The answer@` in a word@` is No. Supervenience is not asymmetric -- and neither is determination. This conclusion is of course radically at odds with conventional wisdom@`intuition@` and many very good philosophers. Hence explanations are in order@` indeed at some length@` and so too is the patience to follow them@` step by step.
The first step is to recall that according to physicalism@` the physical enjoys a fundamental ontological primacy over the nonphysical. In connection with this asymmetric primacy@` physicalists assert not only the composition thesis that every concrete thing is composed solely of the basic physical entities@` but also the determination thesis that the physical properties of things determine all their properties. As Jaegwon Kim says@` "Any robust materialist position should affirm ... that what is material determines all that there is in the world."(1) Furthermore@` according to Kim@` the relevant relation of determinational dependence@` which is a component of supervenience@` is asymmetric: "Dependence@` or determination@` is usually understood to be asymmetric.... In most cases of interest supervenience seems in fact asymmetric
Kim's argument for this supposed asymmetry of the determination relation proves inconsistent with at least one further property he gives the relation@` as we see in ??2-3. So too for supervenience. In particular@` a premise of his argument conflicts with the relation's transitivity. Nor does the literature appear to contain any considerations congenial to physicalists that would negate transitivity in favor of Kim's argument for asymmetry. To the contrary@` physicalists require the transitivity of determination/supervenience in order to marshal adequate empirical support for their claim that the physical determines/subvenes all there is in the world.
Worse@` the supposed asymmetry of determination and supervenience proves inconsistent with any identity or equivalence between the nonphysical properties of a thing and its physical properties@` according to ?4. Because such identity and/or equivalence does hold for (at least) some non-physical properties@` determination and supervenience are not asymmetric. Reductivists@` therefore@` including Kim@` can ill afford either asymmetric determination or asymmetric supervenience. So too for eliminitivists@` who require the higher-level properties that survive elimination to be identical with or at least (nomically) equivalent to physical properties. But even nonreductive physicalists will be sobered@` if they expected determination and supervenience to be asymmetric@` since they agree that some higher-level properties are indeed identical or at least equivalent to physical properties@` just not all.
If determination and supervenience are not asymmetric@` explications of them cannot be faulted for failing to entail asymmetry@` as a number of them have been@` whatever their other merits. This includes explications according to which determination and supervenience are nonreductive and/or "global."(3) On the other hand@` anyone who rejects the asymmetry shoulders a twofold burden. Some explanation must be given of why the contrary intuition is so entrenched and widespread. And some explanation must be given of how the asymmetric ontological primacy of the physical is to be understood@` if determination and supervenience are not asymmetric. The purpose of ?5 is to provide the needed explanations.
This task is complicated by the tendency of different philosophers to understand "ontological primacy" in different ways@` using the phrase in divergent unanalyzed senses. We need therefore to distinguish the main senses@` in ?5@` and then@` for each such sense@` provide a positive account of the ontological primacy of the physical@` and of the corresponding dependence of the nonphysical@` according to which such primacy is asymmetric but determination and supervenience are not. Here I exploit neglected relations among determination/supervenience@` explanation and the empirical evidence for the physical determination/supervenience of all that there is in the world. These relations enable us to understand why the intuition of asymmetry of determination and supervenience is so entrenched and widespread@` as well as why the supposed asymmetry is not required by the ontological primacy of the physical.
A relation is never asymmetric "absolutely" but only in a given set or field. For example@` in the set of integers the relation "less than or equal to" is neither asymmetric nor symmetric; it is false that given any x and y in this set@` if x is less than or equal to y@` then y is not less than or equal to x@` and false also that for any such x and y@` if x is less than or equal to y@` then y is less than or equal to x. But the relation "less than or equal to" is symmetric in a singleton set of integers@` say {3}@` since for any x and y in this set@` if x is less than or equal to y@` then y is less than or equal to x (that is@` if 3 is less than or equal to 3@` then 3 is less than or equal to 3).
Thus we need to be clear about the set or field in which the physicalist's determination relation is supposed to be asymmetric. Here we may follow Kim@` who treats the relation as holding between properties from various sets of properties. For example@` in a general claim of supervenience@` as he calls it@` the properties in "a given family of properties@` say mental properties@` supervene on [hence are determined by] another family@` say neurobiological properties."(4) In this kind of case@` the properties between which determination and/or supervenience holds form sets that amount to whole families of properties -- say the mental@` the neurobiological@` the physical.
But@` as Kim says@` physicalists need also to make specific claims of supervenience and/or determination. For example@` they might claim that the specific property of being in pain supervenes on (hence is determined by) the activation of specified nerve fibers. In this kind of case@` the properties between which determination and supervenience hold -- those of being in pain and of certain fibers' being activated -- form subsets (often singleton subsets) of whole families (the mental@` the neurobiological). As Kim says@` physicalists need to make these specific claims of determination in connection with explaining why the general claims hold and providing evidence for them.(5)
On this view@` then@` which is widespread@` the field of the physicalist's relation of determinational dependence is the set of properties of things@` both those properties that form whole families (the mental@` the physical) and those from specific subsets of a family (say being in pain@` certain fibers' being activated). But it will not matter for what follows whether the field is thought of in terms of properties@` predicates@` conditions@` facts@` phenomena@` or states of affairs@` all of which have their advocates. What will matter is that not only whole families of these but specific subsets of them are included in the field of the determination relation. So too for supervenience.
Let us follow Kim in a further particular as well. There is a difference between covariance and dependence@` as there is between correlation and cause. A relation of covariance holds between properties of kind A and those of kind B when those in A covary@` either "accidentally" or of necessity@` with those in B. Specifically@` we are only asserting covariance when we assert that there is no difference of sort A without a difference of sort B@` or@` modalizing@` that difference in respect of A entails difference in respect of B. Dependence@` on the other hand@` requires more than covariance even when the covariance involves a strong modality.
For example@` chemical kinds and their microphysical structures seem necessarily to covary with each other@` in the sense that given identities like water = H2O@` there can be no difference between two things in respect of the property of being water without some difference in respect of the property of being H2O@` and vice versa (or@` equivalently@` any two worlds alike as regards which things have the property of being H2O are alike as regards which things have the property of being water@` and vice versa). Thus the covariance in this kind of case appears not to be asymmetric. Yet we want to say that the chemical kind "water" is asymmetrically dependent on the microphysical structure H2O. Covariance can be non-asymmetric@` whereas dependence seemingly cannot. Furthermore@` questions of asymmetry aside@` "it seems clearly possible for there to be three sets of properties A@` B@` and C@` such that A and B depend on C@` A covaries with B but B does not covary with A@` and A does not depend on B."(6) This is largely because it could be in virtue of having certain properties in C@` not B@` that something has certain A-properties; it is the C-properties that play the relevant explanatory role.
In line with this distinction between covariance and dependence@` we may again follow Kim@` as we have been@` in using the word 'determination' to mean not some variety of covariance but a kind of dependence. "For there to be property dependence there must be property covariation@`" but the converse does not hold@` and "it is the dependence aspect of supervenience@` not the covariation aspect@` that can sanction many of the usual philosophical implications drawn from@` or associated with@` supervenience theses@`"(7) including the asymmetric primacy of the physical.
What other properties should the physicalist's relation of determinational dependence have? According to Kim@` the relation involves not only ontological directionality but explanatory. "That upon which something depends is ... explanatorily prior to ... that which depends on it." The lower-level or base property on which the higher-level depends is explanatorily prior because a thing's "having the relevant base property explains why it has the [higher-level] property." It is because@` or in virtue of the fact that@` the thing has the base property that it has the higher-level@` supervenient property. Thus if properties of kind B determine those of kind A@` then a thing's having certain B-properties is that in virtue of which@` in the sense of explaining why@` it has certain A-properties.(8)
Call this supposed feature of the determination relation that of implying an in-virtue-of or explanation relation. The in-virtue-of relation is implied in the sense that if the determination relation obtains between (sets of) properties F and G@` so does the in-virtue-of or explanation relation: if F determines G@` then a thing's having F explains its having G@` and it is in virtue of having F that it has G. This feature of implying an in-virtue-of or explanation relation enables Kim's argument for the asymmetry of determination: The in-virtue-of or explanation relation is asymmetric@` since if x's having F explains why x has G@` then x's having G does not explain why x has F. Because this asymmetric relation is implied by the determination relation@` the latter must be asymmetric too.(9)
Kim gives determination two further properties that will be relevant here. One is that "this determinative relation [say from body to mind] is an objective matter; it does not depend on whether anyone knows anything about it@` or what expressions are used to talk about mind and body."(10) This suggests that the relation is extensional@` since a mark of the extensional is that the relation obtains (or not) regardless of what expressions are used to talk about or denote its relata. In any event@` "supervenient determination ... is a metaphysical thesis about an objectively existent dependency relation between the two domains; it says nothing about whether or how the details of the dependency relation will become known so as to enable us to formulate explanations@` reductions@` or definitions."(11) In line with this@` let us say that the physicalist's determination relation has the property of being "objective@`" whether or not it is also extensional.
