On the Relation of
Computing to the World
William J. Rapaport
Department of Computer Science & Engineering,
Department of Philosophy, Department of Linguistics,
and Center for Cognitive Science
rapaport@buffalo.edu
http://www.cse.buffalo.edu/~rapaport
Thanks
• To IACAP for this honor!
• To Preston Covey, for early inspiration
• My journey:
– from Meinong & Philosophy of Mind
– to AI & Philosophy of Computer Science
Philosophy of Computer Science
• What is CS?
– Science?
• What is science?
– Engineering?
• What is engineering?
– Both?
– Neither?
Philosophy of Computer Science
• What is CS the scientific study of?
– Computers?
• What is a computer?
– Computation?
• What is computation? Algorithm? Recipe?
• Church-Turing Computability Thesis
• Hypercomputation
Philosophy of Computer Science
• What is a computer program?
– Implementation of an algorithm?
• What is implementation?
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–
–
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Relation of program to what it simulates/models
SW vs. HW
© vs. ℗
Program verification
Philosophy of Computer Science
• Philosophy of AI
– Turing test
– Chinese room
• Computer Ethics
– Should we trust decisions made by computers?
– Should we build AIs?
• Other topics not covered:
– information
– social uses of computers, etc.
Computing & the World
• Common theme found in most of these topics
• Is computing about:
– the world?
– or descriptions of the world?
• Overview of these issues
• More questions than answers
(semantic)
(syntactic)
Some Preliminaries
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•
•
•
What is CS?
Thought experimental data
Input-Output
What is an algorithm?
Computing & the World
• CS ≈ scientific study of:
–
–
–
–
what can be computed
how it can be computed
how it can be computed efficiently
how physical computers can be engineered to do this
• 2 “what” questions:
– “Narrow” / theoretical:
• what mathematical functions are computable?
– “Wide” / practical:
• what real-world tasks are computable?
Thought-Experiment Data
• Rey’s & Fodor’s chess-wargame computer(s)
– 1 algorithm? Or 2?
– cf. Necker cube!
• Cleland’s hollandaise sauce recipe
– Is it computable?
– Works on Earth, fails on Moon
• Rescorla’s GCD program in bases 10 & 13
– Does it compute GCD?
Thought-Experiment Data
• Winston’s blocks-world program
– Robotic implementation drops blocks
– Behaves as “intended”?
• Spreadsheet instructions to naïve user
– Is “blindly” entering data into cells “adding”?
Input & Output
• What is the role of a TM tape?
– I-O device?
– internal memory?
• Is tape qua I-O device necessary?
– TMs don’t accept external-world I/P!
– TM begins with all data pre-stored on tape
• then computes
• final result is stored on tape
– not necessarily reported to external world!
Input & Output
• Any external-world I/P would have to be
– encoded by user / decoded by TM
• Any external-world O/P would have to be
– encoded by TM / decoded by user
• Coding uses an (algorithmic) semantic interpretation
• more on this later…
What Is an Algorithm?
• Algorithm (for E) [to accomplish G] is:
– a procedure P
• finite set of statements such that each S is:
– composed of finite # of “symbols” from finite alphabet
– unambiguous (for E)
» (E “knows how” to do S
» E can do S
» S can be done in finite time
» after doing S, E “knows” what to do next)
– P takes finite time
– [P ends with G accomplished]
What Is an Algorithm?
• Algorithm (for E) [to accomplish G] is:
– a procedure P
• finite set of statements such that each S is:
– composed of finite # of “symbols” from finite alphabet
– unambiguous (for E)
» (E “knows how” to do S
» E can do S
» S can be done in finite time
» after doing S, E “knows” what to do next)
– P takes finite time
– [P ends with G accomplished]
What Is an Algorithm?
• Algorithm (for E) [to accomplish G] is:
– a procedure P
• finite set of statements such that each S is:
– composed of finite # of “symbols” from finite alphabet
– unambiguous (for E)
» (E “knows how” to do S
» E can do S
» S can be done in finite time
» after doing S, E “knows” what to do next)
– P takes finite time
– [P ends with G accomplished]
Must Algorithms Be
Intentional / Teleological?
