these relations between them, by combining them
with one another in a single proposition; on the contrary, the relations are internal, and their existence is an immediate result of the existence of the propositions.
the internal relations of propositions exist if propositions are placed in relation to each other - that is if an argument is constructed
otherwise you are committed to some Platonic like notion of logical forms
a proposition has a form and structure - (things do have structure) - relationships are made / constructed - they are not the immediate result of the existence of propositions
5.1311. When we infer q from p v q and ~p, the relation between the propositional
forms of 'p v q' and '~p' is masked, in this case, by our mode of signifying. But if
instead of 'p v q' we write for example, 'p\q.\ .p\q', and instead of '~p', 'p\p' (p\q = neither p nor q), then the inner connection becomes obvious.
(The possibility of inference from (x). fx to fa shows that the symbol (x). fx has
generality in it.)
how a proposition is stated will determine how it is revealed
a proposition can fulfill a number of functions
these function are dimensions of possibility
their articulation or representation is found in the set of propositions that the original proposition represents
the original proposition is a flagship
the logic of a proposition - how it works - its internal workings can be stated in the kind of propositions that are found in the 'Tractatus'
this is to see the proposition as a logical function - to represent it as such
the veridical use of a proposition - i.e. its effect - the use it is put to is yet another - indeed more common characterization
'the' proposition as such is a 'place of possibility'
it is a given - once given - but is given in another question or set of questions
Wittgenstein I think regards his logical signage as something other than language -
perhaps its depiction
the point is though that the proposition may be expressed in any number of ways
- and logical sign language is just another expression
one may ask why express the proposition in such a manner?
Wittgenstein's answer that such an expression clarifies the logic of the proposition is good enough
why do this you may ask?
perhaps to find another way of seeing and understanding the world?
that would be good enough
p.s.
I would put that we create ontologies to enable functions to be performed
the notion of logical form for instance is needed given the kind of issue that
Wittgenstein is addressing
perhaps it will be argued by someone that it is not necessary - but this is just the point
what we say exists is determined by what we wish to achieve
in this case explanation of the relation of language to the world -
and from this it can be seen that languages are created to express the ontologies
postulated
and I suggest that there is never a case of one to one correspondence between
languages
that is to say a new language will always in some respect be different from the
language it was developed out of -
and how it will be different will be in terms of its ontology
new things are created in new ontologies -
what you need to factor in - in any translation is the fact of intellectual leap
that is to say essentially there will always be gaps - chasms - between languages
always though enough connections to suggest coherence - these of course can be
argued for or against
in language we are always writing on the unknown or speaking to it
5.132. If p follows from q, I can make an inference from q to p, deduce p from q.
The nature of the inference can be gathered only from the two propositions.
They themselves are the only possible justification of the law of inference.
'Laws of inference', which are supposed to justify inferences, as in the works of Frege and Russell, have no sense, and would be superfluous.
the inference is expressed in 'q then p'
the inference is not a property of p and q
it is a relation that can exist between two propositions - i.e. p and q
the inference may only be 'active' in an actual propositional argument
we can nevertheless refer to it as a possible relation - as a kind of relation
Wittgenstein is forced into this corner - just because he cannot explain logical
relations as propositions
(his theory of propositions - and particularly of internal relations - rests on a
distinction between expression and display
in short internal relations cannot be expressed in or by propositions - but they can be displayed in the logical syntax
as I have said quite an ingenious argument - but it is based on a suspect premise
- that display is something other than expression -
and further that a display of the logical syntax of a proposition is something other than its expression (albeit in alternative sign language)
we can state inference in any number of ways -
we can refer to as I have as a relation between entities (propositions)
we can even give it a behavioural definition - as in what people do under certain
circumstances (i.e. infer)
we can state it as Wittgenstein has above
it may even be expressed / represented artistically
etc.
5.133. All deductions are made a priori.
deductions are logical streams
5.134. One elementary proposition cannot be deduced from another.
an elementary proposition can be the conclusion of a deductive argument
the form of the deductive argument is such that an elementary proposition cannot be
the first premise
NB.
an elementary proposition -
the argument is that an elementary proposition is one that does not contain any other
proposition
it is a statement of a simple fact - not a complex fact
is an elemental statement just the reflection of a singular fact - or is it that the
statement makes or constructs the fact as simple?
can we speak i.e. of pure observation statements - statements that cannot be reduced to anything else?
we can understand the desire to base our theories on such a foundation
but is this simply a form of sentence construction - and meta pragmatism - or an
accurate account of how the world is?
do we make facts or do we come upon them?
(b)
we can also ask does it make sense to speak of elementary propositions in isolation
- that is outside of a theoretical context?
the individual proposition I suggest only has meaning and significance in a broader
context of understanding
statements in theoretical physics will not make sense outside of - separate from the
theories that produce them
veridical statements likewise only have significance given certain presuppositions
regarding the nature of the world
5.135. There is no possible way of making an inference from the existence of one
situation to the existence of another, entirely different situation.
we need a clear drawing here of the logic of 'situation' - what is an 'entirely different' situation?
if I infer from the presence of clouds in the sky that it will rain I may or may not be
right - but it is a valid inference
is this because we are speaking of different aspects of the one situation - the weather?
now if I also infer from the presence of clouds that I will be unhappy today - on the
face of it not a valid inference - two different situations - the weather and my
emotional state?
however it is conceivable that there is some underlying connection - for example let
us say there is in certain individuals a peculiar sensitivity to sunlight so that the less sunlight they have the less well being they experience - this let us say turns out to be explainable as a matter of chemistry - something to do with a connection between sun light and endorphin production in individuals with a certain variation in brain chemistry
in such a case we would not in linking clouds and happiness be dealing with different
situations
the point this leads to is that what is to count as one situation and what is to count as another is an open question
'situation' is just a matter of where you are
change your position you change the situation
5.136. There is no causal nexus to justify such an inference.
we can't decide causal nexus a priori
Wittgenstein assumes there are situations that are independent of each other - in some extreme sense
how can such situations (it is a suitably vague notion isn't it?) exist in the same world?
if x causes y then x is in y
the observation of such an outcome - y - is the observation of a causal relation
between x and y
5.1361. We cannot infer the events of the future from those of the present.
Superstition is nothing but belief in the causal nexus.