Another property Kim gives determination is transitivity. Determination is a component of@` or implied by@` supervenience@` in the sense of supervenience that include dependence.(12) But "Supervenience@` whether in the sense of covariation or in the sense that includes dependence@` is transitive."(13) It follows that determination is transitive too (for the relevant cases@` in which there are F@` G and H such that F determines G and G determines H). Surely Kim is right about transitivity. When physicalists assert the determination of one sort of property by another@` they presuppose transitivity. For example@` they want to say that because the quantum-physical properties determine the quantum-chemical properties@` and the latter determine the biochemical properties@` it follows that the quantum-physical properties determine the biochemical.
Furthermore@` as Kim himself might add@` without this transitivity of determination@` physicalists would be unable to marshal adequate empirical support for their claim that the higher-level scientific facts are determined ultimately by the physical facts. To see why@` consider the claim that the physical facts determine the facts at the level of psychology.(14) A natural way to justify this claim empirically -- perhaps the only way -- is to look at a number of sciences between physics and psychology. The facts of physics can more readily be shown to determine those of its near neighbors@` such as quantum chemistry. The latter can more readily be shown to determine the facts in sciences a bit further removed from physics@` such as biochemistry. These in turn can more easily be seen to determine those in sciences still further removed@` and so on@` until finally we reach the psychological facts. Provided determination holds at each step of the way in this chain@` we may infer by transitivity of determination that the physical facts determine the psychological.
Sometimes@` of course@` the higher-level phenomena are determined (and explained) not by matters in a single lower-level science but only in a cluster of lower-level sciences@` in each of which the facts are determined (and explained) in turn by some closer still to physics. What get pairwise connected at each step@` strictly@` include such clusters of sciences@` not always single sciences.(15) But for simplicity let us continue to speak as though it is single sciences that get pairwise connected and form chains.
For in any event@` the problem of providing adequate empirical evidence for the determination of the psychological by the physical divides into a number of intermediate problems that concern relations between sciences that are near neighbors. Scientists in a couple of neighboring fields will often already have explored key relations between them@` including evidential relations in light of which we may infer determination of one by the other. This amounts to a division of labor@` in which physicalists can let the particular sciences do much of their work for them. If determination were not transitive@` this division of labor would be of no use to physicalists who want to marshal adequate empirical support for the claim that the psychological facts are determined ultimately by the physical facts. Without transitivity of determination@` physicalists would have to shoulder the heroic and probably hopeless burden of spelling out some direct or unmediated connection between psychology and physics -- a connection that would leapfrog the intervening sciences and enable us to infer determination of psychological fact by physical. The prospects of some such leapfrog approach should strike us as dim (as we see in detail in the next section@` in connection with interlevel theories).(16)
Summing up@` the properties Kim ascribes to the physicalist's determination relation include the following. The field of the relation (and also of supervenience) consists of properties@` both those that form whole families and those that form specific subsets of them. The relation is both objective and a relation not merely of covariance but of directional dependence@` having an asymmetry derived from an implied in-virtue-of or explanation relation. But the conjunction of these supposed properties of determination@` as we see next@` proves inconsistent with the transitivity Kim also assumes and physicalists require. So too for supervenience@` insofar as supervenience shares these properties.
3. Determination@` Supervenience@` Explanation and Transitivity
For simplicity@` we start with determination. The argument of this section will then apply@` essentially unchanged@` to supervenience@` insofar as supervenience shares the relevant properties.
Suppose determination has an asymmetry that derives from an implied in-virtue-of or explanation relation. That is@` if F determines G@` it is asymmetrically in virtue of@` hence explained by@` having F that something has G (for any F and G in the field of the determination relation). It can be proved that for any relation R@` if (i) R implies relation Q (in the sense that for any F and G@` if RFG then QFG) and (ii) there are F@` G and H such that RFG and RGH but not QFH@` then R is not transitive.(17) In particular@` if (i) the relation D of determination implies an in-virtue-of relation V@` in the sense that for any F and G@` if DFG then VFG@` and (ii) there are cases in which DFG and DGH but not VFH@` then D is not transitive@` a result that is inconsistent with the transitivity Kim assumes and physicalists require.
Since there are cases in which DFG and DGH but not VFH@` the supposition of an asymmetry of D that derives from an implied in-virtue-of or explanation relation V is incompatible with the transitivity of determination.(18) The likely place to look for such cases is where the implied relation V is non-transitive and DFG and DGH; indeed it can be shown that if V is non-transitive for F@`G@`H when DFG and DGH@` then D is non-transitive@` inconsistent with the transitivity of determination.
To see why the relevant kinds of explanation are not transitive@` note to begin with that the relevant kinds are "interlevel" explanations@` in which some higher-level property N is supposed to be explained by some lower-level properties Bi. Now consider the following kind of interlevel explanation. Often we want to say both that in some sense the best explanation of why x has N is that x has Bi and that Bi determine that x has N@` where the properties Biare from some science more fundamental@` or closer to physics@` than the science from which N is drawn. Given the unifying and explanatory role of the more fundamental properties or phenomena Bi (among other things)@` an interlevel explanation in terms of Bi of why x has N is to be preferred@` other things being equal@` to any other explanation@` and in that sense is the best explanation. In addition@` and partly in light of this explanatory evidence@` we want to say that Bi determine that x has N.
For example@` there are occasions or contexts in which@` at least from the point of view of the physicalist@` (i) not only is the best explanation of why a certain cell x has the biological property N that the cell has certain biochemical properties Bi@` but Bi determine that x has N; and (ii) not only is the best explanation of the biochemical properties Bi in terms of certain quantum-chemical properties Pi@` but Pi determine that x has Bi. If transitivity held@` we would have to say that the best explanation of why the cell has N is that it has these quantum-chemical properties Pi. But this contradicts the hypothesis that the best explanation of why it has N is that it has the biochemical properties Bi; presumably there can be only one best explanation.(19) So not only does this transitivity fail@` we have a case in which DFG and DGH but not VFH@` from which it follows that D is not transitive. Since this conflicts with the transitivity of determination@` we must conclude that the in-virtue-of or explanatory relation is not implied by determination after all.
Perhaps the moral here is simply that the relevant notion of interlevel explanation involved in the implied explanation relation is never that of the best explanation. But this move would come at too high a price. When physicalists say that x's having N is determined by and thus had in virtue of the more fundamental properties Bi@` frequently they do also have in mind that the best explanation of why x has N is that x has Bi. To repeat@` given the unifying and explanatory role of the more fundamental properties or phenomena Bi (among other things)@` frequently an interlevel explanation in terms of Bi of why x has N is to be preferred@` other things being equal@` to any other explanation@` and in that sense is the best explanation. If we were to insist on the transitivity of explanation@` we could no longer say that the lower-level properties in virtue of which x has N provide@` in this sense@` the best explanation of why x has N. Since we do want to retain this notion of the best explanation here@` the relevant interlevel explanation relation cannot be transitive if or insofar as it involves a notion of the best explanation. So let us consider some other varieties of interlevel explanation.
According to some varieties@` the explaining factors merely make it sufficiently probable that x has N. Among these varieties are deductive-statistical@` inductive-statistical and certain statistical-relevance explanations. Such varieties of explanation become relevant when the lower-level Bi are said to determine not that x has N@` but the chances of x's having N. Now suppose for the sake of argument that we set .6 as the sufficient degree of probability of x's having N. Suppose further that the probability that x has Bi given that x has Pi is .6@` and the probability that x has N given that x has Bi is also .6. Then the probability that x has N given that it has Pi is only .36. Transitivity fails for this variety of explanation@`(20) but more to the point@` we again have a case in which DFG and DGH but not VFH@` and again we must conclude that the in-virtue-of or explanatory relation is not implied by determination after all.
