A Critique of Pure Reason

1. A Critique of Pure Reason by John McDermott (1987) in Computational Intelligence, 3, pp. 151-160, with commentaries pp 161-237. as (mis)interpreted by Peter Clark

2. PART I: McDermott’s Position

3. But! • Assumption:A significant amount of thought is deductive • Claim: This isn’t the case! • Implication: The logicist approach to AI is doomed. The Logicist’s Argument • AI programs need a lot of knowledge • We should write down that knowledge in FOL • Forget about “grubby details” of programming; instead study knowledge “free from the confines” of computer programs “You cannot write down axioms independent of a program for manipulating them if the inferences you are interested in are not deductions...Hence we must resign ourselves to writing programs.”

4. Some Examples “If I come across an empty cup of soda pop that was full a while ago, I may infer that my wife drank it, but that isn’t a deduction.” “[Deductive planning] is an interesting problem, but it has nothing to do with planning as practiced by…ordinary people…Could you have proven [your last] plan would work?” “The clock is two minutes fast. So perhaps the battery-powered clock is inaccurate.” “Your car is probably where you left it last.” Medical diagnosis. “Birds normally fly.”

5. Six Defenses of Logicism • The Idealization defense: • View deductive formulations as idealizations (eg. Planning) • But: • “Many concepts from the real domain will not be found in the idealization. Contrariwise, there is a danger that too many concepts from the ideal domain will not be found in the real one, and the idealization will be so askew as to be useless.”

6. Six Defenses of Logicism • The Idealization defense • The Vocabulary defense • We can provide a deductive theory of “fuzzy” predicates, eg. “interesting-concept(C)”, “appears-provable(theorem)”. • But: • Show me one! “So far it hasn’t helped.”

7. Six Defenses of Logicism • The Idealization defense • The Vocabulary defense • The “Queen of Sciences” defense • Non-deduction = variant of deduction • eg. Abduction = “inverse deduction” (Q, PQ, hence P) • But: • often we can’t prove a consequence Q from an explanation P, but we’ll believe P anyway. • Eg. “Selma won the lottery twice.” (Q). Explanation: “Occasionally someone wins twice.” (P). But P doesn’t Q. • Many explanations possible! Abduction to weak (no preference) • Eg. “My clock radio was two minutes fast.” hence: “running slow”? “someone changed the clock”? “cosmic rays”? • “The no. of planets is the least odd square of a prime”  9 planets

8. Six Defenses of Logicism • The Idealization defense • The Vocabulary defense • The “Queen of Sciences” defense • The “Metatheory” defense • Meta-knowledge to manipulate deductive theories • But: • vacuous! What is the meta-theory? • “If you can craft metatheories of arbitrary power, we might as well admit we are programming after all.” • “You will have to construct a very complex model, and long before you are done it will be irrelevant whether it’s a deductive metatheory or a Lisp program.”

9. Six Defenses of Logicism • The Idealization defense • The Vocabulary defense • The “Queen of Sciences” defense • The “Metatheory” defense • The “Deducto-technology” defense • We can write Prolog programs, so deduction’s okay! • But: • Any computation is in some sense deduction = meaningless argument • “Deduction doesn’t provide a theory of computing arbitrary things, just verifying them.”

10. Six Defenses of Logicism • The Idealization defense • The Vocabulary defense • The “Queen of Sciences” defense • The “Metatheory” defense • The “Deducto-technology” defense • The “Non-monotonic” defense

11. The Non-Monotonic Defense • Allow non-monotonic reasoning • “Your car is still where you parked it last” • “Birds normally fly” • But: • Logicist approach to this is hopeless: • unusable: often not clear what the consequences of a theory are • “Logicists use nonmonotonic constructs, and state in the accompanying text what conclusions they hope will follow, without really knowing if they will.” • too weak: doesn’t draw the conclusions we want anyway! • Yale shooting: Fred alive, gun loaded, fire gun -- does Fred die, or does gun unload? • Can write a program instead…but now we’re back where we started.

12. Doing without Deduction... • Not much inference is deductive... • “So no matter how many axioms you write down, most of the inferences you want will not follow from them. For that to happen, you must also supply a program. There is no way to develop a ‘content theory’ without a ‘process model’.” • Can’t we just axiomatize what our programs do? • “The chances of being able to find a denotational semantics for any such system are slim.” • “If a student comes to me with a denotationless representation, the student can always point to his program and claim it doesn’t draw absurd conclusions. If the program works, what’s wrong with it?” “You cannot write down axioms independent of a program for manipulating them if the inferences you are interested in are not deductions...Hence we must resign ourselves to writing programs.”

13. PART II: Responses to McDermott’s Position

14. But! • Assumption:A significant amount of thought is deductive • Claim: This isn’t the case! • Implication: The logicist approach to AI is doomed. The Logicist’s Argument • AI programs need a lot of knowledge • We should write down that knowledge in FOL • Forget about “grubby details” of programming; instead study knowledge “free from the confines” of computer programs “You cannot write down axioms independent of a program for manipulating them if the inferences you are interested in are not deductions...Hence we must resign ourselves to writing programs.”