(a)
we cannot infer events of the future from those of the present - why not?
causation is a reasonable attempt to explain a dynamic world
we see repeated correlations of events (a following b) we say a causes b therefore if a then b -where's the drama?
any such inference is light -
it is a way of correlating events -
and a little more seriously the positing of an underlying relation between surface
events
on the face of it in normal circumstances a useful way of conceptualizing the world
- emotionally satisfying anyway
it's like saying there must be a connection between events
a fair enough metaphysical 'observation' - and OK you can call such superstitious
nevertheless in dynamic situations we see that one event comes out of another
what this in fact means - well that's another question -
a question perhaps for science -
science - that is - a more empirical form of superstition
(b)
in general it makes sense to regard the causal nexus as just a working hypothesis - a
way into the study of things
5.1362. The freedom of the will consists in the impossibility of knowing actions that
still lie in the future. We could know them only if causality were an inner necessity
like that of logical inference. - The connection between knowledge and what is known
is that of logical necessity.
('A knows that p is the case', has no sense if p is a tautology.)
the argument that if we did know the future - there would be no freedom of will
there would be no choice - any matter would be determined -
therefore freedom of will is prefaced on not-knowing
ignorance (metaphysical) is our guarantee of freedom
if causality was an inner relationship rather than as it is thought or proposed - an
external relationship then we could know what lies in the future?
that is if the causal relation was a logical relationship - etc.
logical necessity is an inner relation between propositions
logical necessity is essentially a syntactical relation / operation - the relation of signs as in a tautology
one might argue that Wittgenstein's argument for freedom demands that freedom is
the absence of knowledge per se
that is in so far as we have knowledge we are not free -
if I know now (don't worry about the future) - I cannot be free
on the other hand if free - I have no knowledge
his idea of knowledge here is logical necessity -
my view is that logical necessity has nothing to do with knowledge -
that logical necessity is just a syntactical arrangement - a relation of signs
and if so freedom of the will as he puts it - is another matter altogether
5.1363. If the truth of a proposition does not follow from the fact that it is self-evident to us, then its self-evidence in no way justifies our belief in its truth.
if self-evidence is not self-evidence of truth - what is it self evidence of?
if self-evidence does not justify belief - what is the point of it?
is the point being made here that self-evidence is just a feature of the structure of a proposition and that it does not bear on belief and truth?
anyway
a self evident proposition is one that justifies itself or appears to assert it's own truth
now quickly I would say either view of self evidence - can be shown to be without
sense -
that a proposition cannot justify itself and cannot assert it's own truth
if so whither self evidence?
is the point here that self evidence is a false notion?
that we should actually abandon it - take it from the logical lexicon?
yes I think so
if this is Wittgenstein's point - it was made badly
self evidence (if it means anything) is given in the proposition - in the propositional argument
whether someone accepts the conclusion - believes in its truth - is not itself a matter of the truth of the proposition - it is a matter of psychology
5.14. If one proposition follows from another, then the latter says more than the
former, and the former less than the latter.
I would say the opposite here - if p follows from q - p is contained in q -
therefore q has more content than p
5.141. If p follows from q and q from p, then they are one and the same proposition.
if p = q then q = p therefore p does not follow from q and q does not follow from p -
p and q can be placed in a propositional form i.e. p and q - however this is a false
proposition if p = q
the point is we should be wary of being too carried away with syntactical form - the
fact is we can be deceived -
and this may be quite an important point against Wittgenstein - display is not
necessarily what is real - let alone what is 'really real'
what presents is what presents that is all you can strictly speaking predicate of it
reality is always a question
5.142. A tautology follows from all propositions: it says nothing
isn't it time to get real about the tautology - the tautology is a false as in deceptive proposition - I think for all intents and purposes you could drop it - drop it as a real propositional form - use it as an illustration of false syntax - bad display
5.143. Contradiction is that common factor of propositions which no proposition has
in common with another. Tautology is the common factor of all propositions that have
nothing in common with one another.
Contradiction, one might say, vanishes outside all propositions: tautology vanishes
inside them.