Perhaps the moral here is that an implied in-virtue-of or explanation relation can be transitive only if the properties in virtue of which x has a certain chance of having N do not explain why x has N by way of making it sufficiently probable that x has N (unless we set the probability at 1). But again the price is too high. There are important interlevel explanations that are both statistical or probabilistic in character and relevant when lower-level properties determine the chances of x's having N. Such explanations are involved in@` among others@` meteorology@` the social sciences@` and population genetics. And of course physics itself is no stranger to the statistical and the probabilistic.
Perhaps@` however@` there is some other relevant kind of interlevel explanation that is transitive@` neither best explanation nor probabilifying explanation. It would seem not. Consider to begin with the interlevel explanation of temperature in terms of mean molecular kinetic energy. Strictly speaking@` the bare physical fact that the molecules in my coffee have a certain mean kinetic energy does not by itself explain@` because it does not itself imply@` that the coffee is piping hot. What is required in addition is some correspondence rule or bridge principle that connects mean molecular kinetic energy with temperature. Likewise@` the bare physical fact that certain protein molecules on a cell's surface have bonded to certain other molecules does not itself explain@` because it does not itself imply@` that there has been communication of significant biological information to the cell from its environment. We need an appropriate correspondence rule or bridge principle connecting the two@` if we want the assertion of interlevel explanation actually to be an explanation or to explain.
What this suggests is that an assertion to the effect that the lower-level properties Bi explain the higher-level N is elliptical. What is called interlevel explanation of N by Bi is typically explanation of N by Bi within or relative to an interlevel theory. For it is only within interlevel theories that we find the appropriate bridge principles@` those that enable us to connect Bi with N so as to warrant the elliptical assertion that N is explained by Bi. What explains N@` more strictly@` is the conjunction of Bi with some principle connecting Bi with N.
Even the latter assertion is somewhat elliptical@` since what the relevant principle is and just how it is to be interpreted and applied depend on the theory. So we should say that what explains N@` strictly@` are Bi conjoined with a bridge principle within a specified interlevel theory T. For example@` it is only within the interlevel theory we call a kinetic theory of temperature@` and given the appropriate bridge principle it contains@` that my coffee's being hot has an interlevel explanation in terms of the mean kinetic energy of its molecules. Likewise@` it is only within a molecular biology that cell communication has an interlevel explanation in terms of the biochemical properties of certain molecules. Interlevel explanations ride on interlevel theories.
Whether and in what sense an interlevel explanation is an explanation or does explain@` and to what extent it is or does@` obviously depend heavily on whether and to what extent the relevant interlevel theory satisfies certain conditions. This in turn is mostly a matter of how successful the interlevel theory is in connecting a higher-level theory T2 (say@` cell biology) with a lower-level theory T1 (say@` biochemistry). The most successful interlevel theories are those that among other things effect the greatest degree of "unification" of T1 and T2 (as in the case of molecular biology). Such interlevel theories involve at least the following sorts of connections between T1 and T2:(21)
I. INVISIBLE@` INCONSCIENT@` MYSTÈRE : DU DIEU INCONSCIENT Selon le point de vue qui va être exposé ici@` les pensées humaines se distinguent selon leur plus ou moins grand degré de sensibilité à l’invisible. La métaphysique n’est en effet d’abord@` selon l’enseignement du Phédon@` qu’un savoir de l’Hadès (Aidès@` A-eidès). On lui reproche son monde d’abstractions et son refus du corps. La métaphysique cependant ne condamne pas les sens ou la vie@` elle se donne sur la vie un point de vue qui n’est autre que celui des morts. On n’a sans doute pas assez médité cette condition du savoir métaphysique@` que Virgile ou Dante illustrent pourtant à plein dans leur cheminement aux Enfers. Toutes les abstractions de l’ontologie qui semblent avoir raison de la vie ne sont en fait que l’esquisse d’un savoir des morts. L’Enfer y précède largement l’immortalité — ou lui donne son sens authentique. Vico explique ainsi le sens du mépris des anciens pour le corps :
Les optimates étaient les lettrés de la littérature héroïque@` grâce à laquelle ils gardaient la sagesse héroïque dont le fondement était que les âmes humaines étaient immortelles. Il s’agit quasiment là d’une tradition du genre humain. Ils tenaient pour rien les corps@` parce que les corps@` ils les touchaient@` tandis que les images des ancêtres@` non.Telle est la théologie des poètes qui font des âmes les «imagines humanae maiorum»@` les images humaines des ancêtres.
Les «imagines humanae maiorum» résumeront toujours l’ontologie profonde du monde idéal des philosophes@` qui n’est d’abord qu’un monde fantomatique. L’invisible@` né de la tombe et transmis par le rituel@` est l’authentification secrète des abstractions spéculatives@` et les «mystères de l’amour» transmis par Diotime à Socrate ne sont qu’un exercice pour rendre les corps à une invisibilité d’abord funéraire. Le Phédon et le Banquet sont plus que des oeuvres illuminées qui nous font regretter la pente dialectique du platonisme ultérieur@` ils sont les gardiens définitifs de la dimension bachique de la philosophie@` c’est-à-dire de la dimension orphique et souterraine qui est seule à même de donner son sens philosophique au culte religieux de la lumière.
Tout mythologique qu’il soit dans son expression@` ce sens appartient par priorité à la raison@` il est vrai non pas définie par ses procédures formelles@` mais par sa destination de gardienne de l’intelligible. La raison est fille de la mort et de l’amour. Il faut soutenir bien haut@` contre toutes les tentations de l’irrationalisme@` que la raison est la première faculté de l’invisible@` loin devant la sensibilité et les sentiments. Les hommes en effet sont peut-être devenus intelligents à force desupposer le monde des relations possibles que pouvaient entretenir les morts avec l’au-delà qui les cache à la vue. De même@` il n’y a pas que les jeunes filles pour acquérir de l’esprit dans le décryptage de la sexualité. Les lois secrètes de la sexualité@` lois d’engloutisssements et de restitutions comme celles de la tombe@` sont parmi les grandes éducatrices de l’intelligence. La raison est le damier de la présence et de l’absence; mort et sexe en sont les premiers exercices.
Dans ses origines les plus assurées@` la philosophie est donc le surgissement@` depuis l’invisible@` d’un régime particulier de la discursivité@` le possible. Ce n’est pas le rêve@` comme le suppose un romantisme un peu facile@` qui entretient des rapports constitutifs avec l’invisible@` c’est la raison elle-même@` conçue comme déploiement des mondes virtuels que suscite la rencontre des phénomènes. La raison est la plus qualifiée pour assumer cette fonction car la raison par essence est libre du visible. La réminiscence@` principe de l’intelligence rationnelle@` vérifie la pure intériorité de la raison à elle-même et son indépendance à l’égard du visible. La spontanéité de nos idées révèle leur appartenance au monde méta-physique de l’invisible. Inversement@` l’invisible exige la purification des esprits de toute attache visible. Platon a discerné dans l’usage de la raison le véritable «catharme»@` l’instrument de purification@` qui donne à l’âme la capacité de traverser l’épreuve de la mort. Ce n’est que par la raison@` principe universel des relations@` que l’invisible établit une relation constante avec la conscience d’abord tournée vers la seule perception@` quand elle ne s’abandonne pas à la simple fatalité de l’incompréhensible.
Mais la raison n’est pas que relation@` elle est aussi causalité. Ici tout bascule. En engendrant la causalité dans son efficience@` la raison passe du monde intemporel de l’invisible au monde des successions. En cherchant à donner un sens (même si c’est toujours sous la forme d’une relation) à une suite d’événements (posés comme réels parce que constatés ou mesurés)@` la raison devient un arpentage du visible. Plus tard@` sans doute@` la force redonnera sa part d’invisible à l’interprétation causale du monde. Mais pour l’instant@` soyons attentifs à cette conversion à l’apparence qui caractérise la causalité. Aristote est peut-être ici le grand coupable. Alors que la cause est toujours une forme finale invisible chez Platon@` il semble avec Aristote que la causalité se dégrade@` au moins en partie@` en efficience physique. L’invisible se voit asservi à une opération et l’ensemble du pouvoir efficace de la causalité est reconduit à des réalités positives qui sont des actes déterminés. Mais la véritable dimension métaphysique réside dans les puissances indéterminées et les actes ne sont certainement que des limites.