• No
– Fodor:
– Dennett:
computations are “formal”
Turing’s “strange inversion”
• Don’t have to know arithmetic
in order to be a computer that does arithmetic
• Spreadsheet adds w/o my knowing what I’m doing
• Searle-in-CR understands Chinese
w/o understanding that he’s understanding it
Must Algorithms Be Intentional / Teleological?
• Yes
– Robin Hill:
• Not just:
• But:
Do P
To accomplish G, do P
– and David Marr…
David Marr’s 3 Levels
of Information Processing
• “computational” level:
– specification of what a system does
– e.g., mathematical-functional level:
f(i) = o
• “algorithmic” level:
– how (theoretically)
– i.e., computational-algorithmic level:
Af (i) = o
• “implementation” level:
– how (physically):
I(Af)(i) = o
– I = brain, computer, beer cans/levers/windmills…
David Marr’s 3 Levels
• Is Marr’s “computational” level teleological?
– Egan:
No (“Do f”)
– Anderson:
Yes (“To G, do f”)
– Shagrir & Bechtel: Yes & no
• “computational”-“what” level:
• “computational”-“why” level:
math-functional
teleological
Algorithms Can Be Multiply Teleological
• To G1, do P
• To G2, do P
– If G1 ≠ G2 & G1 !≤ G2, then 2 algorithms?
– But only 1 P, so only 1 algorithm?
• chess-wargame computer
Can P Succeed but G Fail?
• Examples:
– blocks-world robot
– HS recipe on Moon
– GCD in base 13
• Wide, external-semantic perspective:
– HS fails on Moon (even if recipe verifiable)
– GCD in base 13 doesn’t compute GCD (?)
• Narrow, internal, syntactic perspective:
– HS works on Moon (even if produces goop)
– both GCDs work, but only one is usable (?)
• Differences due to I-O interpretations (G-P interface),
not due to P itself
4 Neo-Marrian Levels
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•
•
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“what” level:
Do f(i) = o
“why” level:
To G, do f(i) = o
“algorithm” level:
To G, do Af(i) = o
“implementation” level: To G, do I(Af)(i) = o
• NB: The “to” and “do” clauses can vary independently
– of course:
– but also:
one G, many A
one f or A, many G
(multiple realizations)
(as we’ve seen)
Do We Compute with Symbols or Meanings?
• TM: with symbols (numerals, not numbers)
– we need algorithmic semantic interpretation
– (recursive functions: with numbers & functions)
• If we compute with symbols, then:
– chess-wargame computer is 1 algorithm
– HS works on Moon
• If we compute with meanings, then:
– chess-wargame computer uses 2 algorithms
– HS fails on Moon
Do We Compute with Symbols or Meanings?
• Piccinini − 2 questions:
– “Which TM is this?”
• has only 1 (syntactic) answer
• = my neo-Marrian “what” level
– “What does this TM do?”
• has n+1 answers:
– 1 syntactic answer
– n semantic answers (for n different Gs)
• = my neo-Marrian “why” level
• Piccinini’s patterns vs. colors:
– Loom that weaves (outputs) pattern p
does so independently of input thread colors c
• algorithm is insensitive to input
• if p = pattern above, then:
if c = (red, white, blue), then O/P =
else if c = (red, black, green), then O/P=
– “Is p more important than c?” --- wrong question
• If just want p, then c unimportant
• If want American flag, use c=RWB;
– need specific I/P
Syntactic Semantics
• Usually:
– ‘syntax’ = grammar of a language
– ‘semantics’ = relation of syntax to meanings/world
• Morris:
– syntax = properties & relations of elements of 1 set
• internal, local, narrow: intra-system
– semantics = relations between elements of 2 sets
• external, global, wide: extra-system / inter-system
• “what”-level P (f or A) can be identified syntactically
• “why”-level G needs to be identified semantically
– then P can be interpreted semantically in G’s terms
2 Ways to Get Syntactic Semantics
1. Named subroutines
– repeat 4 [forward 1 right 90]
– to square
repeat 4 [forward 1 right 90]
end
– turnleft;turnleft;turnleft
– DEFINE-NEW-INSTRUCTION turnright AS
BEGIN
turnleft;turnleft;turnleft
END
1. Named Subroutines
• McDermott’s Warning:
– The name is meaningless!