Contradiction is the outer limit of propositions: tautology is the unsubstantial point at the centre.
yes one can wax poetical regarding tautology and contradiction - vanishing acts and
vanishing points - outer limits and non-existent centres
the tautology and the contradiction are useless propositions
this illustrates the deception of logic -
yes shock horror
well formed syntactical 'arrangements' can mean nothing - have no significance
in this sense they might function as reminders that logic is not without deception
5.15. If Tr is the number of truth grounds of a proposition 'r', and if Trs is the number of truth grounds of a proposition 's' that are at the same time truth-grounds of 'r', then we call the ratio Trs: Tr the degree of probability that the proposition 'r' gives to the proposition 's'.
propositions are related in terms of their truth conditions
probability as a measure of the 'truth strength' one proposition gives another
probability is measured in terms of the number of truth grounds common to
propositions
however probability it needs to be understood is a relation between propositions if
they are placed in relation to each other and ordered in relation to each other
probability is thus a function of propositional action - an assessment of relative truth strength
Wittgenstein always leaves propositional action out of the analysis as if logic has a
life of its own - independent that is of - life - wishful thinking
5.151. In a schema like the one above in 5.101, let Tr be the number of 'T's' in the
proposition r, and let Trs be the number of 'T's' in the proposition s that stand in
columns in which the proposition r has 'T's'. Then the proposition r gives to the
proposition s the probability Trs: Tr.
propositions stand in relation to each other in the form of propositional arguments -
schemas are the representation of the ground of any argument
probability arguments are propositional actions
5.1511. There is no special object peculiar to probability propositions.
probability is a calculation premised on the absence of object
5.152. When propositions have no truth arguments in common with one another, we
call them independent of one another.
Two elementary propositions give one another the probability 1/2.
If p follows from q, then the proposition 'q' gives to the proposition 'p' the probability 1. The certainty of logical inference is a limiting case of probability.
(Application of this to tautology and contradiction).
how can it be that propositions have no truth arguments in common?
i.e. if a proposition q is either T or F and a proposition r is either T or F - what they have in common is a truth argument
all propositions are related in terms of truth arguments
elementary propositions do not give each other probability
elementary propositions can be related to each other in a probability argument
- in an argument of two possible outcomes the probability is 1/2
if p follows from q then q has the same probability as p
this application does not apply to tautology or contradiction as these are not real
propositional arguments (as I argued above) -
p does not follow from p as p is not contained in p - p simply is p - the idea of it being contained in itself is non-sensical -
the same is true of p and ~p - are we to say p and ~p follows from p and ~p?
p and ~p does not contain - p and ~p - you can put one after the other - but there is no deduction
the propositional argument that is p and ~p - a contradiction - is like the tautology
without truth value - it is simply not a valid propositional formulation - it is
syntactically innocent but semantically senseless
the so called tautology and contradiction are useless propositional strings
any theory of probability based on the idea of tautology as the centre point of
probability and contradiction as the outer limit of probability is founded on nonsense
5.153. In itself, a proposition is neither probable nor improbable. Either an event
occurs or it does not: there is no middle way -
probability is assigned in the absence of happening
probability theory is the logic of imagination - of imagined states - weighted against experienced or given reality
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 in the urn. By this experiment I can establish that the number of black balls drawn and the number of white balls drawn approximate to one another as the draw continues.
So this is not a mathematical truth.
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 one event than to the other. That is to say, they give each the probability 1/2 as can easily be gathered from the above definitions.
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.
what is confirmed here is that in order to perform the experiment in the terms outlined the decision is taken to limit the field of knowledge to the operation performed -
the two events are defined as independent of more detailed knowledge
the operation is performed on the assumption of a uniformity of nature during the
whole operation - i.e. - that balls will remain balls - colours colors - perception
'veridical' etc. -
probability assessments are only possible given these assumptions and the definition
of the domain of knowledge
probability it seems can only occur in a context of necessity - or its assumption
5.155. The minimum unit of probability proposition 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.
yes probability - or the minimum unit of probability propositions - depend on the
absence of knowledge - or the decision to absent knowledge
NB.
crucial understandings -
a sign or symbol represents what happens - represents an act - we may not be able to
make sense of the event without the sign - but let us never forget it is always of a
secondary order to what happens - to what occurs
the second crucial point to get is that a sign - any sign represents a relation between consciousness and the world
I have a distinct feeling that Wittgenstein would have us believe that the essential
relationship - in fact the only relationship is between the sign and the world -
this I think is the idea behind his idea of logical form - the relation between language and the world - he asks what do they have in common?
it's the wrong question - and it comes about because the logic that underlies it is all wrong to begin with
language is a window to the world yes - and a window to consciousness
otherwise language is not possible
I can well understand Wittgenstein's attempt to deny the place and relevance of mind - Wittgenstein is smart enough to see that a physicalist reduction of mind is not on - it's not even what it's about - I guess he just hoped he get to where he wanted to by going around - and leaving the centre unspoken for - not an invalid approach - any monk looking up from his prayer book or any housewife putting out the washing would see the point -
5.156. It is in this way that probability is a generalization.
It involves a general description of the propositional form.
We use probability only in default of certainty - if our knowledge of a fact is not
indeed complete, but we do know something about its form.
(A proposition may well be an incomplete picture of a certain situation, but it is
always a complete picture of something.)
A probability proposition is a sort of excerpt from other propositions.
probability must be able to formulated outside the issue of certainty - for there is an argument that no proposition can be regarded as certain
probability as a calculation of what might happen given the parameters of the situation and its objects
such an idea suggests probability as an exercise in uncertainty
I think it best to regard probability theory as meta game theory
a proposition is never a complete picture of anything - it can be a proposal to view a situation as complete - and it can be a proposal to regard a situation as incomplete
any proposition is an expression of much more than the situation and objects it refers to -
hence a proposition never stands alone - though it may be presented in such a way and
appear to have a stand alone form - it always entails a view of the world - a
metaphysic - for practical purposes this is rarely stated - and in most cases it is not in fact 'known' or articulated - but it is there
a proposition is like this - it is what appears to the world of the world proposed
a third and most important point to make I think is that Wittgenstein's theory of logic - or logical form is a proposal - is a proposal for how we should (or in my terms can) view the world - it is finally a proposition
and like all meta propositions it is not guaranteed from the outside - any support it has is internal - that is if you accept certain premises the conclusion follows - it is a way of seeing -
to understand this way of viewing metaphysical / philosophical theories you have to
understand what is seen is not known -
this is the reason for conception - for ways of seeing - for perspective
metaphysical views are essential for without them we have no way of mapping or
navigating the world we are in -
the fact of meta theory is simply the fact of consciousness - consciousness in relation to the unknown