La philosophie a cependant été longtemps assez sûre de son essence orphique pour réduire@` autant que possible@` l’action causale à une relation analytique@` et donc pour réduire l’extériorisation de la cause à un moment dans un système de relations. En son fond@` celui-ci demeurait un système de l’invisible. Dans cette logique la cause s’est vue même dépouillée de sa puissance@` au point de n’apparaître plus que comme une simple occasion pour l’agir d’une puissance soumise aux seules lois de l’invisible. Pourtant ces efforts de Leibniz ou de Malebranche venaient trop tard@` le mal était fait. La métaphysique@` depuis Averroès en particulier@` était définitivement devenue le savoir des causes. Le grand pouvoir de la raison allait se trouver asservi par les idéologies.
On ne soulignera jamais assez que c’est le Dieu-cause qui a fait sombrer la philosophie@` au point qu’on peut se demander si l’immense effort de savoir qui s’est honoré du nom d’amour de la sagesse n’a jamais été autre chose qu’un instrument au service des idéologies. D’où viennent ces idéologies? Elles ne viennent pas d’une source triviale@` sans doute@` mais elles ne proviennent pas de l’invisible pour autant. Elles résultent plutôt de l’extrême détresse du visible@` autrement dit de la crainte. Les idéologies proviennent toujours du malheur. Elles voudraient ne plus craindre le malheur et elles appellent cette espérance providence. Elles voudraient donner des causes au malheur@` et elles vont trouver ces causes dans la faute — ou dans l’innocence — de celui qui en est le responsable.
Très vite la philosophie fut requise pour organiser ces symptômes de la détresse du visible. Les religions se consacraient au malheur@` elles avaient besoin que le savoir de l’invisible participe à la conjuration du malheur@` et d’abord de l’invisible dans sa forme la plus épurée@` la raison. Il y aurait désormais une causalité rationnelle intégrale du visible. La raison ne sera plus l’émergence des mondes virtuels dans le temps@` elle sera la mobilisation du virtuel pour rendre raison des désordres du temps. On appelle histoire de la philosophie l’instauration progressive de ces liens entre l’éternel et le temps.
Cet asservissement de la raison n’a pas été général ni unanime. La théologie du malheur et du Sens n’a pas toujours occupé les philosophes et il en est de la rationalité philosophique comme des mathématiques@` tous ses axiomes ne sont pas destinés à une application physique. Il reste que ce fut un événement d’envergure proprement millénaire@` lorsque Freud prononça le mot d’«inconscient»@` comme ce furent des événements proprement incalculables lorsque@` dès 1710@` Giambattista Vico supposa que notre condition présente n’était intelligible qu’à supposer un état antérieur et incoupçonné de l’esprit «humain»@` ou lorsque Schopenhauer fit l’expérience d’une volonté sans raison au fondement des lois phénoménales. Il faudrait ici invoquer encore les poètes@` le caïnisme de Nerval@` la raison ardente d’Apollinaire@` l’antithétique de Yeats@` et d’abord le surnaturalisme de Baudelaire. On peut cependant résumer ces événements en avouant simplement que l’ensemble de ce mouvement a offert la possibilité à l’humanité de sortir de l’âge de la causalité théologique@` et ceci d’une façon bien plus radicale que Comte ne le proposera en son temps@` lui qui n’a jamais soupçonné les pouvoirs d’une raison libre de la causalité. La pensée pouvait alors renouer avec sa seule source authentique@` l’élément pré-déistique@` dont elle est la certitude morale. Penser sera désormais servir le Dieu inconscient.
L’inconscient a beau être une notion contradictoire en son fond@` il est la seule alternative au règne de la cause première dans la pensée. Dieu lui-même lui doit quelque chose. Car il n’est pas d’union à Dieu@` comme il n’est pas d’union à Béatrice@` qui ne soit toujours en un sens une tentative de relation avec les puissances de l’inconscient. Mais la causalité revient toujours@` et la raison asservie par son horizon physique perd l’ouverture qu’elle s’était donnée. Nous sommes au contraire dans le siècle où la qualité des hommes se mesure à leur ouverture à l’inconscient@` comme l’ont très vite reconnu les successeurs d’Apollinaire. Les savoirs sans inconscient sont des savoirs de l’oppression et il faut tenir pour équivalent un savoir causal de la vie et un savoir sans inconscient. L’inconscient est la religion de l’avenir car c’est la seule source des oracles. Le concept d’inconscient est la forme la plus moderne de résurgence de l’invisible@` et de l’invention rationnelle qu’il suscite. Nous lui devons une perpétuation du platonisme antique sous une forme inattendue dont il faut analyser maintenant les profondeurs et les attentes.
Car si l’invisible suscitait jadis@` jusque dans les pouvoirs de la raison@` une ontologie du mystère@` il en va tout autrement de l’inconscient@` du moins dans l’élaboration par Freud de la technique analytique. Nous n’avons d’autre tâche aujourd’hui que de définir l’ontologie qu’exige le fait de l’inconscient et la rupture qu’il effectue dans la tradition théologique. Un dieu plus proche que le Dieu-cause de fait s’est uni à notre âme. Ce dieu est consubstantiel à nous-même et répond à notre nom. Nous sommes les acteurs d’un âge qui est devenu l’âge de l’inconscient@` et nous serons jugés par nos successeurs sur notre capacité à forger de nouvelles rationalités à partir d’une condition sans doute originelle@` mais dont la crainte et le malheur généralisés nous ont fait perdre la mémoire. A ce prix@` le philosophe retrouvera sa véritable vocation@` qui est d’être un gardien pour la cité@` gardien cependant ni seulement de l’être ni de l’intelligible@` mais d’abord et fondamentalement@` de l’invisible. Il n’est de veille de l’esprit que de l’invisible@` et seul l’invisible peut autoriser la philosophie à se constituer en critique des autres savoirs. Inversement@` il n’est pas de doctrine qui ne puisse trouver un bon sens sous la raison de l’invisible qui lui donne ou retire sa vérité. C’est l’invisible qui donne sa portée absolue à un savoir qui revendique ne rien savoir. Selon sa vocation authentique@` la philosophie n’est jamais qu’un «spectre bord d’un centre obscur».
Wenige Begriffe haben das abendländische Denken der Neuzeit so stark beeinflußt und so oft fehlgeleitet wie der Fortschrittsbegriff mit der ihm zugrunde liegenden Idee@` daß die Evolution@` die Entwicklungsgeschichte des Lebens@` des Menschen@` eine Entwicklung zum “Besseren” bedeutet. (1) Was darunter zu verstehen wäre@` scheint weniger klar. Natürlich denken heute die meisten Menschen “fortschrittlich” – verteidigen damit aber nicht selten jenen blanken Unsinn@` der ihnen von der Industrie@` Politik und Werbung aufgezwungen wird@` ohne zu wissen@` daß sich dahinter bloß eine mehr oder weniger geschickte Strategie verbirgt@` die all jene diskriminiert@` die dem sogenannten Fortschritt gegenüber eine gewisse (und@` so wie die Dinge liegen@` natürlich berechtigte) Skepsis hegen. Manchmal jedoch gilt der Hinweis auf die angebliche Notwendigkeit des Fortschritts auch als Entschuldigung für die Zerstörung unserer Erde. Der dramatische wirtschaftliche Aufschwung der “Tigerstaaten” Asiens lebt derzeit von einem destruktiven Fortschrittsglauben@` der schon in naher Zukunft seine Auswirkungen (auch auf andere Staaten) mit voller Härte zeitigen dürfte. Als der taiwanesische Minister für Erziehung und Sport vor laufenden Fernsehkameras von einem Reisbauern@` der seine Tränen nicht ersticken konnte@` auf die Zerstörung der Lebensgrundlagen seines Landes angesprochen wurde@` wußte er keine andere Antwort als diese: “Mir bleibt doch keine Wahl@` die Gesellschaft verlangt nach Fortschritt.”(2) Wer oder was “die Gesellschaft” sei@` soll hier nicht hinterfragt werden. Welche Blüten aber die Idee des Fortschritts treibt@` auf welchem Denkfundament sie steht und warum die Vorstellung einer “progressiven Evolution” (im biologischen wie auch im soziokulturellen Bereich) bloß Mythen@` Illusionen und Hoffnungen zum Ausdruck bringt@` soll in diesem Beitrag kurz untersucht werden.
