The Lucas-Penrose Argument

Brace yourselves, this one can melt your brain.

In the early 20th century, it was thought that mathematics could be made into a complete formal system. This is a system in which every element has a complete definition, every entailment is deductive (so that conclusions necessarily follow from premises), and which contains no contradictions. But some basic concepts are unformalizable. "Truth," for example, allows us to form the Liar Paradox: "This statement is not true." If it's true, then it's false, and if it's false, it's true. So no formal system can have a truth predicate in it. (This isn't a mark against truth, btw.) One motive for this is a system with a contradiction leads to the principle of explosion, since ex falso quodlibet -- from a contradiction, everything follows.

Anyhoo, Kurt Gödel, inarguably the greatest logician of the 20th century, suggested we use a concept in place of truth that IS formalizable and doesn't lead to a paradox: provability. "This statement is not provable" doesn't lead to a problem like the Liar Paradox. But since such a statement can be made within any formal system, and since any such system must involve deductive provability, it follows that there can be no complete formal system. This is the intuition behind Gödel's Incompleteness Theorems. We'd been chasing a mirage.

This was around 1930. About the same time we had huge strides made in artificial intelligence by the likes of Alan Turing, Alonzo Church, etc. Turing came up with the idea of a Turing machine, which is an instantiation of a formal system, the cause-and-effect processes of the machine standing in for the deductive ground-consequent relations of the formal system. But since any formal system will have a statement within it to the effect of "This statement is not provable within this system" (called a Gödel sentence), such would also have to be the case for a Turing machine.

This is a problem because a Turing machine can only affirm provable claims, so any given machine will have a Gödel sentence which it cannot affirm. Human minds, however, have no such limitation: we can see that there is a Gödel sentence within our own systems of thought and affirm it, recognizing that it is correct. It is correct that "This statement is not provable within this system" is not provable within that system. This has two consequences: 1) Human minds cannot be reduced to Turing machines. They cannot be fully explained by the mechanistic cause-and-effect processes that are going on in the brain. There is an element of the mind that goes beyond it, and this element is truth-conducive. 2) Turing machines, and artificial intelligence in general, cannot fully duplicate the processes of human minds. They may be able to duplicate the end-products, but they can't produce them the same way that human minds do: through non-deductive (non-formal) reasoning. They can only do it via mechanistic cause-and-effect processes which don't have to be truth-conducive in order to arrive at those end-products.

This conclusion was reached by Gödel himself in his 1951 Gibbs Lecture, "Some Basic Theorems on the Foundations of Mathematics and Their Implications", but it wasn't published until the third volume of his Collected Works came out in 1995. J.R. Lucas -- who in writing this post I have learned passed away earlier this year, which devastates me -- however, wrote an enormously influential essay in 1961, "Minds, Machines, and Gödel" which presented the same idea. It motivated a lot of objections which Lucas responded to in philosophy journals, and then he published his book "The Freedom of the Will" in 1970, the last third of which is on the implication of Gödel's Incompleteness Theorems for the mind and AI. You can read most of his essays online at https://web.archive.org/web/20160718073705/http://users.ox.ac.uk/~jrlucas/. Later, mathematical physicist Roger Penrose defended the argument in his own way in his books The Emperor's New Mind and Shadows of the Mind.

Simple, no?

Gödel and mechanism

The Stanford Encyclopedia of Philosophy has a new entry on Gödel's Incompleteness Theorems (they also have an entry on Kurt Gödel himself). A subcategory of the article is on Gödelian arguments against mechanism, which, as is often the case, paints a somewhat bleak picture of such arguments' success. In addition to listing J.R. Lucas as a proponent of an anti-mechanist argument à la Gödel, the article also mentions mathematical physicist Roger Penrose who argued along these lines in The Emperors New Mind and Shadows of the Mind (and elsewhere). Two other philosophers the article points me to, who I was unaware had argued similarly, are John Searle in The Mystery of Consciousness and a couple of essays by Crispin Wright (along with a rebuttal by Michael Detlefsen). So I have some reading to do.

Paraconsistency

Here is the Stanford Encyclopedia of Philosophy's entry for Paraconsistent Logic. I think you probably need to embrace some form of paraconsistency if you're going to reject J.R. Lucas's Gödelian Argument against physical determinism, in order to avoid explosion. In fact, I think Douglas Hofstadter does precisely that.

C.S. Lewis's Argument against Naturalism, part 7

Further Objections and Influences
In addition to objections made specifically against C.S. Lewis’s argument, other objections have been made to similar arguments that have relevance to it. I will now go over those I have encountered.

Computers
Computers process information, and yet are completely physical in nature. Their processing functions are entirely cause-effect rather than ground-consequent, but they still give the right answers.{1} Therefore, this shows that we need not posit something more than the physical world with its cause-effect relations in order to account for the validity of our reasoning processes.

While Lewis did not directly address this objection, he did present an argument that can be seen as relevant to it: his claim that a news broadcast cannot be reduced to the functioning of the television set. If a broadcast were entirely produced by the functioning of the set, we would not ascribe any degree of validity to it.{2} This holds true of computers as well. The reason why we ascribe validity to the functioning of a computer is precisely because there is something “behind” it; namely a programmer, an intelligent agent, who designed it. If we thought the computer’s programming was the result of some random, non-intelligent process, we would not trust its results. Even if the results turned out to be true, it would not have reached those results because they are true. As William Hasker writes,

Computers function as they do because they have been constructed by human beings endowed with rational insight. And the results of their computations are accepted because they are evaluated by rational human beings as conforming to rational norms. A computer, in other words, is merely an extension of the rationality of its designers and users; it is no more an independent source of rational thought than a television set is an independent source of news and entertainment.{3}

Appealing to computers as purely physical processors of information begs the question. The only reason they can process information is because of the human being standing behind it, who organizes it in such a way that the computer’s cause-effect processes correspond to the programmer’s ground-consequent processes. And whether that human being’s capacity to process information can be reduced to purely cause-effect physical processes is precisely the question under discussion.

Perhaps a related objection could be made at this point. The naturalist might say that the supernaturalist view of God endowing us with the capacity to reason is exactly parallel to our endowing computers with the capacity to process information. Thus, any claim that computers do not really reason applies equally to us, and so there must be something wrong with such claims. Again, Lewis makes a point that is directly applicable: “to talk thus is, in my opinion, to forget what reasoning is like. … Reasoning doesn’t ‘happen to’ us: we do it. … human thought is not God’s but God-kindled.”{4}

Self-reference as nonsensical
Alfred North Whitehead and Bertrand Russell argue in Principia Mathematica that self-reference leads to contradictions, and is therefore nonsensical.{5} If we allow it, it leads to Russell’s paradox: we can think of classes that belong to themselves; for example, the class of concepts is a concept itself. We can also think of classes that do not belong to themselves; for example, the class of blue things is not itself blue. The problem comes in when we ask this about the class of classes that do not belong to themselves. If this class belongs to itself, then it does not belong to itself; and if it does not belong to itself, then it does belong to itself. This creates a vicious circle from which there is no escape.