what metaphysics tells us is that consciousness is indeterminate
this indeterminacy is the source of human creativity
creativity is the essential characteristic of the animal
it is the human tool
5.2. The structures of propositions stand in internal relations to one another.
internal relations - there's more pretty girls than one
the ground of propositional argument is always an assumption - usually undefined - or
unexplored
propositions can be thrown together - and linked up in terms of an underlying notion
or idea - which may eventually emerge as a proposition and its off-spring
the point being the relation between propositions is always the propositional argument
propositions can be plucked out of the sky
or indeed thrown back out there
what's in and what's out is can be a very 'physical' robust matter when the job needs to be done
this is not to argue against 5.2 - rather to point out it is not a one dimensional matter
NB.
logical form
what happens happens - logical form is a description of the happening in terms of its
necessary elements
these necessary elements are really undefined posits - but they are posits of what is
deemed necessary for the occurrence
a theory of logical form thus has the characteristic of generality
logical form is not a property of language
language is an expression of logical form
when we express logical form - put forward an account of - we are proposing a meta
description of reality - based on an analysis of a state of affairs - it is really no more than a description of what has occurred - and the argument that - the event in question points to a view of reality beyond itself - it is to say this event is not unique - rather that it is an expression of reality - this is the full sense of the proposal - or at least a sketch of the full sense
the terms of this proposal - the proposal of a meta description (logical form) depend
on the metaphysical perspective that is adopted
there is no one account of the nature of events - there are any number of perspectives
hence logical form is itself always a question
5.21. In order to give prominence to these internal relations we can adopt the
following mode of expression: we can represent a proposition as a result of an
operation that produces it out of other propositions (which are the bases of the
operation).
propositions can be produced internally -
to do so is really to explore the implications of a given proposal - it is not actually strictly speaking to make a new proposal
5.22. An operation is an expression of a relation between the structures of its results and its bases.
the use of an internal operation can be such an expression
5.23. The operation is what has to be done to the one proposition in order to make the other out of it.
yes this is really the theory of implication
5.231. And that will, of course, depend on their formal properties, on the internal
similarity of their forms.
like can only be produced out of like
5.232. The internal relation by which a series is ordered is the equivalent to the
operation that produces one term from another.
the study of internal relations can bring to awareness what is already given - nothing is actually produced that was not already there
5.233. Operations cannot make their appearance before the point at which one
proposition is generated out of another in a logically meaningful manner; i.e. the point at which the logical construction of propositions begins.
the operation never actually makes an appearance - and it must exist prior to the
construction of propositions otherwise nothing would occur
the operation is an act of consciousness - it can be represented in propositional form i.e. an operational proposition - a proposition that describes / expresses the operation
propositional representation can occur without the operation being performed - as
Wittgenstein's theory of operations as represented in these (his) propositions testifies
5.234. Truth functions of elementary propositions are results of operations with
elementary propositions as their bases.
(These operations I call truth-operations.)
truth functions are results of operations with elementary propositions as their bases
truth operations - give us a picture of the truth possibilities of elementary propositions
the result of truth operations is a statement of the possibilities for assent or dissent in relation to given elementary combinations
all logic is based on the notion of truth - and this is that any proposition whatever that may be is true or false - we begin with is concept - p is T or F -
all logical operations are generated one way or another from this foundation - this
notion
it is simply a notion necessary to practice
we need to have a concept of assent and it's opposite in order to decide
decision which is unavoidable (necessary) - given the nature of consciousness is based on this either / or possibility
logic is disjunction
(the law of the excluded middle is the law of consciousness)
5.2341. The sense of a truth-function of p is a function of the sense of p.
Negation, logical addition, logical multiplication, etc. etc. are operations.
(Negation reverses the sense of a proposition)
sense is defined by p - sense is given in consciousness - sense is consciousness -
consciousness in the world - it is pre-propositional - sense is the ground of
propositional knowledge -
propositions simply describe sense - that is the internal logic of propositions (which is itself an open question - one that Wittgenstein has given an answer to) is a description of consciousness in the world in relation to a particular focus
there is no mystery to sense - it is like the tree or a rock - it is a feature of the natural world - and by this I mean a two dimensional world - the physical outside - the conscious inside - sense is an internal fact -
sense is just what consciousness gives to the world -
and its quality is openness
5.24. An operation manifests itself in a variable; it shows how we can get from one
form of proposition to another.
It gives expression to the difference between forms.