Der Mensch ist ein illusionsbedürftiges Lebewesen. Sein Drang@` die Welt und seine eigene Position in der Welt zu erkennen@` ist verknüpft mit illusionären Denkweisen. (3) In der tief in seiner Evolution verwurzelten “MetaphysikBedürftigkeit” (4) spiegelt sich Ratlosigkeit ebenso wie das fundamentale Bedürfnis nach Sinn. In den Bereich illusionären Denkens gehört auch der Fortschrittsgedanke. Zumindest in funktionaler Hinsicht steht dieser Gedanke auf derselben Stufe wie etwa der Glaube an die Vorsehung oder die individuelle Unsterblichkeit. (5) So scheint es@` wie der Paläontologe George G. Simpson einmal bemerkte@` schier unmöglich@` den Begriff der Geschichte ohne den des Fortschritts zu denken. (6) Was freilich nicht ausschließt@` daß wir Geschichte@` Evolution ga nz anders denken müßten. Aber@` darauf wird noch zurückzukommen sein.
Der Glaube an den Fortschritt ist deshalb ein eminent psychologisches Problem@` weil er die Suche des Menschen nach Sinn sehr gut zum Ausdruck bringt und deutlich macht@` daß der Mensch sich mit den Dingen@` so wie sie für ihn sind@` nicht so einfach zufrieden gibt. Systematisch gesehen gehört dieser Glaube daher@` um an Karl Jaspers anzuknüpfen@` in den Bereich der Psychologie der Weltanschauungen (7)@` die zu untersuchen hat@` aus welchen (irrationalen) Quellen menschliche Weltentwürfe gespeist werden@` an welchen Denkfiguren – gleich@` wie instabil sie sich bei näherer kritischer Prüfung erweisen – der Mensch seine Weltsicht und sein eigenes Selbstverständnis gerne orientiert. Die psychologischen Dimensionen des Fortschrittsgedankens kommen in den revolutionären Ideen der französischen Aufklärung gut zum Vorschein. Der Voltaire-Biograph Theodore Besterman schreibt dazu: “Die Menschen richteten ihren Blick nicht länger nach oben und nach innen. Sie begannen um sich zu schauen und sahen@` daß erstens nicht alles gut war und daß man zweitens gegen das Schlechte ankämpfen konnte. Der Meliorismus@` der Glaube an die Verbesserungsfähigkeit der Welt@` trug einen raschen und beinahe vollständigen Sieg davon.! (8)
Die Psychologie dieses Glaubens wird aber nicht unmaßgeblich von der Idee beeinflußt@` daß Fortschritt eine elementare Kategorie der Natur sei@` daß also schon die organische Evolution im Vorfeld der Menschwerdung progressiv verläuft. Die französischen Aufklärer dachten noch nicht in Begriffen der Evolution@` doch die Idee der Stufenleiter oder scala naturae@` die auf die Antike zurückgehende Vorstellung einer “großen Kette des Seins” (9)@` die alle lebenden Wesen miteinander verbindet@` kam dem Evolutionsgedanken schon sehr entgegen. (10) Demnach schreitet das Leben von einfachen zu immer komplexeren Gebilden fort@` und die Naturhistoriker der Aufklärungszeit artikulierten so ihren Glauben an die kontinuierliche@` graduelle Verbesserung der Lebewesen. Damit aber wurde auch schon die Vorentscheidung getroffen@` daß die Evolution kontinuierlich zum Besseren fortzuschreiten habe. Das heute in evolutionstheoretischen Werken@` in populärwissenschaftlicher Literatur@` aber auch in Karikaturen und in der Werbung hundertfach ge brauchte Schema der Evolution des Menschen spiegelt genau jene “Ikonographie einer Erwartung” (11)@` die schon die Vorläufer des Evolutionsdenkens im späten 18. Jahrhundert in die Natur projizierten: Die Natur beginnt mit einfachen Wesen und schreitet zu immer komplexeren@` “höheren” Wesen fort.
Dabei scheint dieser Prozeß mit Notwendigkeit zu geschehen. Das Bild unserer Ahnenreihe suggeriert die Vorstellung@` daß das Auftreten des Homo sapiens von Anfang an festgelegt war@` daß schon jener noch gebückt daherkommende Affe@` der an der Wurzel der Hominidenreihe anzusiedeln ist@` eigentlich keine andere Wahl hatte als sich allmählich aufzurichten@` um schließlich dem stolzen Homo sapiens Platz zu machen. Und alle zwischen ihm und dem heutigen Menschen aufgetretenen Wesen wären nur als (notwendige@` unumgän gliche) Zwischenformen zu betrachten@` unvollständig aber eben wichtig auf dem Weg zum eigentlichen Ziel der Evolution. Natürlich spielt dabei der Glaube@` daß die Evolution einen Sinn haben muß@` eine hervorragende Rolle@` so daß sich evolutionäre Entwürfe wie die des Jesuitenpaters Pierre Teilhard de Chardin (12) einiger Beliebtheit erfreuen dürfen@` während die (realistischere!) Auffassung@` daß die Evolution kein Ziel habe@` nicht auf viel Gegenliebe stößt. Zwar kann@` worauf Konrad Lorenz hingewiesen hat@` die Vo rstellung einer zweckgerichteten Weltordnung eine demoralisierende Wirkung haben (weil sie den Menschen – scheinbar – von jeder Verantwortung für das Weltgeschehen entbindet) (13)@` aber das Bedürfnis nach Geborgenheit ist nicht zu unterschätzen. Dieses Bedürfnis ist eine starke psychologische Kraft@` und auf sie bauen seit jeher kirchliche und weltliche Priester@` die den einzelnen entmündigen wollen@` indem sie ihn von einer diese Welt lenkenden Gesetzlichkeit überzeugen möchten – und damit freilich nur ihre eigenen Machtansprüche legitimieren: Der Mensch soll seiner eigenen “Lebendigkeit” verlustig gehen und sich in den Schoß der Propheten zurückziehen@` wo ihm jene Geborgenheit verheißen wird@` die er als ein seit alters illusionsbedürftiges Wesen genießen will@` ganz gleich zu welchem Preis. (14)
Nun war es gerade das Ziel der Aufklärung@` den Menschen von den entmündigenden Einflüssen illusionärer Denkweisen zu befreien und den idealistischen und spiritualistischen Weltanschauungen ein Weltbild “von unten” entgegenzustellen (15)@` welches auch ihn@` den Menschen@` auf seine eigenen Fähigkeiten zurückführen sollte. Bemerkenswerterweise erlebte aber gerade im Sog der Aufklärung die Fortschrittsidee enorm an Bedeutung. Man wollte sich den Einflüssen der kirchlichen und weltlichen Fürsten entziehen@` und das ging doch wieder nur über den Weg von Hoffnungen auf eine bessere Welt. Diese Hoffnungen würden freilich an Substanz gewinnen@` wenn sich nachweisen ließe@` daß die Entwicklungsgeschichte des Lebens auf der Erde insgesamt progressiv verläuft.
2. Die Attraktionskraft der Fortschrittsidee in der biologischen Evolutionslehre
Vom Fortschritt in der (organischen) Evolution waren (und sind) keineswegs nur “Geisterseher” überzeugt@` sondern auch manche der Architekten des modernen Evolutionsdenkens. Dazu nur zwei Zitate:
“ Wir können ... mit Vertrauen auf eine Zukunft von ... unberechenbarer Länge blikken. Und da die natürliche Zuchtwahl nur durch und für das Gute eines jeden Wesens wirkt@` so wird jede fernere körperliche und geistige Ausstattung desselben seine Vervollkommnung zu fördern streben. (16)
“Ich glaube an die Macht der menschlichen Vernunft@` ich glaube an die Macht der Selektion und ich glaube@` daß die Vernunft vernünftige Selektion treibt. Ich glaube@` daß dies unseren Nachkommen in einer nicht allzu fernen Zukunft die Fähigkeit verleihen wird@` jene größte und schönste Forderung wahren Menschentums zu erfüllen. (17)
Nesse trabalho tecemos críticas ao movimento construtivista@` que segundo nossa avaliação super-valorizou o papel das construções individuais@` em detrimento da dimensão ontológica do conhecimento científico. Ele será desenvolvido tomando por base alguns trabalhos críticos dirigidos ao movimento construtivismo e uma análise da recepção das idéias de Thomas Kuhn pelas pesquisas em ensino de ciências. Uma de nossas conclusões será mostrar que o construtivismo não valoriza suficientemente a apreensão de uma realidade associada ao mundo físico. Isto acaba por se refletir num enfraquecimento do conhecimento científico frente a outras formas de conhecimento@` instituindo uma espécie de relativismo epistemológico entre as diversas formas de conhecer. Nesse sentido@` apresentamos as idéia de Mário Bunge sobre o papel dos modelos na ciência e sua vinculação com a realidade. Visamos desta forma@` minimizar excessos contidos nas teses construtivistas e realistas@` ou seja a tendência a vislumbrar toda construção humana como atividade desvinculada da dimensão ontológica do mundo e todo realismo como expurgo da ação humana.
