Simulations by Wittgenstein

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Abstract


Wittgenstein’s Tractatus can be read as handbook in simulation technology.


Picture as Simulation

Wittgenstein’s  Tractatus Logico-Philosophicus, considered very difficult to read and understand, is an ambitious project to clarify the relation between language and reality and in particular to identify the nature of science.  We here point to connections to the knols  Simulation TechnologyThe Soul as Simulation of Body

and Hyperreality in Physics and related topics in My Book of Knols. 


We cite from Tractatus:

  • The existence and non-existence of states of affairs is reality.
  • We picture facts to ourselves. 
  • A picture presents a situation in logical space, the existence and non-existence of states of affairs.
  • A picture is a model of reality. 
  • In a picture objects have the elements of the picture corresponding to them. 
  • In a picture the elements of the picture are the representatives of objects.
  • What constitutes a picture is that its elements are related to one another in a determinate way. 
  • A picture is a fact.
  • A picture cannot, however, depict its pictorial form: it displays it.
  • A picture represents its subject from a position outside it.
  • A picture cannot, however, place itself outside its representational form.
  • What any picture must have in common with reality,is logical form, i.e. the form of reality. 
  • A picture whose pictorial form is logical form is called a logical picture.
  • Every picture is at the same time a logical one.
  • Logical pictures can depict the world.
  • A picture has logico-pictorial form in common with what it depicts. 
  • A picture depicts reality by representing a possibility of existence and non-existence of states of affairs.
  • A picture contains the possibility of the situation that it represents.
  • A picture agrees with reality or fails to agree; it is correct or incorrect, true or false. 
  • What a picture represents it represents independently of its truth or falsity, by means of its pictorial form. 
  • What a picture represents is its sense. 
  • The agreement or disagreement or its sense with reality constitutes its truth or falsity. 
  • In order to tell whether a picture is true or false we must compare it with reality.
  • It is impossible to tell from the picture alone whether it is true or false.
  • There are no pictures that are true a priori.
  • A logical picture of facts is a thought.
  • 'A state of affairs is thinkable': what this means is that we can picture it to ourselves. 
  • The totality of true thoughts is a picture of the world.
  • What signs fail to express, their application shows.
  • A proposition is a picture of reality.
  • A proposition is a model of reality as we imagine it
  • Reality is compared with propositions.
  • A proposition affirms every proposition that follows from it.
  • All deductions are made a priori. 
  • Different nets correspond to different systems for describing the world.
  • Mechanics determines one form of description of the world.





Wittgenstein in front of one of his logical pictures/simulations of the world.

We summarize:

  • A picture is a model of reality. 
  • A picture is a fact. 
  • A picture whose pictorial form is logical form is called a logical picture.
  • A logical picture of facts is a thought.
  • A picture must have the logical form of reality. 
  • The totality of true thoughts is a picture of the world.
  • A proposition is a picture of reality. 
  • A proposition is a model of reality as we imagine it.
  • Reality is compared with propositions.
  • An equation marks an aspect of equivalence.
  • Mathematical modeling employs equations.
  • Mathematical modeling uses meshes of finite mesh size.
  • Newtonian mechanics imposes a unified form on the description of the world.

Wittgenstein's logical picture/simulation of a duck-rabbit.


Analysis


Analyzing these statments we are led to the idea that what Wittgenstein describes is, in particular, 

  • simulation of real or imagined reality 
  • performed by solving mathematical equations 
  • by computation using meshes of finite mesh size

which is nothing but the essence of Simulation Technology and Computational Mathematics.


Simulation (without logical form?) of the world in the Situation Room 
of the White House.