(And what the bases of an operation and its result have in common is just the bases
themselves)
an operation does not manifest itself in a variable
an internal - logical operation is nevertheless an act - the act is performed - its result can be shown - we can see difference from one series against another - but the
operation itself is not external - so it cannot be shown - it can be known - and it can be described in a propositional form - yes
an operation of the kind Wittgenstein has in mind - is more in the line of a calculation - it is an operation that is itself strictly defined -
to calculate you must know the principle of the calculation
the act of calculation - changing forms - is in itself without meaning
that is e.g.. - from the point of view of an observer who does not know a calculation is taking place - or what the principle of the act is
the meaning of the act is internal to the act - the meaning can be given external form - in the form of an explanatory proposition
Wittgenstein here as in other places would dearly love to avoid any reference to - or to give any significance to the place - the function - the reality of consciousness
logical operations are acts of consciousness -
5.241. An operation is not the mark of a form, but only the difference between forms.
a form is always the result of a logical operation -
an operation always occur within a form - within a formal context -
the operation has no meaning - no actual existence outside of forms -
what would be the mark of a form?
it's expression -
an operation is in a sense the difference between forms
for their to be a difference there must be an operation
5.242. The operation that produces 'q' from 'p' also produces 'r' from 'q' and so on.
There is only one way of expressing this: 'p', 'q', 'r', etc. have to be variables that give expression in a general way to certain formal relations.
is this Wittgenstein's argument that the proposition is an operation - a logical
operation?
it would seem so
if so this is like confusing number with calculation
it really amounts to an operational view of reality
which cannot make sense - if all you have in your world is operations
for an operation can only be - can only make sense if there is something to operate on
look I don't know - but it wouldn't surprise me if Wittgenstein would like to hold such a view
that the world really is just logical process / operation
5.25. The occurrence of an operation does not characterize the sense of a proposition.
Indeed, no statement is made by an operation, but only by its result, and this depends on the bases of the operation.
(Operations and functions must not be confused with each other.)
no an operation has no bearing on the sense of a proposition
the operation is not the statement of the proposition
I would say an operation can be put in propositional form - and this Wittgenstein
would oppose
he thinks you can talk about logical operations without expressing them -
the relation between operations and functions
an operation is performed on a proposition
a function is a property of a propositional argument
the function is as it were embedded in the propositional argument
to express it an operation is required
5.251. A function cannot be its own argument, whereas an operation can take one of
its own results as its basis.
a function is not an argument - a function is a relation within an argument
an operation can use its results as a basis for itself
5.252. It is only in this way that the step from one term of a series of forms to another is possible (from one type to another in the hierarchies of Russell and Whitehead).
(Russell and Whitehead did not admit the possibility of such steps, but repeatedly
availed themselves of it.)
operations I would argue are logical actions
they are defined by the possibilities of forms
they are what we can do with forms - i.e. the step from one term of a series of forms to another
the operation is the logical action that results in a desired outcome
5.2521. If an operation is applied repeatedly to its own results, I speak of successive applications of it. ('O'O'O'a' is the result of three successive applications of the operation 'O' x' to 'a'.)
In a similar sense I speak of successive applications of more than one operation to a
number of propositions.
an operation is a decision to utilize propositions
it is defined by the possibilities of the propositional argument and it is the exercise of a possibility -
a logical operation is essentially translation
5.2522. Accordingly I use the sign '[a,x, O'x] for the general term of the series of
forms a, O'a, O'O'a.... . This bracketed expression is a variable: the first term of the bracketed series is the beginning of the series of forms, the second is the form of a term arbitrarily selected from the series, and the third is the form of the term that immediately follows x in the series
this is the proposition you are having when you can't have a proposition
it is description of a logical operation - definition
such propositions are propositions which describe actions (logical) that can be
performed on subject propositions
logical propositions establish the ground for logical operations
they are in this sense postulates - proposals for how to operate with
operational propositions per se are directions for action - action in relation to
propositional possibilities - and these possibilities are contained in propositional
arguments
logical objects are really postulates - that are designed to enable logical operations of propositions
logical operations enable the use of propositions
5.2523. The concept of successive applications of an operation is equivalent to the
concept 'and so on'.
'and so on' - so very technical
the point is that logical operation as in 'and so on' is simply a kind of action -
its basis is that consciousness is aware of succession and here I mean temporal
succession
repetition is succession without time - that is time taken out of the equation
it should be clear that such operations are not based in the propositional form - their basis is extra-propositional -
propositions are simply forms that can be operated on - objects are other forms - in
fact any form can be the subject of an operation
5.253. One operation can counteract the effect of another. Operations can cancel one
another.
an action is never actually canceled - an action occurs - it has its time -
nevertheless one act can counteract the effect of another -
and in such a case what you have is the action of denial - that is the logic of negation transformed into action
the world is changed
this is no great shakes - the world you can say is the possibility of change - or just simply possibility
actuality is stillness - and this finally is a deception - even if a necessary posit of consciousness
illusion is necessary for survival
5.254. An operation can vanish (e.g. negation in '~~p': ~~p = p).
vanishing
an operation performs
performance is the act of transformation
in a transformative action objects (of whatever kind) are held in a transitive mode
it is not a magic act - it is that which is in transition
it is a way of regarding things - that is regarding a series as transitive
negation is dissent in the sense of denial
do we say one act denies another?
strictly speaking any action that changes a state of affairs is from a logical point of view at base an action of denial
it might be argued from here that the only logical operation that has real content is
negation -
so what is the place and significance of assertion?
it is at least to recognize a state of affairs
in the pragmatic sense it is perhaps the decision to leave things as they are -
it could be argued that in a changing reality no genuine assertion can be made - or that any such assertion is hollow
and against this has been argued a metaphysic of underlying changelessness
the logic of Parmenides
NB.
the assertion it seems does depend on their being a state of affairs that can be fixed by a proposition
this is not the case with negation
negation is not time or space dependent -
it does not presume a metaphysics
for this reason the negation is logical speaking contained
the assertion on the other hand is like a leaking boat
for this reason the assertion and the negation cannot be regarded as logical opposites
the negation I think is properly regarded as an operation
the assertion as the attempt to state a state of affairs
they are very different matters
p.s.
perhaps this is the reason why there is a sign for negation '~' but not one for
assertion?
and was this the reason behind Frege's idea of the judgement stroke
it would make some sense - even if you are to argue against it finally
5.3. All propositions are results of truth operations on elementary propositions.
A truth-operation is the way in which truth-function is produced out of elementary
propositions.