A abordagem construtivista foi o movimento de maior impacto na educação científica nos anos 80 e 90. Suas críticas ao empiricismo ingênuo que permeava até então as propostas de ensino de ciências geraram transformações positivas no encaminhamento de pesquisas educacionais. Destacam-se nesse contexto de reformulações@` a valorização do papel do indivíduo na apreensão de novos conhecimentos e a conscientização da importância das pré-concepções dos alunos na definição dos currículos e na escolha de estratégias de ensino. Apesar disto@` na última década@` uma série de trabalhos críticos vem levantando questões interessantes relacionadas a implicações e conseqüências do movimento construtivista.
Millar@` em 1989@` já perguntava se a tomada de consciência (tardia no seu ponto de vista)@` de que toda aprendizagem é fruto de uma atividade construtiva do indivíduo@` deveria necessariamente implicar num ensino construtivista. Outros trabalhos procuraram refletir sobre os rumos das pesquisas dentro do movimento construtivista (1).
Recentemente três trabalhos chamaram atenção dentro desse contexto por tecerem críticas à fundamentação epistemológica do discurso construtivista. O alvo das críticas desses trabalhos não foi o movimento construtivista na sua totalidade@` mas a tendência a generalizar e radicalizar a metáfora do fazer associada à ação do sujeito@` em detrimento de outras metáforas como o descobrir e achar que associam-se mais ao objeto do conhecimento. (Ogborn@` 1997) Uma exacerbação deste posicionamento@` pode ser facilmente observado no auto-denominado construtivismo radical proposto por Glasersfeld (1989). "O construtivismo radical tornou-se muito conhecido@` principalmente através das críticas dirigidas ao resto do construtivismo@` que o autor intitula construtivismo trivial – aquele que tem como princípio que o conhecimento não pode ser passivamente recebido@` mas é ativamente construído pelo próprio sujeito cognoscente." (Santos@` 1996@` p. 26) Nas palavras de Glasersfeld:
Construtivismo radical é radical porque ele quebra com o que está concebido e desenvolve uma teoria de conhecimento na qual o conhecimento não reflete uma realidade ontológica "objetiva"@` mas exclusivamente uma ordenação e organização de um mundo constituído pela nossa experiência. O construtivismo radical abandonou o "realismo metafísico" de uma vez por todas. (Glasersfeld@` apud Matthews@` 1994).
Nessa concepção@` a a produção de conhecimento não é a busca da realidade ontológica associada ao mundo experiencial@` mas apenas e tão somente a sua organização a partir de um processo de contínua adaptação cognitiva. Os aspectos epistemológicos de análise recaem sobre a impossibilidade de um mundo físico exterior acessível direta ou indiretamente. Seu foco de atenção recai sobre o mundo subjetivo interno do indivíduo e sobre seus processos de construção. Matthews sintetiza as teses epistemológicas de Glasersfeld da seguinte forma:
1. Conhecimento não se relaciona com um mundo independente de observadores ;
2. Conhecimento não representa um tal mundo; teorias de conhecimento correspondentes são errôneas; ;
3. Conhecimento é criado por indivíduos num dado contexto histórico e cultural;
4. Conhecimento refere-se a experiência individual mais do que a um mundo;
5. Conhecimento é constituído por estruturas conceituais individuais;
6. Estruturas conceituais constituem conhecimento quando indivíduos olham-nas como viáveis em relação a suas experiências; construtivismo é uma forma de pragmatismo. (Matthews@` 1994@` ca 7@` p. 149)
Especificamente sobre as teses de Glasersfeld@` Sucthing (1992) apontou vários problemas presentes na sua argumentação. Em particular@` há confusão entre imutabilidade@` certeza e objetividade@` não há definição clara sobre o conceito de construção e a utilização do termo experiência é associada a versão mais radical e ortodoxo do empiricismo. Além disso@` ele chamou atenção para negligência dos aspectos sociais na análise empreendida sobre a produção de conhecimento@` face a um grande acento na sua coerência individual.
Não nos proporemos a realizar uma análise estrutural das propostas contidas no construtivismo radical@` mas@` como Matthews(1994)@` utilizar a forma clara de apresentação de tais premissas e posicionamentos epistemológicos para tentar depreender tendências e/ou vocações que sejam pertencentes ao movimento construtivista como um todo. Embora não se possa com isto garantir que as posições de Glasersfeld sejam exemplares do movimento construtivista como um todo@` a partir delas é possível vislumbrar conseqüências de determinados posicionamentos epistemológicos para as versões não-radicais do construtivismo. Neste caso@` o que nos interessa é analisar algumas implicações possíveis para as premissas construtivistas@` no que tange a valorização extremada dos processos cognitivos individuais presentes na apreensão de conhecimento. Aí reside@` a nosso ver@` um dos maiores riscos dentro do movimento@` pois se não é possível generalizar a totalidade das idéias presentes no construtivismo radical@` parece-me que a valorização do caráter individual das construções de conhecimento é uma característica amplamente enfatizada pelo movimento construtivista como um todo. Mesmo o construtivismo originado a partir dos trabalhos de Piaget valorizam sobremaneira o papel do indivíduo na construção do conhecimento. Neste sentido@` a super-valorização do papel ativo do aprendiz no processo de ensino/aprendizagem não é exclusividade do construtivismo radical. Apesar de menos enfáticos@` outros autores construtivistas apresentam idéias semelhantes. Matthews (1994@` cp. 7) realiza uma ampla análise de trabalhos indicando que a maioria deles sobre-valorizam o papel do indivíduo na construção de conhecimento@` em detrimento de elementos pertencentes ao mundo físico.
Dentro desde contexto@` propostas didático-pedagógicas que justificam a manutenção de concepções alternativas (mesmo que de forma provisória) por jovens estudantes (2)@` aparecem como conseqüências das teses construtivistas e podem transformar a tomada de consciência da importância das concepções pessoais dos alunos para o ensino de ciências@` em consciência da importância das mesmas frente às concepções científicas (3). Nem sempre fica suficientemente enfatizado o papel desempenhado pelo contexto social e principalmente pelo contexto empírico dentro destas idéias. O mundo físico nem sempre assume função na forma final do conhecimento produzido. Os riscos estão@` então@` associados menos ao que o movimento construtivista explicitamente prega@` mas por aquilo que ele ao não pregar deixa livre ao esquecimento.
God and Gödel: Gödelian Incompleteness in Mathematics and the Confirmation of Theism
James Baird
In 1931@` Kurt Gödel published his monumental findings on undecidable formulas in formal systems of mathematics.1 His incompleteness theorems demonstrated the inability of any strictly formal system of calculation to prove every true mathematical formula. Gödel himself took them to mean that no formal system could capture the full range of human mathematical insight.2 This result changed the discipline of mathematical logic forever.
In what follows@` I want to show that Gödel's results also change the way that humans must look at themselves and the world in which they live. Gödel's incompleteness theorems make the philosophical position of naturalism untenable because they imply that human rationality is forever out of reach of complete scientific explanation. Because of this result@` Gödel's theorems aid Richard Swinburne's rigorous Bayesian confirmation of theism. They remove an important objection to Swinburne's approach@` and they also make available the existence of human rationality itself as another piece of evidence for the hypothesis that God exists and is the creator and sustainer of the world.