The only way to avoid this, Russell and Whitehead argue, is to disallow all self-reference. This would make the concepts of classes that do or do not belong to themselves incoherent, and so the paradox is avoided. They apply this to a common refutation of skepticism: a man says we cannot know anything, and a detractor then asks him whether he knows that we cannot know anything. If he does, then his statement is false, and if he does not, then it remains possible for us to know something. Yet the question, “do you know that we cannot know anything?” is self-referential, and therefore nonsensical. “Hence any significant scepticism is not open to the above form of refutation.”{6}

Now go back to Lewis’s argument: if all of our beliefs are caused by nonrational processes, this would include the belief that all of our beliefs are caused by nonrational processes. Therefore, such a belief would not be rational, and is thus self-refuting. However, according to Russell and Whitehead, such an argument is incoherent because it refers to itself.

The first problem to note here is that self-reference is unavoidable. If we say, “no proposition can be self-referential,” then this would either apply to this proposition itself, or it would not. If it does not apply to itself, then it is false, since there remains a proposition that can be self-referential; that is, the ban on self-referential propositions does not apply to it, in which case it would remain possible for that proposition to refer to itself. On the other hand, if it does apply to itself, then it refers to itself; which leads to contradiction, since the statement that propositions are not self-referential is a self-referential proposition. So the ban on self-referential statements is either false or contradictory; regardless, in either case, we end up with self-reference.

Another problem is that many self-referential statements seem perfectly coherent. Semantic paradoxes, such as “this statement is false,” can be incoherent, but this is “neither due to the fact that they arise in self-referential statements nor to the fact that the self-reference is semantic. The precise difficulty is that there are no propositions expressed in these supposed statements; there is nothing definite to which the referring terms might refer. Like a mirage, the supposed referent continually recedes.”{7} What this demonstrates is that there are different types of self-reference, and not all of them are problematic.{8} “Russell and Whitehead regard as identical in kind the self-reference of the application of formal notions to themselves, the self-reference of the semantical paradoxes, and the performative self-reference of skepticism. These are clearly different, as are the paradoxes which arise in each case.”{9}

So what of Russell’s class of all classes that do not belong to themselves? One can simply deny that such a class exists without thereby discounting all examples of self-reference. The class of all classes that do not belong to themselves is incoherent, but it does not lead to a genuine antinomy, like the liar paradox.{10} On the other hand, the skeptic who says we cannot know anything is making a performative self-referential statement. Such statements “imply certain propositions about their speaker, their audience, and so on. If the implied propositions are false, then the utterance is irrational. … There is nothing formally wrong with the circularity involved in this fallacy. The fallacy arises because the circularity makes impossible the successful achievement of the purpose of the argument.”{11} Thus, the skeptic is refuted by the detractor who says that if we cannot know anything, we cannot know that we cannot know anything: “We are always prevented from accepting total scepticism because it can be formulated only by making a tacit exception in favour of the thought we are thinking at the moment.”{12} Similarly, Lewis’s argument, that if naturalism is true, we could have no reason to think it is true, still stands.

Begging the question
Eliminative materialists argue that all mental properties, such as beliefs, can be reduced to non-intentional content, and explained in purely physical terms of the brain’s biochemistry. Moreover, the brain’s function is derived from the struggle for survival, so the pursuit of truth is irrelevant to it. Such concepts (“belief,” “truth”) amount to “folk psychology,” the popular way of thinking about our minds that is no more valid than folk religion. “Looked at from an evolutionary point of view … a nervous system enables the organism to succeed in the four F’s: feeding, fleeing, fighting, and reproducing. The principal chore of nervous systems is to get the body parts where they should be in order that the organism may survive. … Truth, whatever that is, definitely takes the hindmost.”{13}

There are, of course, many possible objections one could raise to this position -- for example, whether folk psychology constitutes a hypothesis. However, when Paul Churchland presented this thesis, one of the first questions put to him was whether this applied to his own beliefs regarding eliminative materialism.{14} This is very similar to Lewis’s argument from reason. It seems as though the eliminativists are asking us to believe that there are no beliefs. In order to be consistent, they would have to say that they are not asking us to believe their thesis, that they do not even believe it themselves, and that, at any rate, eliminative materialism is not true (or has no truth-value). But then it becomes exceedingly difficult to continue paying attention to them.

The response has been that such objections beg the question. It assumes that the tenets of folk psychology are the only way to explain how our minds work. However, if these tenets can be reduced to the physical -- which is, after all, the premise of eliminative materialism -- then there is another way to explain how our minds work. Once we have achieved a complete cognitive science, “truth” and “belief” will be replaced with “successor concepts.”{15} We may not have fully achieved it yet, but it’s coming. Thus, charging eliminative materialism with self-refutation is analogous to charging the denial of vitalism with self-refutation. After all, the anti-vitalist would not be alive to deny vitalism if he did not have a vital spirit.{16}

Many remain unconvinced. For one thing, the analogy is a poor one. The appropriate parallel would be an anti-vitalist who argues that he is not alive.{17} However, the anti-vitalist is not denying that he is alive; he just has a different conception of what “being alive” means. The eliminativist, on the other hand, does not merely have a different conception of what “having a belief” means; he is denying that we have beliefs at all. Beliefs are to be “eliminated,” they are to be evacuated of any intentional content. Insofar as he appeals to these successor concepts, the eliminativist is not merely giving a different definition of belief; he is denying it altogether.

Another problem is that these successor concepts are empty: we literally have no idea what they might entail; if this were not the case, it would be incumbent upon the eliminativist to produce them. This means, however, that the eliminative materialist cannot employ them in explaining his theory. Say the successor concept for “believe” is “believe_suc.” When asked if he believes that there are no beliefs, he can respond, “No, I do not believe that there are no beliefs; however, I believe_suc that there are no beliefs.” Unfortunately, as Hasker writes,

It is important to realize that this option is not available. We simply have no grasp of these successor concepts, and cannot use them to make any assertions, no matter how they are named. Indeed, we have no assurance (as Churchland’s scenario makes clear) that the roles played by the successor concepts will be even “remotely analogous” to those occupied by the concepts of our present scheme. No. The concepts involved … the only concepts available to him, are precisely the concepts of the commonsense conception renounced by eliminativism. The charge of falsehood and contradiction remains. And if a theory which admittedly contains self-contradiction and massive falsehood is not self-refuting, what more does it take?{18}

Or to put it another way, I very much doubt an eliminativist would be willing to grant to his opponent the use of terms that have no meaning in order to argue that eliminativism is false -- especially if the argument’s validity hinges on those terms.

Yet another problem is that there is no evidence that these successor concepts can ever be developed; indeed, the evidence available to us seems to indicate that they cannot.{19} The eliminativist may respond that thousands of years ago, there was insufficient evidence that the sun is the center of the solar system; so the absence of evidence today does not prove that such concepts will never be developed. However, there are two problems with this: first, simply pointing out that true things are not always accepted does not do much to advance one’s claims in the face of contrary evidence. After all, thousands of years ago there was no evidence that fire is cold, or stones fall upward, or two plus two is five either.

Second, while the available evidence did not support the heliocentric model thousands of years ago, such a model would have been completely understandable in the terms employed by geocentrists. They understood what the terms “sun,” “earth,” “center,” and “revolve” mean, and could therefore comprehend the claim that the sun is the center of the solar system, although they would have denied it. This is true of all modern science; we might have to introduce new concepts and terminology, but we would still ultimately be able to explain it to a pre-modern. The claim of the eliminativist, however, is that these successor concepts are completely beyond our imagining; again, if they were not beyond our imagining, it would be incumbent upon him to produce them.

