Tag Archives: Ludwig Wittgenstein

Tractatus Logico-Philosophicus

Just the facts, ma’am.

— Detective Joe Friday

  1. The World (Die Welt): The world is everything that is the case.
  2. The Case (Der Fall): What is the case, the fact, is the existence of atomic facts.
  3. The Picture (Das Bild): The logical picture of the facts is the thought.
  4. Thought (Gedanke): The thought is the significant proposition.
  5. Propositions (Der Satz): Propositions are truth-functions of elementary propositions.
  6. The Form (Die Form): The general form of truth-function is: [p-bar, xi-bar, N(xi-bar)].
  7. Silence (Schweigen): Whereof one cannot speak, thereof one must be silent.
  8. ( ):

The Tractatus has seven propositions, most with sub-propositions and sub-sub-propositions, etc. I have added the eighth, which is the actual silence of all one cannot speak of. Quite a large section, for all its emptiness.

I also thought it would be nice to have an internet version where you could click and expand down through the sub-sentences. There are already many such versions available for your enjoyment.

I can’t decide whether I like the English or the German version better, so here are both.

Further Reading:

https://en.wikipedia.org/wiki/Tractatus_Logico-Philosophicus

http://www.tractatuslogico-philosophicus.com/

http://www.bazzocchi.com/wittgenstein/tractatus/eng/index.htm

http://www.kfs.org/jonathan/witt/ten.html

https://pbellon.github.io/tractatus-tree/#/

https://tractatus-online.appspot.com/Tractatus/jonathan/index.html

http://daxoliver.com/tractatus/

http://people.umass.edu/klement/tlp/

The Tricky Truth about Tractatus Trees (updated)

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Snakes and Ladders

sq_snakes_and_ladders2

My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) He must surmount these propositions; then he sees the world rightly.

— Ludwig Wittgenstein, from Tractatus Logico-Philosophicus 6.54

Consider the children’s game of “Snakes and Ladders”.

The object of the game is to traverse a sequence of locations on a game board, numbered from one (the beginning) to some maximum goal (the end), with the numbers increasing from the bottom of the board to the top. The player usually competes with other players to win the goal first, because otherwise why do it. Ladders join lower numbers at their base with higher numbers at their top. Snakes join higher numbers at their head with lower numbers at their tail.

The players take turns and each move forward a number of locations determined with a roll of a die. If a player lands on the bottom of a ladder, she can immediately climb to the top of it, skipping the locations in between. However if she lands on the head of a snake, she must slide down the snake to its tail, essentially losing her recent gains of several turns.

The game progresses by chance, and indeed the winner is completely chosen by luck. There are no choices that players can make to increase their chance of winning the game, and so it is completely random. It is evidently an ancient game and older versions often portrayed the ladders as virtues and the snakes as vices. What can this game teach us about morality and life in general?

Unfortunately the player cannot gain knowledge or experience along their journey to help them. There is no way to increase one’s chance to land on a ladder’s bottom or decrease one’s chance to land on a snake’s head. The game is on the other end of the spectrum from a choice driven game such as tic-tac-toe, or even chess. I’m also reminded of the card game “War”, which is another random game played by children. Such completely random games equalize chances of winning among different ages, I imagine.

From Wikipedia: The game (Snakes and Ladders) is a central metaphor of Salman Rushdie’s Midnight’s Children. The narrator describes the game as follows:

All games have morals; and the game of Snakes and Ladders captures, as no other activity can hope to do, the eternal truth that for every ladder you hope to climb, a snake is waiting just around the corner, and for every snake a ladder will compensate. But it’s more than that; no mere carrot-and-stick affair; because implicit in the game is unchanging twoness of things, the duality of up against down, good against evil; the solid rationality of ladders balances the occult sinuosities of the serpent; in the opposition of staircase and cobra we can see, metaphorically, all conceivable oppositions, Alpha against Omega, father against mother.

Notes:

Actually, it reveals the fourness of things. The snake tails and ladder tops are different in kind from the snake heads and ladder bases, because landing on the former the player doesn’t change position. She can instead contemplate possibly backsliding and revisiting this location via snake or the experiences of having taken the long way instead of just climbing to this location via  ladder.

