Well, it's high noon at the center of town and me and you got a show-down. I've got advantage on being the faster draw, being still living ... but you put up a good fight for being long dead in your grave. Your Tractatus sent chills down my spine when I opened the slim volume and saw that it was an axiomatization.
Who else does this, who else cares? O Witty, so systematic, so ordered, so aware of the nuances of logic. No one was surprised I slept with you on the first night. I wasn't surprised when we began to fight. And I'm telling long-dead-you that I am here to redeem our mutual father figure's hope for life, When Bert said in the introduction, "Yet I do not see how any easier hypothesis can escape from Mr Wittgenstein's conclusions," I knew my path was righteous and good, and ...
I will destroy you, Witty.
all my love,
Witty wants simplicity and systematization, if you are axiomatizing, this is the only start. He discusses the problems with language and notation. He understands the gap between logic and ethics, he favors approaching the inductive from a base in physics. He asserts that philosophy is an activity, a critique on "the limits on meaningful language." He claims that inference is inherently a priori (5.133).
What's useful about Witty?
To axiomatize is to attempt to reduce a thing to essential components. Without this understanding and tool in your thinking arsenal, one cannot fully understand any thing.
He gives limited tools: true and false. Contradiction ( => <= ): This is a blog. This is not a blog; and Tautology ( <= => ): I know this is either a blog or not a blog. Sense and nonsense.
He claims all axioms are inherently tautologies, which is what causes such things to be transendental. He is unwittingly asserting an absurd universe whenever he transcends ... for instance, the most profound moment of his thinking is when he is asked why one should practice philosophy under these circumstances, he claims that one does so in order to "throw away the ladder after he has climbed up it." This is a stunning claim for a person who also claims no absolutes and no ought. The logician tells us we ought to abandon logic. This is an essential moment.
He also encourages destabilization, breaking illusions of the mind, destroying paradigms and rebuilding them based on observation and with conscious choice. He does this at an axiomatic level, but later these same ideas will make excellent elements for the set of ethics.
Wittgenstein understands the difference between a model and physical reality. This conversation is glossed over frequently, and is as important as the solipsistic paradox. Are maths invented or discovered? He neatly skirts this with a statement of fact: "4.01: The proposition is a model of the reality as we think it is."
What is important to note about models is that they take a chosen set of elements and name those legos axioms of the set.
Now we get to enter the world of meta-logic. The logic of logic. Observations of models reveals the nature, structure, proposition, function, equation; in short, the relationship, of things. It is a very useful practice to unearth the commonalities between modes of "truth-finding." Popularly, Zen and Quantum Mechanics are grouped in just this sort of meta-logic.
We are searching for isomorphisms. This is what we have in lieu of proof at the axiomatic level.
He has a great definition for logic: "logic is the theory of forms and of inference." And if, as I compel in the next section, the forms of the universe include the random and chaotic, our humble charge is to order disorder.
We will infer a form which allows logically for self-destruction, obviation, meaninglessness.
What's outdated about Witty?
He cannot get past Descartes' existence/knowledge paradox. He claims "closed system" as a solution, which still leaves an "extant universe" problem. Hence why he dedicates any space in an axiomatization treatise to Solipsism, and both entries are extremely important to the whole of his logic.
Start with the famous 5.61: "... What we cannot think, that we cannot think: we cannot therefore say what we cannot think."
The first reference to Solipsism appears next in 5.62: "This remark provides a key to the question, to what extent solipsism is a truth. In fact what solipsism means, is quite correct, only it cannot be said, but it shows itself. That the world is my world, shows itself in the fact that the limits of the language (the language which I understand) mean the limits of my world.
Witty dances about this paradox through the end of subsections of axiom 5, it is the conclusion of "Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)". Axiom 6 takes the solipsistic paradox and is chosen to be: "The limits of my language mean the limits of my world."
So, to Witty, he asserts that we must logically close the system in order to put disclaimers about our inherent problem of perspective. I think he makes a small mistake in focusing so much on the nature of our language, though I'm glad he covered the ground and the rest of that species can be left as exercises for the reader. The real problem is that our perspective is limited physically and we are trapped in the senses our ACGT doled us out.
However, this is by no means a death sentence on the existence of reality or place for logic and systems. What Witty is missing is the distinction between general and specific, between axioms and emergence patterns. Language emerges from perspective, perspective from existence. We are talking existence, so it is a mistake to apply the logic of language to the logic of existence.
The logic of existence is what we are chasing.
Interestingly, Witty also mentions "a priori" in this section, something he talks rarely of considering the book is an axiomatization ostensibly. He also mentions in 5.64, "an extensionless point and ... the reality co-ordinated with it." This is one of the many points he approaches my concept of the importance of the dimension shift. (that's gonna have to be its whole own post).
2.021: Objects form the substance of the world.
Here is a good example of how Witty could be much more careful about his own language. And we don't have to have a special lexicon of unique metaperturbation language to be more precise and clear. We can just use the very loose understanding we share and have lots of meaningful discourse.
ENERGY, not objects, forms the substance of the world.
Energy forms the substance of the UNIVERSE, not of (just) the world.
Energy IS the substance of the universe. Forms might imply a "form"-er, so is unnecessary.
Energy EXISTS. Because we've assumed the substance of the universe is real.
That's a mighty fine axiom.
Witty is outdated here because he frequently uses emergent things as general things: ie world instead of universe, or object instead of energy.
I assert Witty is no basic bitch,
A critical error of Witty is inside axiom 4.211 where he asserts, "It is a sign of an elementary proposition that no elementary proposition can contradict it."
My contention is that it is precisely paradox which is an earmark of "elementary propositions" or axioms. Just as "energy exists" is the a priori assumption based upon the solipsistic paradox. By finding paradox, we find "truth".
For one admitting he knows math language is a model, Witty is awfully dogged about his notational nuances. It seems to me that both precision and accessibility are important in a math language. He needlessly dwells on semantics due to his consistent error of treating language as elemental rather than emergent. None of his internal semantic battles are actually about the universe, but about our ability to communicate about the universe, therefore a bit misplaced in an axiomatization.
What's after Witty?
5.4541 reads: "The solution of logical problems must be neat because they set the standard of neatness. Men have always thought there must be a sphere of questions whose answers - a priori - are symmetrical and united into A CLOSED, REGULAR STRUCTURE."
There is much to unpack here. Most important is simply that: because men think there is a grand unifying theory which implies a closed universe does not mean that is the case.
I assert the opposite. Energy exists. Infinity exists. Therefore the things of the universe have infinite potential, of which irregularity is included. I would rephrase Witty to say: The solution of logical problems is neat when there is a limited set of axioms and the model fully describes the chosen system. The analysis of closed, regular structures reveals an underlying symmetry and unity. We call this logic.
However, the universe does not care if solutions are neat, there are also random and chaotic solutions. The truth of the universe must have the characteristic of allowing for open, irregular organics as well as closed, regular structures.
Witty asserts that, on principle, nothing can be said about that which is unbounded. All advancement into the attempt of truth finding outside of the solipsistic paradox ends here. He accepts that raw information is impossible to offer.
I fundamentally disagree. The problems of philosophy do not magically disband because I assert an opinion, the canon of significant questions remain. What is interesting to me, though, is the set of questions which arise if one, as a thought experiment, just takes the assumption REALITY EXISTS and applies it to existing models and (importantly) paradoxes.
For instance, we then exist, perhaps even existence matters. Think of that: EXISTENCE MATTERS. Matter as in has inertia, takes up space, substance of which objects are composed. Matter as in to be of importance, significant.
This might be the stuff ought is made of.