Moreover, the appeal to a future science that would dispel all appearance of inconsistency would be available to any self-refuting statement; in which case, self-consistency would no longer be needed nor desired. In this scenario, self-refuting statements only appear to be contradictions within the limitations of the tenets of the folk psychology that we use to express ourselves. When cognitive science has advanced sufficiently so as to provide us with successor concepts for these tenets, however, the apparent inconsistencies will disappear.

What this demonstrates is that this scenario amounts to a deus ex machina: anything can be explained by it. Of course, the eliminativist might counter that our displeasure with deus ex machina solutions is just another aspect of folk psychology, and will be eliminated along with everything else when the revolution comes -- and that is precisely the point: any conceivable objection could be dismissed on the grounds that it will no longer hold once it is reduced to the successor concepts.

Finally, by denying the concept of truth, eliminativists take away the only advantage they have in their corner. Any plausibility they may have is due to naïve scientific realism, “the view that science aspires to show us the real structure of the objective world, and our best present-day science is at least roughly successful in doing this.”{20} Eliminative materialism, however, is radically inconsistent with naïve scientific realism, since it holds that the brain’s function is not to pursue truth but to enable the organism to survive long enough to produce progeny. As Churchland writes, “Truth, as currently conceived, might cease to be an aim of science.”{21} Insofar as such a realism is unacceptable to eliminativists, whatever credibility they had is lost: if naïve scientific realism is false, “why be materialists at all, let alone eliminativists?”{22}

So it seems as though the eliminative materialist is unable to escape from “the threat of cognitive suicide.”{23} Lewis’s argument still holds.

Similar arguments and influences
Arguments similar to Lewis’s have played a significant role in philosophy. As the flipside of the computer objection mentioned above, J.R. Lucas writes that his Gödelian argument against strong AI (the theory that a computer can completely duplicate the processes of the human brain) is based on the same intuition as Lewis’s argument against naturalism.{24} Kurt Gödel proved that any mathematical system must assume the truth of statements that cannot be proved within the confines of the system itself; “truth is more than provability.”{25} Yet the human mind with its reasoning processes can transcend this limitation. Therefore, the human mind is more than just a computer, and no computer system will be able to completely duplicate it.{26} This argument has amassed a huge amount of literature, both for and against it, and there are hints of it in Bishop Berkeley’s 44th Query in The Analyst: “Whether the Difference between a mere Computer and a Man of Science be not, that the one computes on Principles clearly conceived, and by Rules evidently demonstrated, whereas the other doth not.”{27}

Alvin Plantinga’s argument against naturalism bears a striking resemblance to Lewis’s. According to Plantinga, if naturalism were true, the likelihood that we could form valid beliefs would be either improbable or inscrutable. Obviously, science depends upon our capacities to form valid beliefs; for example, for our belief in evolution to be valid, our abilities to perceive and assess the available evidence must be reliable. Thus, either evolution is true or naturalism is true. Not both.{28} Plantinga’s argument has also created its own literature,{29} with some explicitly linking it to Lewis’s.{30} The argument from reason also bears some similarity to the Transcendental Argument for God (TAG) employed by Christian presuppositionalist theologians.{31}

In 1985, John Beversluis wrote a critique of Lewis’s entire apologetic, with one chapter which deals with the argument from reason. In 2007 he published a significantly reworked second edition. Beversluis is something of an iconoclast, having also criticized Socrates and defended his interlocutors.{32} There is a tension in his critique of the argument from reason, insofar as he approves of G.E.M. Anscombe’s critique of it, but decries the “Wittgensteinian fideists” in general.{33} However, it is uncertain whether Anscombe’s critique still carries as much weight when divorced from its Wittgensteinian framework.

Victor Reppert, in addition to commenting on the argument against eliminative materialism mentioned above,{34} has defended Lewis’s argument against the criticisms of Anscombe and Beversluis, both in his book C.S. Lewis’s Dangerous Idea and in philosophical journals,{35} receiving criticism from Keith Parsons,{36} William Hasker,{37} and others.{38} Reppert has derived a family of arguments from Lewis, which can be summarized as follows:

1. If naturalism is true,
     a. “There is no fact of the matter as to what someone’s thought or statement is about.”
     b. “No states of the person can be either true or false.”
     c. “No event can cause another event in virtue of its propositional content.”
     d. “Logical laws either do not exist or are irrelevant to the formation of beliefs.”
     e. “There is no single metaphysically unified entity that accepts the premises, perceives the logical connection between them and draws the conclusion.”
     f. Our faculties are not “reliable indicators of the nonapparent character of the world.”
2. None of these statements is true.
3. Therefore, naturalism is not true.{39}

Conclusions and prospect
C.S. Lewis’s argument from reason has a great deal of relevance for the philosophy of mind, the contemporary status of which seems to be, largely, the attempt to explain the properties of mind in terms of naturalism. In fact, I would argue that in order for the argument from reason to be thorough today, it must address the issues of the philosophy of mind. William Hasker, for example, has done precisely this: the first chapter of his book, The Emergent Self, deals with eliminative materialism, the second with theories of supervenience, and the third presents his version of the argument from reason, employing possible worlds.{40} Other issues in the philosophy of mind, such as artificial intelligence, dualism, and mind-brain identity, will also be affected by Lewis’s argument.

In part 1 of this series, I wrote that Lewis’s argument is less ambitious than similar arguments from consciousness.{41} This is because if beliefs are determined by what is known, then they are true, epistemically justified, and hence valid, and we need not appeal to anything beyond this. However, if naturalism is true, beliefs are not determined by what is known. Even if, for the sake of argument, we granted that naturalism allows beliefs to be so determined, it does not demand it. As long as this is the case, naturalism cannot account for knowledge. In other words, in order for determinism to be compatible with knowledge, it would have to be a determinism in which every belief is caused solely by what is known.

Here's an example: if some of my beliefs may be false or unjustified, how will I decide whether a particular belief is? Any belief I draw about that belief may itself be false or unjustified, and so would require its own justification; and so on, ad infinitum. This can be applied, for example, to the claim that religious beliefs are a sort of evolutionary holdover that should be rejected now that they no longer play a role in our survival. The obvious response is, why couldn’t a similar argument be used to dismiss these beliefs about religious beliefs? What makes them immune to the same criticism? The simplest way to avoid this is to allow for all of our beliefs to be true and justified, so this scenario never arises.

But of course, this is not the world we live in. People have contradictory beliefs. When beliefs are caused by what is known, innumerable other factors play a role in their occurrence as well. Therefore, in order to be able to distinguish between beliefs determined by what is known from beliefs not so determined, it is necessary to posit a “space” where we can step back from these beliefs and assess them independently of how they occurred in the individual’s mental life. This roughly lines up with what people mean by “consciousness.” Moreover, this means that we have to posit some sort of free will. The only determinism we can accept is one in which all beliefs are solely determined by that which makes them true, because then the belief that determinism is true could be trusted. Any other kind of determinism would lead to the infinite regress problem noted above.

I have been analyzing Lewis’s argument only insofar as it relates to whether naturalism is true or false, but of course, Lewis did not leave it at that. He argued that, since naturalism cannot be true, we have to posit a supernaturalist worldview in order to account for our reasoning processes. Note that he is not presenting a false dichotomy between naturalism and supernaturalism: he discusses another possibility, namely, the sub-natural or indeterminism. However, something less that naturalism does not solve the problem. We need something more than naturalism. In order for us to have any knowledge, including scientific knowledge, we have to presuppose that there is more than just the natural world of cause-effect events. Science presupposes supernaturalism.

