We know that Wittgenstein's views evolved far afield from his initial bombshell Tractatus But why should that prevent us from discussing his discarded ideas? Tractatus remains relevant as a work standing on its own merit.
This critique was posted in January 2002. I have made some editorial changes, which include corrections in logic transformations, as of July 2017.
From Wittgenstein's Tractatus Logico-Philosophicus, Proposition 1:
1 The world is all that is the case.
1.1 The world is the totality of facts, not of things.
1.11 The world is determined by the facts, and by
their being all the facts.
1.12 For the totality of facts determines what is the
case, and also whatever is not the case.
1.13 The facts in logical space are the world.
1.2 The world divides into facts.
1.21 Each item can be the case or not the case while everything
else remains the same.
We include also two other of Wittgenstein's claims as relevant to our discussion.2 What is the case—a fact—is the existence of atomic facts. 2.01 An atomic fact is a combination of objects (entities, things).According to Ray Monk's astute biography, Ludwig Wittgenstein, the Duty of Genius (Free Press division of Macmillan 1990), Gottlob Frege aggravated Wittgenstein by apparently never getting beyond the first page of Tractatus and quibbling over definitions.
And yet it seems to me that there is merit in taking exception to the initial assumption, even if perhaps definitions can be clarified. As we know, Wittgenstein later repudiated the theory of pictures that underlay the Tractatus; nevertheless, a great value of Tractatus is the compression of concepts that makes the book a gold mine of topics for discussion.
First, however, I recast the quoted propositions as follows:
1. The world is a theorem [i.e., the perceived world is organized in
accord with a master theorem, which as yet remains
fuzzily, if at all, understood].
1.1 The world is the set of all theorems, not of things [a thing
requires definition and this definition is either a 'higher'
theorem or an axiom].
1.12 The set of all theorems determines what is accepted
as true and what is not.
1.13 The set of theorems is the world [redundancy acknowledged].
2. It is a theorem -- a true proposition -- that axioms
exist [the existence of axioms is axiomatic].
My reinterpretation, I hope, helps us identify with the desires of philosophers such as Bertrand Russell, A.N. Whitehead, David Hilbert and others to form a modern, physicalist framework for reality.
After all, is not Tractatus founded in Wittgenstein's extensive mining of Principia Mathematica by Russell and Whitehead, along with his for fascination with Russell's paradox?Rather than cope with the vast Principia, let us instead consider a toy system S of logic based on two axioms. We can build all theorems and anti-theorems of S from the axioms (though we cannot necessarily solve basic philosophical issues).
With p and q as axioms (atomic propositions that can't be durther divided by connectives and other symbols except for vacuous tautologies and contradictions), we can begin:
1. p, 2. ~p
3. q, 4. ~q
and call these 4 statements the Level 0 set of theorems and anti-theorems. If we say 'it is true that p is a theorem' or 'it is true that ~p is an anti-theorem' then we must use a higher order system of numbering. That is, such a statement must be numbered in such a way as to indicate that it is a statement about a statement.
We now can form set Level 1:
5. pq [theorem]
6. ~(pq) [anti-theorem]
7. p v q
8. ~(~p~q)
9. p v ~q
10. ~(~pq)
11. ~p v q
12. ~(p~q)
Level 2 is composed of all possible combinations of p's, q's and connectives (as we can do without the implication arrow), with Level 1 statements combined with Level 2 statements, being a subset of Level 2.
By wise choice of numbering system, we can associate any positive integer with a statement. Also, the truth value of any statement can be ascertained by the truth table method of analyzing such statements. And, it may be possible to find the truth value of statement n by knowing the truth value of sub-statement m, so that reduction to axioms can be avoided in the interest of efficiency -- as long as the Deduction Theorem has already been satisfied.
So I have no objection to trying to establish an abstract system using axioms. But the concept of a single system as having a priori existence gives pause, even without the ontological results of Goedel and Turing. And significantly, I would say, the early Wittgenstein has proposed a set of axioms which he has divined by some intuitional process. As my reinterpretation shows, it appears that the existence of axioms is axiomatic, not that this is necessarily a bad thing.
If I am to agree with Prop 1, I must qualify it by insisting on the presence of a human mind, so that 1 then means that there is for each mind a corresponding arena of facts. A 'fact' here is a proposition that is assumed true until the mind decides it is false.
I also don't see how we can bypass the notion of 'culture,' which implies a collective set of beliefs and behaviors which acts as an auxiliary memory for each mind that grows within that culture. The interaction of the minds of course yields the evolution of the culture and its collective memory.
Words and word groups are a means of prompting responses from minds (including one's own mind). It seems that most cultures divide words into noun types and verb types. Verbs that cover common occurrences can be noun-ized (gerunds).
A word may be seen as an auditory association with a specific set of stimuli. When an early man shouted to alert his group to imminent danger, he was at the doorstep of abstraction. When he discovered that use of specific sounds to denote specific threats permitted better responses by the group, he passed through the door of abstraction.