Gödel's proof was aimed at answering the question of whether or not it would be possible to prove all the truths of mathematics by completely formal means@` that is@` simply by following rules about how to manipulate marks on paper@` without the need for understanding@` insight or intelligence. At the time@` confidence in logic was nearing its zenith@` and many took it for granted that mathematics could be completely formalized. Gödel's solution was stunning@` because it used the simplest part of mathematics@` arithmetic@` to show that mathematics could not be formalized in this way. In effect@` Gödel showed that if a formal system for logic included the ability to do addition and multiplication@` and if it was constructed so that it was consistent@` i. e. did not prove contradictions3@` then a true sentence@` call it the Gödel sentence@` could be constructed following the rules of that system which could not be proved by that system.4 His proof was completely general@` so that even if the system were modified so that it could prove the Gödel sentences which baffled it before@` unless the modifications made the system incapable of arithmetic or prone to contradiction@` the modifications themselves could be taken into account to generate new Gödel sentences which would be unprovable by the new system. In this way@` Gödel dashed all hope for a completely formal mathematics.
This finding was dramatic in its effect on the mathematical community@` but it seems to be of limited interest otherwise. But almost immediately@` further research showed that Gödel's results have radical implications in other areas as well. In 1936 and 1937@` a British mathematician named Alan Turing@` described abstract machines which lie at the foundations of all modern computers.5 These machines@` now called Turing machines@` carry out calculations in extremely simple ways@` but given sufficient time and resources@` they are apparently capable of carrying out any procedure which can be carried out by strictly formal means. Indeed@` Turing showed that any formal system can be translated into a Turing machine with equivalent output@` and any Turing machine can be translated into a formal system. An implication of this is that anything which can be done by any modern computer can also be done by a Turing machine@` (though for any interesting calculation@` the Turing machine is likely to take trillions of years).
Because of the intertranslatability of formal systems and Turing machines@` it was to be expected that Gödel's incompleteness would arise for Turing machines. Turing showed that and more in his original works.6 The consequence is that modern computers@` and all imaginable extensions of modern computers@` face the same incompleteness which Gödel demonstrated in 1931. No computer can generate all mathematical truths. It is sometimes thought that computers which used massively parallel architecture@` or heuristic programming@` or which can learn from past failures (even past failures to prove Gödel sentences) might be able to escape the bounds of Gödelian incompleteness. But as long as such improvements are mechanical (as long as computer wizards aren't actual wizards)@` and as long as they do not cause the computer to start proving contradictions or degrade the computer's ability to do arithmetic@` then the improved computer will be describable as a consistent@` arithmetically competent formal system which is subject to Gödel.7 A computer is subject to Gödel's results even if it incorporates random elements@` whether the actual randomness of quantum effects or the pseudo-randomness of some chaotic system@` as long the randomness does not lead to inconsistency or arithmetical breakdown.8 Thus@` no imaginable advance in computer science will give computers the power to overcome Gödelian incompleteness. There will always be mathematical truths beyond the reach of any particular computer.
Naturalism's problem with Gödel Given the common assumption that any lawlike natural process can be computationally simulated to any degree of accuracy@` if only we have enough time and resources@` it has occurred to several thinkers that Gödelian incompleteness may pose a serious threat to naturalism by putting human thinking beyond the power of any scientific theory to explain. The Oxford logician@` J. R. Lucas published an article to this effect in 1961@` claiming that Gödelian incompleteness implied the incompleteness of any mechanistic model of human thinking.9 He was met with a storm of (often mutually destructive) refutations in succeeding years@` but answered them adequately enough to republish his argument as the key element of his 1970 book@` The Freedom of the Will.10 Lucas's work helped stimulate Douglas Hofstadter@` a dedicated believer in the computational model of the mind@` to publish the 1979 best seller and Pulitzer Prize winner@` Gödel@` Escher@` Bach.11 In this book@` Hofstadter developed a particular objection to Lucas's argument which will be reviewed later. In 1985@` the Harvard philosopher@` Hilary Putnam@` used Gödel's theorems to show that human rationality could not be prescriptively formalized.12 More recently@` the Oxford physicist@` Roger Penrose@` has published The Emperor's New Mind13 in 1989@` and Shadows of the Mind14 in 1994@` expounding his argument that Gödel's theorems show that human thinking cannot be entirely the result of mechanical@` computable processes. Indeed@` Penrose goes to great lengths to show that human thinking cannot be the result of any known physical processes. Penrose has been subjected to his own storm of objections15 mostly the same ones which had been aimed at (and refuted by) Lucas earlier. Whatever else may be concluded about them@` the reactions to Lucas and Penrose indicate that they are striking at something that is dear to many.
To see the nature of the problem Gödel poses for naturalism@` let's engage in a little science fantasy. Imagine the grandest possible scientific research program@` the Human Genome Project. The aim of this project is nothing less than the mapping of human intellect in its entirety. Imagine that after years or centuries of work@` the project is completed@` and humans beings are furnished for the first time with the completed Human Genome Map. Using the Human Genome Map@` psychologists can trace the origin of any thought@` at least in principle. Every belief@` hope and perception of which humans are capable finds it explanation in the laws and principles of the Human Genome Map. Mental illness can be treated with pinpoint precision. Mental energy can be channeled at maximum efficiency. The dark sources of superstition@` war and hatred can be brought into the light and eliminated. The future of mankind seems forever bright.
But there is a catch for those who remember the work of the 20th century logician@` Kurt Gödel. The Human Genome Map can be translated into a formal system which should be able to prove every mathematical truth which the human intellect is capable of recognizing. Since human beings are capable of addition and multiplication@` we would expect this formal system to be able to prove the truths of addition and multiplication. So the system has one of the characteristics@` arithmetical competence@` which is needed to make it subject to Gödel.
Would the system prove contradictions? Humans make errors and contradict themselves all the time@` so we might assume that the system would be inconsistent in the same way. Of course@` the system might well incorporate various guessing mechanisms and heuristic elements which may lead it into error sometimes@` but what about when it is functioning at its best? Imagine that it is functioning under ideal conditions in which there are no constraints of time or resources. If it generates contradictions even under such ideal conditions@` then the entire project will quickly collapse@` because a system which proves a contradiction proves everything.16 Of course@` if every sentence can be proved@` then no sentence is any better than any other. If everything is proved@` then nothing is. Any system which generates such a result becomes absolutely useless.17 To say that the Human Genome Map is such a system and that it truly reflects our best rational capabilities would be to say that all of our beliefs are useless@` including our belief in the Human Genome Map. So we had better say that the system derived from the Human Genome Map would be a consistent system when operating at its best under ideal conditions. Therefore@` the formal system derived from the Human Genome Map would be a consistent@` arithmetically capable system@` and so would be subject to Gödel's incompleteness results.
But this leads to a proof that the Human Genome Map does not completely describe our thinking. For using Gödel's techniques@` we can derive a Gödel sentence for the Human Genome Map system. This sentence will be true@` of course@` and we will see it to be so@` but it will not be provable by the Human Genome Map system. In recognizing the truth of the Gödel sentence@` we will have gone beyond what any reasoning completely described by the Human Genome Map should have been able to do. Of course@` it would be possible to work on the Human Genome Map system until it could prove the old Gödel sentence. But the improvements would allow us to generate a new Gödel sentence@` which could not be proved in the system of the new Human Genome Map. This process could continue indefinitely@` but Gödel's proof guarantees that the human recognition of mathematical truths will always be slightly outside of any Human Genome Map which can be created.
Obviously@` this little thought-experiment hands metaphysical naturalism a stunning defeat. Metaphysical naturalism is the view that everything can in principle be explained as the result of purely natural processes guided only by natural laws. But if the Human Genome Project cannot succeed@` then human thinking cannot ever be completely explained in this way. There is something to human thought which always escapes naturalism's net.
Naturalism's Defenders Naturalism is far too robust a position just to give up in the face of Gödel. Naturalists have an entire list of objections against any deployment of Gödel in this way. Most of these@` though still popular@` have been answered adequately both by Lucas and by Penrose. But there are some objections to the Gödelian attack which show possible escape routes for naturalism. Each however creates interesting problems of its own.