Thus, Lewis’s argument also has drastic repercussions for the philosophy of science. Science is usually thought to presuppose naturalism, and there is an intuitive appeal to this. We observe natural cause-effect events in a natural world, so obviously the systematic study of these natural effects must begin by trying to find their natural causes. If we allowed ourselves to explain natural effects by positing unobservable supernatural agencies, further investigation would be stultified: “the only way that any sort of science can proceed is to assume that there is no divine intervention and to see how far one can get with this assumption.”{42} The more natural causes science discovers, the less room there is for supernatural causes.

But according to the argument from reason, since our formulation of scientific hypotheses and assessment of evidence must be rational acts in order for the hypotheses and assessments to be valid, and since naturalism precludes the potential for any belief to be valid, science is incompatible with naturalism. Some might object that the intuitive appeal of the claim that science must presuppose naturalism overwhelms any abstract argument to the contrary. I would argue, however, that the argument from reason is at least as, if not more, intuitive. When one claims that the mechanical processes of nature wholly determine our beliefs, the question that immediately presents itself is, what about that belief? What about the belief that “the mechanical processes of nature wholly determine our beliefs”? It seems that the arguer is making an exception for the belief he is holding at the moment.

Lewis is sometimes accused of being hostile to science, but this is incorrect. He is hostile to scientism, the claim that science can explain everything,{43} and he sees the argument from reason as a chink in the armor of this view. He is not trying to suggest that the world science has revealed is wrong so much as that it is incomplete: “Science is a good servant but a bad master, a good method for investigating and manipulating the material world, but no method at all for deciding what to do with the knowledge and power acquired thereby.”{44} We need to supplement scientific knowledge with knowledge of a different kind, and from a different source, in order to achieve the full life.

We were told it all long ago by Plato. As the king governs by his executive, so Reason in man must rule the mere appetites by means of the ‘spirited element.’ The head rules the belly through the chest -- the seat, as Alanus tells us, of Magnanimity, of emotions organized by trained habit into stable sentiments. The Chest -- Magnanimity -- Sentiment -- these are the indispensable liaison officers between cerebral man and visceral man. It may even be said that it is by this middle element that man is man: for by his intellect he is mere spirit and by his appetite mere animal.{45}

Those who seek to explain everything in terms of science or physics or nature are essentially trying to remove this middle (and hence, central) element. Lewis thinks such attempts amount to “The Abolition of Man.”

It is an outrage that they should be commonly spoken of as Intellectuals. This gives them the chance to say that he who attacks them attacks Intelligence. It is not so. They are not distinguished from other men by any unusual skill in finding truth nor any virginal ardour to pursue her. … It is not excess of thought but defect of fertile and generous emotion that marks them out. Their heads are no bigger than the ordinary: it is the atrophy of the chest beneath that makes them seem so.{46}

Probably the most significant contribution the argument from reason makes is to the relationship between science and religion. Since science is often equated with naturalism and the denial of supernaturalism, it is often seen as the antithesis of religion. However, the argument from reason resolves this tension: science does not and indeed cannot presuppose naturalism. For those who respect both science and religion, this conclusion is very encouraging. Unfortunately, some people’s interest in science seems to be due to its perceived iconoclasm. For them, building a bridge between the two would be anathema.

The argument from reason essentially pokes a hole in the façade of ontological naturalism. However, it is primarily a negative argument, arguing against a position rather than arguing for one. It does not provide any criteria on how we should proceed on a practical level. The issues it raises for the philosophy of science make this particularly evident. How can science function without presupposing naturalism? How can that which is teleological and non-mechanistic form a part of the prediction and falsification upon which science relies? How can we systematically observe that which is inherently unsystematic? These are the objections that most naturalists will pose in response to the argument from reason, and it seems to me that detailed responses are lacking.