A more modern version could replace the snakes and ladders with one entity, perhaps wormholes, which would deliver one instantly to the opposite end, either forward or backward. The name could be revised to “Shortcuts and Backtracks”, perhaps. Or maybe it would be too confusing.

References:

http://en.wikipedia.org/wiki/Snakes_and_Ladders

http://en.wikipedia.org/wiki/War_%28card_game%29

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J.-Y. Girard’s Transcendental Syntax, V2

sq_transcendental_syntaxMeaning is use.

– Ludwig Wittgenstein

If people never did silly things nothing intelligent would ever get done.

– Ludwig Wittgenstein

The latest two preprints by logician J.-Y. Girard continue his program for transcendental syntax, divided into deterministic and nondeterministic. He defines transcendental syntax as the study of the conditions of the possibility of language: to begin by discovering the preliminary suppositions in the creating of a logical sentence such as a proposition or deduction.

What are the presuppositions for using propositions? Girard claims the main one is the balance between the creation and the use of words, which is at the heart of meaning. But the notion that a proposition has a meaning that is well defined is prejudice, albeit one that allows us identify the terms of a sentence and thus to perform deductions.

Girard wants instead to find inner explanations of logical rules: explanations based on syntax instead of a semantics that correlates to a mandated “reality”. To emphasize this, he gives the term Derealism as another expression for transcendental syntax. Logical rules should have a normative aspect because of their utility, so his project appears to be one of pragmatism. Others have said that Linear Logic is the logic of the radical anti-realist.

Girard divides all of logical activity into four blocks that weave together: the Constat, the Performance (please forgive my shortening on the diagram above), L’usine (factory), and L’usage (use). These four blocks are partitioned by Kant’s analytic-synthetic and a priori-a posteriori distinctions. The analytic is said to have “no meaning”, that is, “locative”. The synthetic is said to have “meaning”, that is, “spiritual”. The a priori is said to be “implicit”, and the a posteriori is said to be “explicit”.
transcendental_syntax_tableCan we find all the explanations we need to create logic internally? If so, perhaps it is only because of how the brain works, like how John Bolender posits that social relations described by the Relational Models Theory are created out of symmetry breaking structures of our nervous systems, which are in turn generated by our DNA. A realist would certainly say that our understanding of logical rules is enabled but also limited by our brains, whereas an idealist would say that our minds could “transcend” those limits. But it seems pragmatic to say that the mind is what the brain does.

I believe a closer analogy for the fourfold of Transcendental Syntax is to Hjelmslev’s Net than to Kant’s Analytic-Synthetic Distinction. If so, then Performance and L’usage are Content (Implicit), whereas Constat and L’usine are Expression (Explicit). Performance and Constat are Substance (Locative), and L’usine and L’usage are Form (Spiritual). Hjelmslev was a linguist that developed a theory of language as consisting of only internal rules.

Or even to analogy with Aristotle’s Four Causes, which is how I’ve arranged the first diagram: the Constat is the Material cause, the Performance is the Efficient cause, L’usine is the Formal cause, and L’usage is the Final cause. Material and Efficient causes are often considered mere matter in motion, which could be Locative, or meaningless (physical). Formal and Final could be Spiritual, or meaningful, as patterns of matter and motion, respectively.

Notes:

How can we know that a given named term is the same as another one in a different part of our formula? Rather than using names, or linking them through semantics or a well-defined meaning, we can tie terms together by their locations in our sentences and deductions.

References:

J.-Y. Girard / Transcendental syntax 1: deterministic case (January 2015 Preprint)

J.-Y. Girard / Transcendental syntax 2: non deterministic case (February 2015 Preprint)

http://iml.univ-mrs.fr/~girard/Articles.html

V. Michele Abrusci, Paolo Pistone / On Transcendental Syntax: a Kantian Program for Logic?

https://www.academia.edu/10495057/On_Trascendental_syntax_a_Kantian_program_for_logic

http://en.wikipedia.org/wiki/Synchrony_and_diachrony

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