– Unless linked to concepts / objects external to program
• external semantics
– Or linked to other parts internal to program
• syntactic semantics
• Syntactic semantics ≈
Rescorla’s “indigenous” semantics
– causal, rather than conceptual-role
– “intra-system” semantics
2 Ways to Obtain Syntactic Semantics
2. Internalization:
– Can turn external semantic relations
into internal syntax (syntactic semantics)
– by internalizing semantic domain
into syntactic domain
SYN
DOM
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Syntax
SYN
DOM
SYN
DOM
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Syntax
SEM
DOM
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•
Semantics
SYN
DOM
SYN
DOM
Syntax
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SEM
DOM
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Semantics
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•
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Syntactic
semantics
Internalization via Perception
• Perception = I/P encoding
– Brain:
•
interpretation of external world in biological neural net
– TM “perception”:
•
interpretation of external (user) I/P on tape
– That interpretation becomes part of TM/brain’s
intra-system, syntactic/indigenous semantics
SYN
DOM
SEM
DOM
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extra-system
semantics
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I/P encoding
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TM or mind/brain
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intra-system
semantics
TM tape / biological neural net / mental concepts
representing external semantic domain
S.C.Shapiro’s Internalization Tactic
• Algorithms are teleological & narrow!
“To G, do P” must include everything:
–
–
–
To make HS on Earth, do P
To find GCD in base 10, do Q
To play chess, do R,
where R’s vars range over chess pieces & chess board
– To simulate wargame battle, do R,
where R’s vars range over soldiers & battlefield
• Cf. Deduction Thm: G |- P equiv |- if G then P
• Once all of G has been internalized as pre/postconditions of P,
then can formally verify even teleological algorithms
–
modulo Fetzer’s worry…
(later)
Hypercomputation
• Interactive, reactive, oracle computation
– TMs don’t accept I/P from external world,
but interactive oracle computers do!
• Can simulate I/A computer by statically
pre-storing all I/P
– Kleene Substitution/Recursion
• But computers must act in the world
– Interaction requires dynamic I-O & interpretation
– giving rise to G-P “slippage”
Program Verification
• Internalization & syntactic/indigenous semantics
allows for program verification of teleological algorithms
• But there are limits:
– Fetzer’s limit: real world can “break”
– B.C.Smith’s limit:
• syntactic computers deal with representations of (partial) models of world
– twice removed from reality
• no way to verify that the model is correct
– there’s a “gap” between model & world
– akin to Church-Turing Computability Thesis “gap” between formal & informal
Concluding Remarks
• Either: Can distinguish between:
– algorithms
– algorithms for accomplishing G
– G & P can vary independently
(P)
(To G, do P)
• Or:
– all P accomplish some G
– some Gs are more “interesting” than others
– Ps with uninteresting Gs may become useful
• cf. non-Euclidean geometry, Hilbert spaces, etc.
Concluding Remarks
• Mathematical computation theory studies P
• To decide if G is computable,
– need to find appropriate, computable P
– some P can accomplish multiple Gs
– some P may be verifiable but fail to G
because of real-world interface (I-O encoding)
– at that interface, we face Smith’s gap
• But computer will still act in real world
– whether it does what was intended is another matter!
– there are no “partial functions” in the real world!
Concluding Remarks
• Can make teleological algorithms more likely to
succeed by…
• Internalizing G into P
– Converts explicit “To G, do P”
to P (with implicit G)
– Can internalize by:
• expressing G as pre-/post-conditions of P
– “specs can & should be embedded as comments in code”
» Leslie Lamport, CACM 2015
• expressing G using named subroutines (modules)
– uses syntactic/indigenous semantics
– can connect to external/inherited semantics
Concluding Remarks
• My goal:
– To show how “computing & the world”
permeates the philosophy of computer science
• I have raised more questions than I have answered
• That’s what philosophy is supposed to do!