Notes:
{1} Ignoring, for the sake of argument, that computers can be programmed to give the wrong answers.
{2} C.S. Lewis, Miracles: A Preliminary Study, 1st ed. (London: Bles, 1947), 50; 2nd ed. (London: Collins, Fontana Paperbacks, 1960), 43-44.
{3} William Hasker, Metaphysics: Constructing a World View (Downers Grove, IL: InterVarsity, 1983), 49, italics in original.
{4} Lewis, Miracles, 1st ed., 37; 2nd ed., 32-33.
{5} Alfred North Whitehead and Bertrand Russell, Principia Mathematica, vol. 1, 2nd ed. (Cambridge: Cambridge Univ. Press, 1927), 37-38, 60-65.
{6} Ibid., 38.
{7} Joseph M. Boyle, Jr., Germain Grisez, and Olaf Tollefsen, Free Choice: A Self-Referential Argument (Notre Dame, IN: Univ. of Notre Dame Press, 1976), 129.
{8} Ibid., 122-38.
{9} Ibid., 128.
{10} Ibid., 127-30.
{11} Ibid., 124.
{12} C.S. Lewis, “De Futilitate,” in Christian Reflections, ed. Walter Hooper (1967; Grand Rapids, MI: Eerdmans, 1977), 61.
{13} Patricia Smith Churchland, “Epistemology in the Age of Neuroscience.” The Journal of Philosophy 84 (1987): 548-49.
{14} Paul Churchland, “Postscript: Evaluating Our Self Conception,” in Paul K. Moser and J.D. Trout (eds.) Contemporary Materialism: A Reader (London: Routledge, 1995), 170-72.
{15} William Hasker, The Emergent Self (Ithaca, NY: Cornell Univ. Press, 1999), 7-8.
{16} Patricia Smith Churchland, “Is Determinism Self-refuting?” Mind 90 (1981): 99-101; idem, Neurophilosophy: Toward a Unified Science of the Mind-Brain (Cambridge, MA: The MIT Press, 1986), 397-99; Paul Churchland, “Eliminative Materialism and the Propositional Attitudes,” in A Neurocomputational Perspective: The Nature of Mind and the Structure of Science (Cambridge, MA: MIT Press, 1989), 21-22; idem, Matter and Consciousness: A Contemporary Introduction to the Philosophy of Mind (Cambridge, MA: MIT Press, 1984), 47-48; Andrew D. Cling, “Eliminative Materialism and Self-Referential Inconsistency,” Philosophical Studies 56 (1989): 53-75; William Ramsey, “Where Does the Self-Refutation Objection Take Us?” Inquiry 33 (1990): 453-65.
{17} Lynn Rudder Baker, Saving Belief: A Critique of Physicalism (Princeton, NJ: Princeton Univ. Press, 1987), 139.
{18} Hasker, Emergent Self, 18-9, italics in original.
{19} Ibid., 13.
{20} Ibid., 15, italics in original.
{21} Paul Churchland, “The Ontological Status of Observables: In Praise of the Superempirical Virtues,” in Neurocomputational Perspective, 150.
{22} Hasker, Emergent Self, 15.
{23} Baker, Saving Belief, 134-48; Victor Reppert, “Eliminative Materialism, Cognitive Suicide, and Begging the Question,” Metaphilosophy 23 (1992): 378-92.
{24} J.R. Lucas, “The Restoration of Man,” Theology 98 (1995): 453-55.
{25} Ibid., 455.
{26} J.R. Lucas, “Minds, Machines, and Gödel,” Philosophy 36 (1961): 112-27; idem, The Freedom of the Will (Oxford: Clarendon, 1970), 115-72.
{27} George Berkeley, De Motu and The Analyst: A Modern Edition, with Introductions and Commentary, ed. and trans. Douglas M. Jesseph (Dordrecht: Kluwer, 1992), 218. J.R. Lucas’s Web site contains most of his contributions, as well as an extensive bibliography . Etica e Politica, an online journal, republished some of the more important essays in 2003 . Michael Harris brought the Berkeley quote to Lucas’s attention .
{28} Alvin Plantinga, Warrant and Proper Function (New York: Oxford Univ. Press, 1993), 216-37; idem, “Naturalism Defeated” (1994), online; idem, Warranted Christian Belief (New York: Oxford Univ. Press, 2000), 227-40, 281-85.
{29} James Beilby, ed., Naturalism Defeated? Essays on Plantinga’s Evolutionary Argument against Naturalism (Ithaca, NY: Cornell Univ. Press, 2002).
{30} N.M.L. Nathan, “Naturalism and Self-Defeat: Plantinga’s Version,” Religious Studies 33 (1997): 135; Angus J.L. Menuge, “Beyond Skinnerian Creatures: A Defense of the Lewis and Plantinga Critiques of Evolutionary Naturalism,” Philosophia Christi 5 (2003): 143-65.
{31} Cornelius Van Til, The Defense of the Faith (Philadelphia: P & R, 1955), 116-22, 282-88.
{32} John Beversluis, Cross-examining Socrates: A Defense of the Interlocutors in Plato’s Early Dialogues (Cambridge: Cambridge Univ. Press, 2000).
{33} John Beversluis, C.S. Lewis and the Search for Rational Religion (Grand Rapids, MI: Eerdmans, 1985), 127-34. My comments here are based on the first edition, as the second edition had yet to be published when I originally wrote this.
{34} Reppert, “Eliminative Materialism, Cognitive Suicide, and Begging the Question”; idem, “Ramsey on Eliminativism and Self-refutation,” Inquiry 34 (1991): 499-508.
{35} Victor Reppert, ““The Lewis-Anscombe Controversy: A Discussion of the Issues,” Christian Scholar’s Review 19 (1989): 32-48; idem, “The Argument from Reason,” Philo 2 (1999): 33-45; idem, “Reply to Parsons and Lippard on the Argument from Reason,” Philo 3 (2000): 76-89; idem, “Several Formulations of the Argument from Reason,” Philosophia Christi 5 (2003): 9-33; idem, “Some Supernatural Reasons Why My Critics Are Wrong: A Reply to Drange, Parsons, and Hasker,” Philosophia Christi 5 (2003): 77-89.
{36} Keith Parsons, “Defending Objectivity,” Philo 2 (1999): 87-9 n. 7; idem, “Further Reflections on the Argument from Reason,” Philo 3 (2000): 90-102; idem, “Need Reasons Be Causes?” Philosophia Christi 5 (2003): 63-76.
{37} William Hasker, “What About a Sensible Naturalism?” Philosophia Christi 5 (2003): 53-62.
{38} Jim Lippard, “Historical but Indistinguishable Differences: Some Notes on Victor Reppert’s Paper,” Philo 2 (1999): 47-49; Theodore M. Drange, “Several Unsuccessful Formulations of the Argument from Reason: A Response to Victor Reppert,” Philosophia Christi 5 (2003): 35-52.
{39} Reppert, “Several Formulations of the Argument from Reason” 9-23; idem, C.S. Lewis’s Dangerous Idea: In Defense of the Argument from Reason (Downers Grove, IL: InterVarsity, 2003), 72-85. Bibliographies of arguments similar to Lewis’s, both for and against, can be found in James Jordan, “Determinism’s Dilemma.” Review of Metaphysics 23 (1969): 48 n. 1; William Hasker, “The Transcendental Refutation of Determinism,” Southern Journal of Philosophy 11 (1973): 175 n. 3; Boyle, et al., Free Choice, 181 n. 41-42; and Ted Honderich, A Theory of Determinism, vol. 1: Mind and Brain (Oxford: Clarendon, 1990), 361. In addition to the works referenced there, and thus far in the present work, I would also point to Joseph M. Boyle, Jr., Germain Grisez, and Olaf Tollefsen, “Determinism, Freedom, and Self-Referential Arguments,” Review of Metaphysics 26 (1972-73): 3-37; Robert Young, “A Sound Self-Referential Argument?” Review of Metaphysics 27 (1973-74): 112-19; Barbara Wootton, Testament for Social Science: An Essay in the Application of Scientific Method to Human Problems (London: Allen & Unwin, 1950), 92; George Trumbull Ladd, Philosophy of Mind: An Essay in the Metaphysics of Psychology (London: Longmans, Green, & Co., 1895), 233-34; Boyd H. Bode, “Consciousness and Psychology,” in John Dewey, et al., Creative Intelligence: Essays in the Pragmatic Attitude (1917; New York: Octagon, 1970), 253-54; James Bissett Pratt, Matter and Spirit: A Study of Mind and Body in Their Relation to the Spiritual Life (New York: MacMillan, 1922), 18-21, 156-66, 187-93; idem, “The New Materialism,” The Journal of Philosophy 19 (1922): 338; Richard Purtill, Reason to Believe (Grand Rapids, MI: Eerdmans, 1974), 43-47; Huw P. Owen, Christian Theism: A Study in Its Basic Principles (Edinburgh: Clark, 1984), 118; William Hasker, “Can Action Be Explained Mechanistically,” University of Dayton Review (1972): 53-61; A.C. Ewing, Value and Reality: The Philosophical Case for Theism (London: George Allen & Unwin, Ltd., 1973), 77-78, 177-78; Jonathan Bennett, Rationality: An Essay Towards an Analysis (London: Routledge & Kegan Paul, 1964), 16-17; Hans Jonas, On Faith, Reason, and Responsibility (Claremont, CA: The Institute of Antiquity and Christianity, 1981), 43; and William Desmond, “On the Betrayals of Reverence,” in Is There a Sabbath for Thought? Between Religion and Philosophy (New York: Fordham Univ. Press, 2005), 265, 273-75. Several of the essays in Craig and Moreland, Naturalism: A Critical Analysis (London: Routledge, 2000) are also relevant. Arthur O. Lovejoy drew similar conclusions regarding Behaviorism as Lewis did regarding Freudianism and Marxism (“The Paradox of the Thinking Behaviorist,” The Philosophical Review 31 [1922]: 135-47; idem, “Pragmatism as Interactionism,” The Journal of Philosophy 17 [1920]: 592, 630-32). Antony Flew (“The Third Maxim,” The Rationalist Annual 72 [1955]: 63) refers to C.E.M. Joad as a proponent of the argument from reason, but does not cite a specific text.
{40} Hasker, Emergent Self, 1-80.
{41} Although he does sometimes state the argument in terms of consciousness (C.S. Lewis, A Grief Observed (1961; San Francisco: HarperSanFrancisco, 1989), 41; idem, That Hideous Strength [1946; New York: Macmillan Paperback, 1965], 357-58).
{42} Steven Weinberg, Dreams of a Final Theory (New York: Pantheon, 1992), 247.
{43} C.S. Lewis, The Abolition of Man (1943; New York: Macmillan, 1947), 86-91; Michael D. Aeschliman, The Restitution of Man: C.S. Lewis and the Case against Scientism (1983; Grand Rapids, MI: Eerdmans, 1998).
{44} Aeschliman, Restitution of Man, 33.
{45} Lewis, Abolition of Man, 34.
{46} Ibid., 34-35; cf. idem, That Hideous Strength, 357-58.