It is of the essence of truth-propositions that, just as elementary propositions yield a truth-function of themselves, so too in the same way truth-functions yield a further truth-function. When a truth-function is applied to truth functions of elementary propositions, it always generates another truth function of elementary propositions, another proposition. When a truth operation is applied to the results of truth
operations on elementary propositions, there is always a single operation on
elementary proposition that has the same result.
Every proposition is the result of truth-operations on elementary propositions.
(a)
when you add a room to a house are you making a new house?
or if you remove a room are you making a new house?
Wittgenstein wants elementary propositions to be the basis of his propositional theory
but let's ask the question - are there such things?
what I mean is this - are not elementary proposition really analytical constructions
from a proposition - that is analyses?
now I am not here suggesting that 'the' proposition is something set in concrete - it is usually I would say a work in progress - stabilized only by decision to stop work and to get going
once decided on - yes you can analyze it into elements - this can be useful in terms of clarification
but the thing is the proposition is not something built up from elements
a proposition is a net cast - what it catches - what's in - while important and of great interest - is a secondary matter
(b)
truth functional analysis of propositions is just that - an analysis
it is the setting up of a form for propositions - propositions as truth functions and then the argument that all propositions are truth functions
so you have a theory of propositions and then the analysis of propositions in terms of that theory
the argument is deductive
therefore in so far as a proposition is a truth function the argument follows
what we can at least say is that such propositions are truth functions
can we argue therefore all propositions are truth functions?
Wittgenstein's argument here is that a proposition has only one form - the form of a
truth function -
any statement that is not of this form is whatever else it is - not a proposition
I think Wittgenstein's concept of the proposition stands in the context of truth
functional use of propositions
if we wish to have a truth functional analysis of a set of propositions then it follows those propositions must be put in truth functional form
this is to suggest that propositional form is not a set piece - form is finally a question of use - of purpose - of end
and truth function is not the only use of propositions
the thing is the propositional form - if you can speak of it in the abstract - outside of use - is without form
5.31. The schemata in 4.31. have a meaning even when 'p', 'q', 'r', etc. are not
elementary propositions.
And it is easy to see that the propositional sign in 4.442 expresses a single truth-
function of elementary propositions even when 'p' and 'q' are truth-functions of
elementary propositions.
the schemata in 4.31 shows us that truth function really has nothing to do with kinds
of proposition
if you decide that a proposition is a truth function - then any proposition can be
analyzed as a truth function
even so the idea of truth function really leaves open the question of the nature of
proposition
how far you want to take this is another question
if i.e. you were to hold that a painting is a proposition - would you then say it has a truth function?
clearly we are used to and comfortable with the idea of truth function applying to the proposition as a statement in language
5.32. All truth functions are results of successive applications to elementary
propositions of a finite number of truth-operations.
the point is - you may want to argue elementary propositions are the subject of truth
function - but the thing is truth function can apply to the proposition as an unknown
the move to elementary propositions is not really a theory of logic - it is I think an onto / epistemological argument - though I think Wittgenstein does not want it viewed this way
5.4. At this point it becomes manifest that there are no 'logical objects' or 'logical constants' (in Frege's and Russell's sense).
an operation does not exist without something to operate on
is there not an argument for saying that Wittgenstein's 'elementary proposition' is such a logical object?
5.41. The reason is that the results of truth-operations on truth functions are always identical whenever they are one and the same truth-function of elementary
propositions.
this would also suggest that the elementary proposition functions at least in the
'Tractatus' as a constant
what is the logical status of the elementary proposition?
is Wittgenstein saying it has no place in logical theory?
and also truth operations - clearly they are an action - but what distinguishes such
operations from any other action?
I say the truth operation is a logical operation
and further that this means it is an essential operation of consciousness
and this might be to distinguish between fundamental actions of consciousness and
any other operation that might derive from such
anyway it doesn't strike me that Ludwig has explained truth function or truth operation - and I think his idea was to try to avoid such - by arguing that logical form is not expressed - but nevertheless shown - as in the schemata of 4.442
I think he thinks logicians just draw pictures - that what we only ever have is display
even so - he really has no account of what they sketch - outside of the sketch
a very clever attempt to avoid metaphysics - or even just some kind of explanation
the thing is we may not know what logic is - OK - nevertheless there is value in the
attempt to give it a place in - the rest of what we don't know
5.42. It is self-evident that v, , etc. are not relations in the sense in which right and left are relations.
The interdefinability of Frege's and Russell's 'primitive signs' of logic is enough to show that they are not primitive signs, still less signs for relations.
And it is obvious that the ' ' defined by means of '~' and 'v' is identical with the one that figures '~' in the definition of 'v'; and that the second 'v' is identical with the first one; and so on.
'v' is not a relation - it is a domain sign
'v' is a sign that signifies logical domain - the domain of discourse - the possibility of discourse
it is a sign of domain
in the case of p q the domain is given in p
q is an argument of that domain
primitive signs only exist if there are primitives
primitives indeed are required for certain operations -
they are posited - that is primitiveness is assumed for the purpose of the operation
the reality of the primitive is an epistemological issue
in truth the only primitive is the unknown 'U'
the beauty of this is that it is a primitive that allows and in fact requires that it be instantiated
relations are facts of the world
given the fact of consciousness
outside of consciousness there is no relation
nothing is related
consciousness brings relation to the world
its very presence - is the fundamental relation
5.43. Even at first sight it seems scarcely credible that there should follow from one fact p infinitely many others, namely ~~p, ~~~~p, etc. And it is no less remarkable that the infinite number of propositions of logic (mathematics) follow from have a dozen 'primitive propositions'.