Still, we are assuming that such men had a sense of time and motion about like our own. Beings that perceive without resort to time would not develop language akin to modern speech forms.
In other words, their world would not be our world.
Even beings with a sense of time might differ in their perception of reality. The concept of 'now' is quite difficult to define. However, 'now' does appear to have different meaning in accord with metabolic rate. The smallest meaningful moment of a fly is possibly below the threshold of meaningful human perception. A fly might respond to a motion that is too short for a human to cognize as a motion.
Similarly, another lifeform might have a 'now' considerably longer than ours, with the ultimate 'now' being, theoretically, eternity. Some mystics claim such a time sense.
The word 'deer' (perhaps it is an atomic proposition) does not prove anything about the phenomenon with which it is associated. Deer exist even if a word for a deer doesn't. Or does it? The deer exists for us 'because' it has importance for us. That's why we give it a name.
Consider the eskimo who has numerous words for phenomena all of which we English-speakers name 'snow.' We assume that each of these phenomena is an element of a class named 'snow.' But it cannot be assumed that the eskimo perceives these phenomena as types of a single phenomenon. They might be as different as sails and nails as far as he is concerned.
These phenomena are individually named because they are important to him in the sense that his responses to the sets of stimuli that 'signal' a particular phenomenon potentially affect his survival. (We use the word 'signal' reservedly because the mind knows of the phenomenon only through the sensors [which might include unconventional sensors, such as spirit detectors]).
Suppose a space alien arrived on earth and was able to locomote through trees as if they were gaseous. That being might have very little idea of the concept of tree. Perhaps if it were some sort of scientist, using special detection methods, it might categorize trees by type. Otherwise, a tree would not be a self-sevident fact in its world.
What a human is forced to concede is important, at root, is the recurrence of a stimuli set that the memory associates with a pleasure-pain ratio. The brain can add various pleasure-pain ratios as a means of forecasting a probable result.
A stimuli set is normally, but not always, composed of elements closely associated in time. It is when these elements are themselves sets of elements that abstraction occurs.
Much more can be said on the issue of learning, perception and mind but the point I wish to make is that when we come upon logical scenarios, such as syllogisms, we are using a human abstraction or association system that reflects our way of learning and coping with pleasure and pain. The fact that, for example, some pain is not directly physical but is 'worry' does not materially affect my point.
That is, 'reality' is quite subjective, though I have not tried to utterly justify the solipsist point of view. And, if reality is deeply subjective, then the laws of form which seem to describe said reality may well be incomplete.
I suggest this issue is behind the rigid determinism of Einstein, Bohm and Deutsch (though Bohm's 'implicate order' is a subtle and useful concept).
Deutsch, for example, is correct to endorse the idea that reality might be far bigger than ordinarily presumed. Yet, it is his faith that reality must be fully deterministic that indicates that he thinks that 'objective reality' (the source of inputs into his mind) can be matched point for point with the perception system that is the reality he apprehends (subjective reality).
For example, his reality requires that if a photon can go to point A or point B, there must be a reason in some larger scheme whereby the photon must go to either A or B, even if we are utterly unable to predict the correct point. But this 'scientific' assumption stems from the pleasure-pain ratio for stimuli sets in furtherance of the organism's probability of survival. That is, determinism is rooted in our perceptual apparatus. Even 'unscientific' thinking is determinist. 'Causes' however are perhaps identified as gods, demons, spells and counter-spells.
Determinism rests in our sense of 'passage of time.' In the quantum area, we can use a 'Russell's paradox' approach to perhaps justify the Copenhagen interpretation.
Let's use a symmetrical photon interferometer. If a single photon passes through and is left undetected in transit, it reliably exits only in one direction. If, detected in transit, detection results in a change in exit direction in 50 percent of trials. That is, the photon as a wave interferes with itself, exiting in a single direction. But once the wave 'collapses' because of detection, its position is irrevocably fixed and so exits in the direction established at detection point A
or detection point B.
Deutsch, a disciple of Hugh Everett who proposed the 'many worlds' theory, argues that the universe splits into two nearly-identical universes when the photon seems to arbitrarily choose A or B, and in fact follows path A in Universe A and path B in Universe B.
Yet, we might use the determinism of conservation to argue for the Copenhagen interpretation. That is, we may consider a light wave to have a minimum quantum of energy, which we call a quantum amount. If two detectors intercept this wave, only one detector can respond because a detector can't be activated by half a quantum unit. Half a quantum unit is effectively nothing. Well, why are the detectors activated probablistically, you say? Shouldn't some force determine the choice?
Here is where the issue of reality enters. From a classical standpoint, determinism requires energy. Event A at time t0 is linked to event B at ta by an expenditure of energy. But the energy needed for 'throwing the switch on the logic gate' is not present.
We might argue that a necessary feature of a logically consistent deterministic world view founded on discrete calculations requires that determinism is also discrete (not continuous) and hence limited and hence non-deterministic at the quantum level.
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