(see also part 1, part 2, part 3, part 4, part 5, and part 6)

(cross-posted at Quodlibeta)

O Hear This!

This is an old post that I just realized I never actually posted. In a post from a few years ago, Humphrey quoted Simon Conway Morris, the evolutionary palaeobiologist (btw, "Conway Morris" is his last name, not "Morris"), where he references Anthony O'Hear, a philosopher who specializes in the philosophy of Karl Popper, among other things. The quote is basically that reducing thought to "memes" would essentially "deny the reality of reflective thought." I asked in the comments where Conway Morris writes this, and what the reference to O'Hear is. Humphrey pointed me to Life's Solution, Conway Morris's book, so I looked up O'Hear in the index. It's on p. 324. The reference to O'Hear is his book Beyond Evolution: Human Nature and the Limits of Evolutionary Explanation, pp. 156-158.

I find this interesting because Karl Popper wrote a lot on evolutionary epistemology of theories (EET) or evolutionary philosophy of science. This is the idea that the growth of knowledge can be seen in evolutionary terms, with better ideas "surviving." So Popper applied evolution about as far as it could go. Yet, even with this, Popper had an argument very similar to Alvin Plantinga's Evolutionary Argument against Naturalism, J. R. Lucas's Gödelian argument against physical determinism, and C. S. Lewis's argument from reason. Popper uses it to argue against determinism. He argued that one who affirms determinism can only do so by implicitly presupposing that determinism is false. In one of his books on Popper as well as the British Journal for the Philosophy of Science, O'Hear critiqued Popper's version of this argument, and was in turn critiqued by Peter Glassen. So I find it interesting that, despite his skepticism towards this argument, O'Hear presents a somewhat similar argument that memes obviates reflective thought. I also find it interesting that he finds "limits" to evolution, and does so in a context of evolutionary philosophy of science which applies evolution to just about everything.

By the way, I quote a passage from Beyond Evolution here, and I quote Glassen's critique of O'Hear here.

J. R. Lucas

Philosophy is all interconnected. This allows someone who is an expert in political philosophy to comment on, say, epistemology or logic without committing the fallacy of irrelevant authority. This doesn't mean, though, that just because someone is an expert in one philosophical field, their opinion in other philosophical fields is just as valuable. Give philosophy's nature I think it's justified to give a philosopher the benefit of doubt when he comments on a philosophical topic outside of his usual focus, but ultimately you have to take it on a case-by-case basis. Bertrand Russell, for example, was an expert in the philosophy of mathematics, and used his credibility there to write books on other subjects such as the philosophy of religion and political philosophy. Unfortunately, it's obvious that he didn't know the first thing about the latter subjects. Anyone who has taken a Bachelor's level course in the philosophy of religion should be able to refute him.

J. R. Lucas on the other hand is one of those philosophers who brings expertise to every subject he approaches. This is partially because he takes philosophy to be a way of life rather than a method to win arguments. So he has written on logic, the philosophy of mathematics, the philosophy of science, the philosophy of mind, the philosophy of religion, political philosophy, the history of philosophy, ethics, metaphysics, etc. You can see a bibliography of his publications here. A list of his books shows his diversity:

The Principles of Politics
The Concept of Probability
The Freedom of the Will
A Treatise on Time and Space
Democracy and Participation
Freedom and Grace
On Justice
Space, Time and Causality
The Future
Responsibility
The Conceptual Roots of Mathematics
Economics as a Moral Science
Reason and Reality

Those are the books he's written by himself. He has also written books with other authors:

The Nature of Mind
The Development of Mind
Spacetime and Electromagnetism
Ethical Economics
An Engagement with Plato's Republic

As far as I'm concerned, Lucas is one of the most important and under-appreciated philosophers of our day. He has written on philosophical subjects so diverse, and yet with a mastery that I could never achieve if I focused my life on just one of them. For one thing, the man thoroughly understands Gödel's Incompleteness Theorems. These theorems are so notoriously complex that I suspect there's only a few hundred people alive who understand them. Yet not only does Lucas understand them, he is able to show that they render strong artificial intelligence and all forms of physical determinism impossible. If I spent my entire life on Gödel's theorems I still wouldn't be able to interact with them as thoroughly as Lucas.

Fortunately Lucas has posted excerpts from several of his books online, as well as most of his published articles. You can read his Reason and Reality in its entirety, as well as Ethical Economics. He is putting another book on the subject, Economics as a Moral Science, online as he writes it. so far he has chapters 1 ; 2 ; 3 ; 4 ; 5 ; 6 ; 7; conclusion ; and two appendices here and here. He has also posted several chapters from his The Conceptual Roots of Mathematics online: chapters 2 ; 4 ; 7 ; 8 ("The Implications of Gödel's Theorem") ; 9a (which replaces his previous chapter 13) ; 9b ; 10a ; and 14. An Engagement with Plato's Republic, co-written with the late great Basil Mitchell, has the introduction and chapters 1 ; 3 ; and 10 posted online.

I'm linking to all of these to invite you to join me in being a student of Lucas. Philosophy students are going to be writing dissertations on him 500 years from now.

Quote of the Day

We understand by a cybernetical machine an apparatus which performs a set of operations according to a definite set of rules. Normally we "programme" a machine: that is, we give it a set of instructions about what it is to do in each eventuality; and we feed in the initial "information" on which the machine is to perform its calculations. When we consider the possibility that the mind might be a cybernetical mechanism we have such a model in view; we suppose that the brain is composed of complicated neural circuits, and that the information fed in by the senses is "processed" and acted upon or stored for future use. If it is such a mechanism, then given the way in which it is programmed -- the way in which it is "wired up" -- and the information which has been fed into it, the response -- the "output" -- is determined, and could, granted sufficient time, be calculated. Our idea of a machine is just this, that its behaviour is completely determined by the way it is made and the incoming "stimuli": there is no possibility of its acting on its own: given a certain form of construction and a certain input of information, then it must act in a certain specific way. We, however, shall be concerned not with what a machine must do, but with what it can do. That is, instead of considering the whole set of rules which together determine exactly what a machine will do in given circumstances, we shall consider only an outline of those rules, which will delimit the possible responses of the machine, but not completely. The complete rules will determine the operations completely at every stage; at every stage there will be a definite instruction, e.g., "If the number is prime and greater than two add one and divide by two: if it is not prime, divide by its smallest factor": we, however, will consider the possibility of there being alternative instructions, e.g., "In a fraction you may divide top and bottom by any number which is a factor of both numerator and denominator". In thus relaxing the specification of our model, so that it is no longer completely determinist, though still entirely mechanistic, we shall be able to take into account a feature often proposed for mechanical models of the mind, namely that they should contain a randomizing device. One could build a machine where the choice between a number of alternatives was settled by, say, the number of radium atoms to have disintegrated in a given container in the past half-minute. It is prima facie plausible that our brains should be liable to random effects: a cosmic ray might well be enough to trigger off a neural impulse. But clearly in a machine a randomizing device could not be introduced to choose any alternative whatsoever: it can only be permitted to choose between a number of allowable alternatives. It is all right to add any number chosen at random to both sides of an equation, but not to add one number to one side and another to the other. It is all right to choose to prove one theorem of Euclid rather than another, or to use one method rather than another, but not to "prove" something which is not true, or to use a "method of proof" which is not valid. Any randomizing devices must allow choices only between those operations which will not lead to inconsistency: which is exactly what the relaxed specification of our model specifies Indeed, one might put it this way: instead of considering what a completely determined machine must do, we shall consider what a machine might be able to do if it had a randomizing device that acted whenever there were two or more operations possible, none of which could lead to inconsistency.