But in fact all the propositions of logic say the same thing, to wit nothing.
nothing follows from p
~~p is not a result of p - it is p in alternative form - which is to say p is not confined to a one sign description - that is all
~~p is like reflecting p in a mirror and ~~~~p reflecting p in another mirror etc.
logic (the propositions of logic) is a description of the basis on which whatever is said can be said
we can say what we say - quite well as it were - without logic - without knowing a
theory of logic that is
however if you wish to know the ground on which possibility and from this actuality
and therefore the possibility of language - of description rests - then the propositions of logic are that description - or at least our best shot at it - well a shot anyway -
logic is like knowing there is an end to the road you are walking down - you may
never reach it - or go to the end of it - but it gives you your bearings to have this
knowledge -
logic is mapping
5.44. Truth functions are not material functions.
For example, an affirmation can be produced by double negation: in such a case does
it follow that in some sense negation is contained in affirmation? Does '~~p' negate - p, or does it affirm p - or both?
The proposition '~~p' is not about negation, as if negation were an object: on the other hand, the possibility of negation is already written into affirmation.
And if there were an object called '~', it would follow that '~~p' said something
different from what 'p' said, just because the one proposition would then be about '~' and the other not.
'~p' is only possible given 'p'
'~p' is an 'external' definition of 'p'
that is what 'p' is not
the assertion of 'p' makes no sense has no definition unless '~p' is understood
'p' and '~p' are the logical domain
'p' and '~p' represent the world
much more is to be found in '~p' than 'p'
the domain of negation in propositional arguments is always greater than that of
affirmation
'~p' contains 'p'
p and ~p both are domain signs
that is the signify logical domain
one cannot be asserted without the other
for in that event no domain is established
and i.e. 'p' has no logical sense - no definition - and I mean definition in the most
literal sense of the term
what this tells us too is that logical domain is only ever brought into existence by the assertion of p
~p is / becomes the ground of p
the sign '~' is a domain sign
5.441. The vanishing of the apparent logical constants also occurs in the case of '~($x). ~fx' which says the same as '(x) . fx', and in the case of '($x) . fx . x = a', which says the same as 'fa'.
yes you can change or rearrange the clothes on the mannequin and have quite a
different shop front display
5.442. If we are given a proposition, then with it we are also given the results of all truth-operations that have it as their base.
what we are talking about here is truth functional propositions - it needs to be
mentioned that propositions can have other functions than truth functions - this seems to have been entirely missed in the Tractatus - as if i.e. people's daily affairs are nothing more than the calculation of truth functions - true enough for the poker machine - but in fact human beings are never so grounded
5.45. If there are primitive logical signs, then any logic that fails to show clearly how they are placed relatively to one another and to justify their existence will be incorrect. The construction of logic out of its primitive signs must be made clear.
this is as it should be - if you are to construct a discourse it must be seen to function internally
bear in mind though - that any such construction will be based on nothing - in a
logical sense
the only basis - and this is without foundation (but it has motion) is practice
we create out of delight and then pretend our constructions have steel
also let's not get too excited about obviousness
what is at issue in any attempt at clarity is the dissolution of an underlying issue or mystery
I don't think we ever get it right - what it's about in fact is the attempt to see clearly
what we know from metaphysics is that there are various ways of seeing and they all
come out of a blindness that is never fully cured by what is ultimately seen
we can't see everything - but we can know that we don't see
5.451. If logic has primitive ideas they must be independent of each other. If a
primitive idea has been introduced, it must have been introduced in all the
combinations in which it ever occurs. It cannot, therefore, be introduced first for one combination and later re-introduced for another. For example, once negation has been introduced, we must understand it in propositions of the form ~p and in propositions like '~(pvq)', '($x) . ~fx', etc. We must not introduce it first for the one class of cases and then for the other, since it would be then left in doubt whether its meaning were the same in both cases, and no reason would have been given for combining the signs in the same way in both cases.
(In short Frege's remarks about introducing signs by means of definitions (in
Fundamental Laws of Arithmetic) also apply mutatis mutandis, to the introduction of
primitive signs.)
the point of a primitive sign is that it applies to each and every instance of the
propositional form - this is the definition of primitive
all we really need to decide to begin with is what propositional form the sign applies to
in the case of '~' we would say it applies to propositions of logical (mathematical)
syntax
if what '~' signifies is negation - and negation is thought to have a broader application than propositional syntax - then in other contests negation is expressed by other signs
if we say negation is a primitive idea of logic - what this means is that it is not defined by any particular sign
the sign or signs point to the idea - and the idea is more than any one application
OK - but what can this really mean?
the primitive idea has different formal applications
but can we actually speak of the primitive idea sensibly?
if negation has meaning in different contexts and we can only represent it by different signs - how do we represent the idea (itself) outside of its applications?
