Wittgenstein's ComputerWittgenstein (Early and Late) and Modeling in Computer Science
Simon D. LevyComputer Science DepartmentWashington & Lee University
Fourth Regional Wittgenstein Workshop11 March 2012
Socrates Plato Aristotle
Aquinas Descartes Locke
Hume Kant Frege
Wittgenstein Angry Birds Phone
Sunday, March 11, 12
Origins: 1939
WITTGENSTEIN: I won’t say anything which anyone can dispute. Or if anyone does dispute it, I will let that point drop and pass on to say something else.
TURING: I understand but I don’t agree that it is simply a question of giving new meanings to words.
WITTGENSTEIN: Turing doesn’t object to anything I say. He agrees with every word.
TURING: I see your point.
WITTGENSTEIN: I don’t have a point.
[Diamond 1976]Sunday, March 11, 12
Computing: 1999
Sunday, March 11, 12
Localist Representations + Explicit Rules =
Brittle Computations
cats
chase
dogs
AGENT PATIENT
Sunday, March 11, 12
Localist Representations + Explicit Rules =
Brittle Computations
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sequential pointer-following:Who chases cats?
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &6
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
One small error = total failure
cats
chase
dogs
AGENT PATIENT
Address Contents
0000 <chase>
0001 &12
0010 &8
0011 &7
0100 <dogs>
0101 <cats>
0110 <AGENT>
0111 &4
1000 <PATIENT>
1001 &5
Sunday, March 11, 12
Usage
The confusions which occupy us arise when language is like an engine idling, not when it is doing work.
Sunday, March 11, 12
Rule-Following
All this, however, can only appear in the right light when one has attained greater clarity about the concepts of understanding, meaning, and thinking. For it will then also become clear what can lead us (and did lead me) to think that if anyone utters a sentence and means or understands it he is operating a calculus according to definite rules.
Sunday, March 11, 12
Family Resemblances
I can think of no better expression to characterize these similarities than "family resemblances"; for the various resemblances between members of a family: build, features, colour of eyes, gait, temperament, etc. etc. overlap and cries-cross in the same way.-And I shall say: 'games' form a family.
Sunday, March 11, 12
Critique of Pure Reductionism
Suppose everyone had a box with something in it: we call it a "beetle". No one can look into anyone else's box, and everyone says he knows what a beetle is only by looking at his beetle. — Here it would be quite possible for everyone to have something different in his box.
Sunday, March 11, 12
Family Resemblances
• Both "primitive" concepts (cat, dog, chase) and "complex" ones (dogs chase cats unless the cats are bigger than them, etc.) are represented in the same way (N-dimensional vector)
• So we can use the same metric (e.g. Euclidean distance) to describe resemblances between objects of arbitrary complexity.
Sunday, March 11, 12
Rule-Following without Rules
• VSA can generalize ("learn a rule") from a single exemplar, because anything can be a "variable" (c.f. Moser 2012)
• E.g. What is the dollar of Mexico?
Sunday, March 11, 12
“What is the Dollar of Mexico?” (Kanerva 2009)• Let X = <country>, Y = <currency>,
A = <USA>, B = <Mexico>
• Then A = X*U + Y*D, B = X*M + Y*PD*A*B =
D*(X*U + Y*D) * (X*M + Y*P) =
(D*X*U + D*Y*D) * (X*M + Y*P) =
(D*X*U + Y) * (X*M + Y*P) =
D*X*U*X*M + D*X*U*Y*P + Y*X*M + Y*Y*P =
P + noise
Sunday, March 11, 12
The Random Beetle in the Box
• VSA representations are essentially random.
• So any two individual agents' internal representations of the same concepts will be unrelated to each other, though perfectly functional.
• VSA reps can also be expressed as neural spike trains (Stewart / Bekolay Eliasmith 2011), making VSA a plausible candidate for perceptual grounding of symbols (à la Barsalou 1999 ).
Sunday, March 11, 12
SourcesBarsalou, L.W. (1999) Perceptual symbols systems. Behavioral and Brain Sciences 22.
Diamond, C., ed. (1976) Wittgenstein's Lectures on the Foundations of Mathematics, Cambridge, 1939, Hassocks: Harvester Press.
Dror, I. E. and M. Dascal (1997) Can Wittgenstein help free the mind from rules? The philosophical foundations of connectionism. In D. Johnson and C. Erneling (eds.), The Future of the Cognitive Revolution. Oxford University Press.
Kanerva, P. (2009) Hyperdimensional computing: an introduction to computing in distributed representation with high-dimensional random vectors. Cognitive Computation 1(2).
Klagge, J.C. (1989) Wittgenstein and neuroscience. Synthese 78.
Moser, C. (2012) Schmagency and the formal character of constitutive principles. Presented at the Fourth Regional Wittgenstein Workshop (10 March 2012), Lexington, Virginia.
Stern, D.G. (1991) Models of memory: Wittgenstein and cognitive science. Philosophical Psychology 4 (2).T
Stewart, T., T. Bekolay, and C. Eliasmith (2011) Neural representations of compositional structures: representing and manipulating vector spaces with spiking neurons. Connection Science 23 (2).
Wittgenstein, L. (1921/1975) Tractatus Logico-Philosophicus (trans. D.F. Pears and B.F. McGuiness). Routledge.
Wittgenstein, L. (1933/1965) The Blue and Brown Books. Harper Torchbooks.
Wittgenstein, L. (1953/1973) Philosophical Investigations (3rd Edition, trans. G.E.M. Anscombe). Prentice Hall.
Sunday, March 11, 12