If such a machine were built to produce theorems about arithmetic (in many ways the simplest part of mathematics), it would have only a finite number of components, and so there would be only a finite number of types of operation it could do, and only a finite number of initial assumptions it could operate on. Indeed, we can go further, and say that there would only be a definite number of types of operation, and of initial assumptions, that could be built into it. Machines are definite: anything which was indefinite or infinite we should not count as a machine. Note that we say number of types of operation, not number of operations. Given sufficient time, and provided that it did not wear out, a machine could go on repeating an operation indefinitely: it is merely that there can be only a definite number of different sorts of operation it can perform.

If there are only a definite number of types of operation and initial assumptions built into the system, we can represent them all by suitable symbols written down on paper. We can parallel the operation by rules ("rules of inference" or "axiom schemata") allowing us to go from one or more formulae (or even from no formula at all) to another formula, and we can parallel the initial assumptions (if any) by a set of initial formulae ("primitive propositions", "postulates" or "axioms"). Once we have represented these on paper, we can represent every single operation: all we need do is to give formulae representing the situation before and after the operation, and note which rule is being invoked. We can thus represent on paper any possible sequence of operations the machine might perform. However long, the machine went on operating, we could, give enough time, paper and patience, write down an analogue of the machine's operations. This analogue would in fact be a formal proof: every operation of the machine is represented by the application of one of the rules: and the conditions which determine for the machine whether an operation can be performed in a certain situation, become, in our representation, conditions which settle whether a rule can be applied to a certain formula, i.e., formal conditions of applicability. Thus, construing our rules as rules of inference, we shall have a proof-sequence of formulae, each one being written down in virtue of some formal rule of inference having been applied to some previous formula or formulae (except, of course, for the initial formulae, which are given because they represent initial assumptions built into the system). The conclusions it is possible for the machine to produce as being true will therefore correspond to the theorems that can be proved in the corresponding formal system. We now construct a Gödelian formula in this formal system. This formula cannot be proved-in-the- system. Therefore the machine cannot produce the corresponding formula as being true. But we can see that the Gödelian formula is true: any rational being could follow Gödel's argument, and convince himself that the Gödelian formula, although unprovable-in-the-system, was nonetheless -- in fact, for that very reason -- true. Now any mechanical model of the mind must include a mechanism which can enunciate truths of arithmetic, because this is something which minds can do: in fact, it is easy to produce mechanical models which will in many respects produce truths of arithmetic far better than human beings can. But in this one respect they cannot do so well: in that for every machine there is a truth which it cannot produce as being true, but which a mind can. This shows that a machine cannot be a complete and adequate model of the mind. It cannot do everything that a mind can do, since however much it can do, there is always something which it cannot do, and a mind can. This is not to say that we cannot build a machine to simulate any desired piece of mind-like behaviour: it is only that we cannot build a machine to simulate every piece of mind-like behaviour. We can (or shall be able to one day) build machines capable of reproducing bits of mind-like behaviour, and indeed of outdoing the performances of human minds: but however good the machine is, and however much better it can do in nearly all respects than a human mind can, it always has this one weakness, this one thing which it cannot do, whereas a mind can. The Gödelian formula is the Achilles' heel of the cybernetical machine. And therefore we cannot hope ever to produce a machine that will be able to do all that a mind can do: we can never not even in principle, have a mechanical model of the mind.

This conclusion will be highly suspect to some people. They will object first that we cannot have it both that a machine can simulate any piece of mind-like behaviour, and that it cannot simulate every piece. To some it is a contradiction: to them it is enough to point out that there is no contradiction between the fact that for any natural number there can be produced a greater number, and the fact that a number cannot be produced greater than every number. We can use the same analogy also against those who, finding a formula their first machine cannot produce as being true, concede that that machine is indeed inadequate, but thereupon seek to construct a second, more adequate, machine, in which the formula can be produced as being true. This they can indeed do: but then the second machine will have a Gödelian formula all of its own, constructed by applying Gödel's procedure to the formal system which represents its (the second machine's) own, enlarged, scheme of operations. And this formula the second machine will not be able to produce as being true, while a mind will be able to see that it is true. And if now a third machine is constructed, able to do what the second machine was unable to do, exactly the same will happen: there will be yet a third formula, the Gödelian formula for the formal system corresponding to the third machine's scheme of operations, which the third machine is unable to produce as being true, while a mind will still be able to see that it is true. And so it will go on. However complicated a machine we construct, it will, if it is a machine, correspond to a formal system, which in turn will be liable to the Gödel procedure for finding a formula unprovable-in-that- system. This formula the machine will be unable to produce as being true, although a mind can see that it is true. And so the machine will still not be an adequate model of the mind. We are trying to produce a model of the mind which is mechanical -- which is essentially "dead" -- but the mind, being in fact "alive", can always go one better than any formal, ossified, dead, system can. Thanks to Gödel's theorem, the mind always has the last word.

A second objection will now be made. The procedure whereby the Gödelian formula is constructed is a standard procedure -- only so could we be sure that a Gödelian formula can be constructed for every formal system. But if it is a standard procedure, then a machine should be able to be programmed to carry it out too. We could construct a machine with the usual operations, and in addition an operation of going through the Gödel procedure, and then producing the conclusion of that procedure as being true; and then repeating the procedure, and so on, as often as required. This would correspond to having a system with an additional rule of inference which allowed one to add, as a theorem, the Gödelian formula of the rest of the formal system, and then the Gödelian formula of this new, strengthened formal system, and so on. It would be tantamount to adding. to the original formal system an infinite sequence of axioms, each the Gödelian formula of the system hitherto obtained. Yet even so, the matter is not settled: for the machine with a Gödelizing operator, as we might call it, is a different machine from the machines without such an operator; and, although the machine with the operator would be able to do those things in which the machines without the operator were outclassed by a mind, yet we might expect a mind, faced with a machine that possessed a Gödelizing operator, to take this into account, and out-Gödel the new machine, Gödelizing operator and all. This has, in fact, proved to be the case. Even if we adjoin to a formal system the infinite set of axioms consisting of the successive Gödelian formulae, the resulting system is still incomplete, and contains a formula which cannot be proved-in-the-system, although a rational being can, standing outside the system, see that it is true. We had expected this, for even if an infinite set of axioms were added, they would have to be specified by some finite rule or specification, and this further rule or specification could then be taken into account by a mind considering the enlarged formal system. In a sense, just because the mind has the last word, it can always pick a hole in any formal system presented to it as a model of its own workings. The mechanical model must be, in some sense, finite and definite: and then the mind can always go one better.