I don't think we can - just creating a sign for the primitive idea - in the end will lead to the question what distinguishes one primitive sign from another - nothing but a decision
and yes we could define the idea of negation by a new sign - but as Wittgenstein says
here it would have to be introduced in all the combinations it occurs
do we therefore drop the notion of primitive idea?
if we define logic as just the operations of propositional syntax - the problem doesn't arise
as to the application or use of an idea like negation outside of logic - to contexts other than propositional logic - we can say 'well it happens'
and what this points to is that propositional forms influence each other and not in a
'logical' way -
that the practice of life is not 'logical' -
and that the inter-relationship of forms happens despite attempts to keep the forms
separate and pure
this attempt to keep forms separate and pure is the origin of much wrongheadedness
and much social evil (i.e. racism sexism etc.)
the only other way out of this that I can see is to say the primitive idea is always
undefined
that what distinguishes one primitive idea from another is the context in which it
arises?
that there is no fixed definition of any primitive notion
primitive notions are known by their signs
the relationship of signs - the inter-relationship of signs is explained in terms of
epistemological communities - what groups know and how they know it
these groups again are not strictly defined - and the knowledge (the inter-relation of sign understandings) is never precise or clear
the study that is the inter-relation of forms and their signs is therefore properly the subject of an epistemological anthropology
is this what semiotics is supposed to be about?
this approach would suggest that logic is to be replaced by empirical study of forms and that forms are not some essential eternal categories or types that we investigate
independently of what goes on in the world - but are in fact - what does goes on
perhaps too we can say there are as many logics as their are forms
this argument world leave propositional logic intact - but very clearly focused
5.452. The introduction of any new device into symbolic logic is necessarily a
momentous event. In logic a new devise should not be introduced in brackets or in a
footnote with what one might call a completely innocent air.
(Thus in Russell and Whitehead's Principia Mathematica there occur definitions and
primitive propositions expressed in words. Why this sudden appearance of words? It
would require justification, but none is given, or would be given, since the procedure is in fact illicit.)
But if the introduction of a new device has proved necessary at a certain point, we
must immediately ask ourselves, 'At what point is the employment of this device now
unavoidable?' and its place in logic must be made clear.
it is a little disconcerting when Russell does that - but it really doesn't matter at all
the sudden appearance of definitions and primitive propositions in words is mostly to
do with literary expression - the logical objection to such has some basis - if there are no correspondence rules implicit or explicit -
really Wittgenstein's argument here is dealt a fatal blow - with what one might call an innocent air
the translatability of forms is necessary if there are to be any forms at all
the argument of the 'Tractatus' - the establishment of the language of propositional
logic - depends on the fact of translation - i.e. natural language to symbolic logic
symbolic language doesn't just come out of nowhere
we begin in any such analysis (and its results) with what we have - natural language
the setting up of a symbolic language does not render natural languages irrelevant or
useless - symbolic languages do not replace - they stand with
so it is no great drama to translate symbolic logic back to natural language mutatis
mutandis
my point is there is no fundamental language - fundamental in terms of hierarchy and
significance -
there is just a table a feast and many exotic dishes - and the chef is still creating - and we are all at the table - the only question - what is your desire?
5.453. All numbers in logic stand in need of justification.
Or rather, it must become evident that there are no numbers in logic.
There are no pre-eminent numbers.
numbers are signs or rightly speaking names of operations - and 'names' here is an
unexpected use of the term - nevertheless - operations can be named
they are functional names - they are utility names
e.g. '0' is the absence of operation or motion - '1' an operation
'an' operation only has conceptual sense given possibility
possibility is the space of action
these notions possibility and space of actions are conceptual creations
that is they only occur given consciousness in the world
in a non-conscious reality possibility and the idea of operation do not exist
in formal logic the 'reality' of numbers is behind the screen of syntactical schemas
that is you can construct propositional logic without reference to numbers
(it's the family picture without grandpa)
mathematics for that matter makes no difference to how the world is
it is a parallel language -
there are no pre-eminent numbers unless there are pre-eminent operations
number theory - mathematics is the language of operation theory
we can say it is developed in logic to give expression to and operational function to
the operational dimension of logic
without such logic is either dead or mute
5.454. In logic there is no co-ordinate status, there can be no classification.
In logic there can be no distinction between the general and the specific.
logic is - propositional logic is - the operation of primitive signs -
the operation is truth function
the theory of all this is the theory of propositional logic
5.4541. The solutions to 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 real subject to the law: Simplex signillum veri.
all very well but does this view of logic provide a definition of a theory of simplicity?
I suspect the answer will be - what you see is what you get -
yes - but hardly good enough
one man's simplicity another's complexity
the point being if simplicity is the standard we need to know how and on what basis
the standard is set
there is no philosopher's stone here
the concept is like every other product of consciousness - made
it is not found
men have always had a presentiment - hardly a basis for argument - if indeed it can be shown that such is in fact the case
assuming for the argument's sake that it is - a presentiment to an a priori self contained system is not as impressive as it seems
men have at various times had various presentiments - in times of war - perhaps there is a presentiment to chaos and violence - so what follows?
presentiments are a good basis for artistic efforts
and are we to see logic as one such creation?
a picture of the world - without paint - sound or movement - or unlike a sculpture -
substance
Wittgenstein's presentiment argument does raise the question what is his structure
based on - built on?
he is saying its basis is a priori - but what can this mean?
is this not - at least in this context - simply to say we have no basis for our argument -
but it does have the aesthetic strength of simplicity?
now I think this presentiment argument is really disingenuous - or at least bad
thinking
I say bite the bullet and state that this theory of logic has no basis
that at the best it is just an outcome of an argument in a field of discourse that is
essentially about the issue of foundation
I am not fazed by this -
yes logic is based on a presentiment - that in the scheme of things has no more
intrinsic value than any other presentiment
just another shot in the dark - another attempt to give form and function to the world
a shot that like all others lives or dies on its usefulness - that is how it enables us to negotiate the unknown
the discussion of Tractatus 5 will continue in Skeptikos III
(c) Copyright: Greg. T. Charlton. 2007.
All rights reserved. Killer Press.