15. Six Defenses of Logicism • The Idealization defense • The Vocabulary defense • The “Queen of Sciences” defense • The “Metatheory” defense • The “Deducto-technology” defense • The “Non-monotonic” defense

16. Resign ourselves to programming? “You cannot write down axioms independent of a program for manipulating them if the inferences you are interested in are not deductions...Hence we must resign ourselves to writing programs.” “So no matter how many axioms you write down, most of the inferences you want will not [deductively] follow from them. For that to happen, you must also supply a program. There is no way to develop a content theory without a process model” MikeU: Is this obviously true? Controversial?

17. Resign ourselves to programming? • Reiter: • “The obvious question is: Why is programming the only option for characterizing unsound inferences?....Whenever a content theroy provides a specification of the conclusions sanctioned by its axioms, an accompanying process model needn’t be provided. But now we see deduction is no way central to process-free axiomatizations...All we need is a nonprocedural specification of those conclusions that we wish to draw from the axioms [deductive or otherwise]....Content theories are precise specifications of the conclusions they sanction, whether or not their conclusions are deductively obtained” e.g Circumscription

18. Resign ourselves to programming? • McDermott: • “If the program works, what’s wrong with it?” • Brachman: • “There’s no convincing sens of ‘works’ without an independent account of what the program should be doing. The flip side of McDermott’s argument is that you cannot just write a reasoning program aqnd expect it to work without saying something about what kind of inference you want it to make in the first place.”

19. Resign ourselves to programming? • McDermott: • “If a student comes to me with a denotationless representation, now all I have is indigestion. The student can always point to his program and claim that it doesn’t draw absurd conclusions from his absurd notation. The fact that I might draw an absurd conclusion is my problem.” • Hayes: • “No, it means the account he gave me of what his notation meant was wrong.” • “Having a model theory should not be a big deal for some notation that claims to talk about the world. It’s such a small matter, in fact, that the shoe is really on the other foot: How can one justify using a notation that doesn’t have a model theory?” • “All a model theory amounts to is a systematic account of the way in which the notation can be related to some kind of possible world.” • Schubert: “No notation without denotation [McDermott]”

20. Are most inferences non-deductive? • Schubert: • “Faulting deduction for not delivering plausible conjectures is like faulting addition for not delivering arithmetic quotients and square roots.” • “A lot of thinking is deductive, even if a lot isn’t. If you have found out that Mary has a poodle, and asked whether she has a dog, you will deduce an affirmative answer.” • “One must learn to walk before one can run” • Hayes: • “I think it’s productive to assume that a lot of the mundane inference-making is closely related to deduction.” • “How much thinking is deductively valid? Not all, but certainly a substantial portion.” • “The NP project never assumed all a thinker did is deduce.”

21. Are most inferences non-deductive? • Hayes: • “How much thinking is deductively valid? A ‘substantial portion’, and more still is closely related to deductive relationships, for example almost all explanations.” • Schubert: • “Suppose an astronomer observes an oscillation in the position of a start, and explains this by postulating a dark companion. Surely part of a justification would consist of a demonstration that the observed oscillation follows from the assumed dark companion.” • McDermott: • “Hayes says: ‘Surely whatever else an explanation of Q must be, it should at least allow us to deduce Q.’ What is argument overlooks is the possibility that Q might be made quite plausible without being true in all models of P. I conjecutre all explanation one ever hear or invents have this “flaw”.”

22. Can we axiomatize our programs? • Forbus, Bobrow: • The deductive component of our systems are crucial and work fine. • McDermott: • Sure, logic’s okay s a component, but a Logicist says that’s all there is. • “It is difficult for a nonlogicist to grasp the awesome centrality of logic in the worldview of the logicist. It is not enought htat logic be one useful technique among many.” • deKleer: • I’ve a very nice truth maintenance system. • McDermott: • “There are a zillion ways to be non-monotonic. Nonmonotonic logic accounts for almost none of them.”

23. Can we axiomatize our programs? • McDermott: • “The chances of being able for find a denotational semantics for any such system are slim.” • “Forbus’s axioms [describing his program] seem silly. None of the conclusions Forbus wanted actually follow from them. This didn’t bother Forbus, who had a perfectly reasonable program to draw those inferences.” • [Or he’d failed to articulate what his program was doing? ] • “Most inference programs embody knowledge that goes beyond any collection of axioms, so they are unlikely to be dreived from such a collection (and no-one is ever going to bother to squeeze axioms out after the program is writen)...” • Allen: • “Rather, logicists share a belief that only formal theories are precise enough to be understood by others besides the original author.”

24. What was the Goal of the Logicists? • JohnB: Logic is only good for toy problems. • Hayes original manifesto: • complains about AI’s emphasis on “toy worlds” and urges the field to “put away childish things by building large-scale formalizations.” • “The subject [of AI] badly needs some non-toy worlds to experiment with.” • “The study of inferential control is one of the most important facing AI at present. But until we have some dense theories to experiment on, we won’t know what the real problems are.”