This is the answer to one objection put forward by Turing. He argues that the limitation to the powers of a machine do not amount to anything much. Although each individual machine is incapable of getting the right answer to some questions, after all each individual human being is fallible also: and in any case "our superiority can only be felt on such an occasion in relation to the one machine over which we have scored our petty triumph. There would be no question of triumphing simultaneously over all machines." But this is not the point. We are not discussing whether machines or minds are superior, but whether they are the same. In some respect machines are undoubtedly superior to human minds; and the question on which they are stumped is admittedly, a rather niggling, even trivial, question. But it is enough, enough to show that the machine is not the same as a mind. True, the machine can do many things that a human mind cannot do: but if there is of necessity something that the machine cannot do, though the mind can, then, however trivial the matter is, we cannot equate the two, and cannot hope ever to have a mechanical model that will adequately represent the mind. Nor does it signify that it is only an individual machine we have triumphed over: for the triumph is not over only an individual machine, but over any individual that anybody cares to specify -- in Latin quivis or quilibet, not quidam -- and a mechanical model of a mind must be an individual machine. Although it is true that any particular "triumph" of a mind over a machine could be "trumped" by another machine able to produce the answer the first machine could not produce, so that "there is no question of triumphing simultaneously over all machines", yet this is irrelevant. What is at issue is not the unequal contest between one mind and all machines, but whether there could be any, single, machine that could do all a mind can do. For the mechanist thesis to hold water, it must be possible, in principle, to produce a model, a single model, which can do everything the mind can do. It is like a game. The mechanist has first turn. He produces a -- any, but only a definite one -- mechanical model of the mind. I point to something that it cannot do, but the mind can. The mechanist is free to modify his example, but each time he does so, I am entitled to look for defects in the revised model. If the mechanist can devise a model that I cannot find fault with, his thesis is established: if he cannot, then it is not proven: and since -- as it turns out -- he necessarily cannot, it is refuted. To succeed, he must be able to produce some definite mechanical model of the mind -- anyone he likes, but one he can specify, and will stick to. But since he cannot, in principle cannot, produce any mechanical model that is adequate, even though the point of failure is a minor one, he is bound to fail, and mechanism must be false.

J. R. Lucas
"Minds, Machines, and Gödel"
Philosophy 36 (1961)

Quote of the Day

There are many other arguments which claim to show us that we can be determinists without upsetting any of our notions of moral responsibility or human freedom. We may keep our concepts in different pockets. The language we use to describe actions is often different from the language we use to describe events: there are different principles of identity and individuation, for what are to count as the same action and what are to count as the same event. And therefore, it is argued, the conflict between free-will and determinism is illusory, because the concepts occur in different languages and so cannot come into collision. Free-will belongs to the agent's language, determinism to the spectator's. I, as an agent, perform some actions freely: he, as a spectator, may predict events correctly. But I am not he; to be an active participator is not the same as to observe from the sidelines, and actions and events are logically very different; and therefore, it is claimed, no conflict can arise between my belief as an agent that I am acting freely and his certainty, as a spectator that events will follow their pre-established course; since the key concepts of the opposition must be formulated in different languages, no contradiction between them can arise.

The distinction drawn between the language of agents and actions and the language of observations and events -- a distinction which seems to be the modern formulation in linguistic terms of one that Kant drew -- is a distinction that needs to be drawn; but, like the one Kant drew, is unable to resolve this particular problem. It is true that agents and spectators do use different languages, and many mistakes have been caused by the unconscious equation of actions and events: many of the legends about Oracles and the fulfilment of their prophecies to the confusion of the enquirer, turn on his having wrongly translated from the Oracle's spectator-language into his own, agent-language. But from the languages' not being the same in all respects it does not follow that they differ in all respects. The languages, though admittedly different, overlap each other in many places. The same man can speak both as an agent and as a spectator, and the same things can be described from the two different points of view. Just as Kant's solution requires a sort of philosophical schizophrenia on the part of the thinker beyond the power of most reflective men, so the solution suggested here requires, as it were, a thorough-going schizoglossia which is blatantly at variance with the facts. We may not be able to equate actions with events: but we can say something in the event language which will translate into something in the action language that is incompatible with some things the agents would have liked to have been able to say. Thus I may think that my action in inviting the visiting professor to dinner was free, and that I could have quite well just asked him how his work was getting on: but if a psycho-physiologist with complete information about the state of my brain and my environment at some previous time can predict that upon my meeting a human being of such and such type, my lips will contort themselves so that such and such sounds come out, then, whatever the niceties of what exactly constitutes an action, I shall no longer be able to maintain that I could have not acted as I did. The argument of the two languages will not work because the spectator and the agent can communicate, indeed may be the same person. So, anything the spectator can know the agent could know also: and if the spectator in his language can predict certain events, then this state of affairs will be describable in the agent's language as well, and may be inconsistent with, or entail, certain courses of action on his part. Therefore if the determinist thesis occurs in the spectator's language, it can be expressed in the agent's language too, and the problem will not have been dissolved.

J. R. Lucas
The Freedom of the Will
(footnotes omitted)

Quote of the Day

Chiefly, however, determinism is self-stultifying. If my mental processes are totally determined, I am totally determined either to accept or to reject determinism. But if the sole reason for my believing or not believing X is that I am causally determined to believe it I have no ground for holding that my judgment is true or false. J. R. Lucas has put the point cogently with reference to Marxist and Freudian forms of determinism thus. 'The Marxist who says that all ideologies have no independent validity and merely reflect the class interests of those who hold them can be told that in that case his Marxist views merely express the economic interests of his class, and have no more claim to be judged true or valid than any toher view. So too the Freudian, if he makes out that everybody else's philosophy is merely the consequence of childhood experiences, is, by parity of reasoning, revealing merely his delayed response to what happened to him when he was a child.' Lucas then makes the same point with regard to a person who maintains, more generally, that our behaviour is totally determined by heredity and environment. 'If what he says is true, he says it merely as the result of his heredity and environment, and of nothing else. He does not hold his determinist views because they are true, but because he has such-and-such a genetic make-up, and has received such-and-such stimuli; that is, not because the structure of the universe is such-and-such but only because the configuration of only one part of the universe, together with the structure of the determinist's brain, is such as to produce that result.'

The exact force of this criticism is sometimes missed. Certainly on deterministic premisses determinism may be true. But we should not have any grounds for affirming that it is true or therefore for knowing that it is so. In order to obtain these grounds we must be free from all determining factors in order to assess the evidence according to its own worth. This principle applies to the assessment of all truth-claims (including those of Christianity). Freedom from determining factors is therefore required in the cognitive as much as in the moral sphere.

Huw Parri Owen
Christian Theism: A Study in Its Basic Principles
(quoting J. R. Lucas, The Freedom of the Will)

The Power of Fiction

Sometimes fiction can make a point more strongly than philosophy. For example, I've always thought (at least for as long as I've considered it) that free will is self-evident and that determinism could not be rationally maintained; but more than that, I think it would be utterly devastating to someone who truly grasped its consequences. I hope this isn't condescending, but it seems to me that determinists simply don't understand the magnitude of what they're saying. They think you can have a "determinism without tears" as J. R. Lucas puts it. But all the philosophical argumentation I've read still doesn't express this devastation.

However, a short story by Ted Chiang does. Chiang has only written a handful of stories (you can read some of them here), but they're all pretty much incredible. He addresses determinism and free will in "Story of Your Life", but the story I'm thinking of is only a page long: "What's Expected of Us". Click on that link and read it now.