Penrose: The Quantum Brain Defense The first of these would be from Penrose himself. Penrose goes to great length to show that human thinking cannot be the result of any known physical processes because he is building a case for a new physical process. Penrose believes that a union of quantum analysis and Einstein's relativity theory would come down on the side of quantum analysis@` with the result being a theory of Quantum Gravity. Penrose hopes that Quantum Gravity might@` in certain special circumstances@` lead to processes which are truly non-computable. By using these processes@` Penrose believes that the human brain might also be non-computable and so transcend the limits of Gödelian incompleteness. In the Emperor's New Mind@` Penrose argues that such processes might be made use of in systems of neurons@`18 but in Shadow's of the Mind@` he suspects that such processes might actually be used by the brain at the far smaller level of the microtubules of neurons.19 In this way@` by suitably expanding physics@` the brain might be an entirely physical object and still transcend the limits of Gödel. This could be viewed as a salvation for a suitably expanded naturalism.
Our brief response to Penrose would have to be: too early to tell@` but unlikely. To be non-computable is to be non-lawlike. We hate the idea of physical lawlessness@` and resist it at every opportunity. Quantum analysis is the only example of scientific acceptance of fundamentally lawless behavior on the part of nature@` and nobody is too thrilled about it. Einstein was notoriously dissatisfied with the lawlessness of quantum analysis until he died@` and very few physicists even today view the lawlessness as real. The standard interpretation of quantum analysis@` the so-called Copenhagen interpretation@` tends to see quantum lawlessness as a limitation on our knowledge rather than a real fact about the world. For Penrose's proposal to succeed@` a realist interpretation of quantum events is not only essential@` but must be expanded to include gravity.
Current quantum analysis is tolerated@` in spite of its lawlessness@` because there is no rival theory which can match its enormous predictive ability. But here Penrose runs into trouble. The only grounds for believing in the yet-to-be-discovered quantum gravity is that it would allow human rationality to be physical and still escape Gödelian limits. If this is the only area in which quantum gravity is relevant@` then it is unlikely to enjoy the kind of predictive success which coaxes physicists to a grudging acceptance of more traditional quantum analysis.
For these reasons@` naturalism does not receive much comfort from Penrose. He correctly diagnoses the dangers which Gödel implies for traditional naturalism@` but as a defense of naturalism he offers only the possibility of a yet-to-be-discovered theory of quantum gravity@` leading to yet-to-be-discovered non-computable processes@` which can be used by yet-to-be-discovered mechanisms in the microtubules of the brain. There is no particular evidence for any of these@` so they seem justified only as an effort to save naturalism in the face of Gödel's theorems. Naturalism would need far stronger support than it has to warrant such a leap. Small wonder that naturalists have been Penrose's most aggressive critics.
Dennett: The Human Fallibility Defense The most outspoken of these critics has been the philosopher Daniel Dennett.20 Dennett proposes that naturalism@` in its computational guise of strong Artificial Intelligence@` can defend itself against Gödelian limits by appealing to the fallibility of human reasoning. He admits that Gödel's Theorem tells us that no formal system or equivalent algorithm (computer) can prove all the mathematical truths humans can recognize. But@` he says:
Gödel's Theorem in particular has nothing at all to tell us about whether there might be algorithms that could do an impressive job of "producing as true" or "detecting as true or false" candidate sentences of arithmetic. If human mathematicians can do an impressive job of just seeing with mathematical intuition that certain propositions are true@` perhaps a computer can imitate this talent@` the same way it can imitate chess-playing or conversation holding: imperfectly@` but impressively. That is exactly what people in AI believe: that there are risky@` heuristic algorithms for human intelligence in general@` _.21
Dennett's argument is that humans guess and take short cuts in order to survive@` and that their rationality thus falls short of the kind of rock solid proof found in the systems Gödel deals with.
This is an interesting suggestion@` but it falls to pieces when we begin to ask a few questions. First of all@` how extensive is the rational fallibility Dennett has in mind? Dennett clearly suspects@` though cautiously@` that we are up to the task of pushing back the boundaries of knowledge until we explain all aspects of our world in purely scientific terms.22 But if our intellects are too fallible@` we simply may not have what it takes to reach his dream. Perhaps Dennett means that we are fallible@` but also self-correcting@` so that we can keep working by trial and error until we get things right. But in this case@` Gödel becomes relevant once more@` for as Lucas pointed out 25 years ago@` "A fallible but self-correcting system would still be subject to Gödel's results."23 So Dennett must be hoping that we have a very special kind of fallibility. It must be severe enough that we will never under any circumstances overcome it completely@` but it must not be so severe that it finally prevents us from completing our scientific explanation of the world. This is a possible hope@` I suppose@` but it cannot be said that it has a lot going for it other than a faith in naturalism itself. Just to cite one problem@` it is hard to imagine what sort of evolutionary pressures could produce just this almost unnoticeable sort of fallibility. How could such a retiring problem have any reproductive significance?
Things are even worse for Dennett if we imagine his hoped for completion of science. Suppose for argument's sake that we have the very well-behaved kind of fallibility which Dennett's position calls for. Once again imagine the completion of the Human Genome Map. Certainly by this time@` if not long before@` the sources of human fallibility will have all come to light. Will we@` or will we not@` be able to eliminate our fallibility at this point@` and gain the ability in principle (thought perhaps not the time or resources in practice) to reason correctly? Either option is catastrophic for naturalism. If we can eliminate our errors@` even in principle@` then the formal system derived from the Human Genome Map will be a consistent@` arithmetically competent system and so subject to Gödel. In this case@` we will discover that we are something other than the Human Genome Map or any improvement thereof@` and naturalism fails.
On the other hand@` if even with the help of Human Genome Map we are unable to eliminate our errors@` then we must be unavoidably inconsistent reasoners. In this case@` as we have seen earlier@` we will have an unavoidable proof of every sentence we can say or think. Everything will be true for us@` and so nothing will be@` including naturalism.
Faced with these looming catastrophes@` Dennett seems forced into the claim that our own understanding of the true Human Genome Map will never be clear enough to carry out the Gödelian refutation of it. This indeed seems to be the escape he was exploring at one time.24 It is certainly the position of his friend@` Douglas Hofstadter.
Hofstadter: The Necessary Ignorance Defense Hofstadter has given a new twist to a long-established defense against Gödelian refutations of naturalism@` put forward most effectively by Paul Benacerraf in his dispute with J. R. Lucas. Benacerraf made several attacks on Lucas's version of the Gödelian argument@` and he concluded with the claim that at best@` Gödel's theorems proves if I am a Turing-machine "I cannot ascertain which one."25. This argument hinges on the fact that we can only see the truth of Gödelian formulas of formal systems we can understand. This means that we can continue to believe that our minds operate entirely according to some algorithm as long as we can come up with some plausible reason why we can never discover enough about the algorithm to be able to derive and understand its equivalent formal system and see the truth of the relevant Gödelian formula. Benacerraf suggested that the complexity of our own algorithm might be sufficient@` and Hofstadter has elaborated on this by suggesting that algorithms can be of any finite amount of complexity@` so that sooner or later any particular human will be so overwhelmed by complexity as to be unable to apply Gödel's procedure.26
The trouble with this defense in either version is a failure to take the power of Gödel's proof seriously. Gödel proved@` not just that it takes too long or costs too much or is practically or physically impossible for a plausible formal system to prove its own Gödel sentence. He proved that it is logically impossible. Therefore@` if our minds are the embodiments of sound formal systems@` it is logically impossible for us to see the truth of our own Gödelian formula. The complexity of the system or the length of the proof is entirely irrelevant to this result. Even if finding some Gödel incompleteness result would take billions upon billions of years@` and consume more paper and ink than could be supplied by a universe filled with nothing but ball-point pens and legal pads@` it would still be logically possible to carry it out. It is therefore useless for Benacerraf or Hofstadter to appeal to mere complexity or length to avoid the refutation Gödel hands naturalism. The only way to escape the implications of Gödel is if it is logically impossible for us to know our mechanism well enough to perform the Gödel operation on it. Our ignorance must be logically necessary.27
I suppose it is possible for naturalists to take this line if they are prepared to admit that our minds are the results of real but necessarily mysterious processes. But this last ditch maneuver generates problems of its own@` problems which have a very familiar sound. One of the great appeals of naturalism is its promise of a non-mysterious universe. It is ironic that in the face of the argument from Gödel@` naturalism cannot escape refutation except by hoping that there is a logically necessary mystery right in the middle of the human head.
Worse still@` versions of almost all the standard objections to dualism now arise within naturalism. How do necessarily mysterious processes interact with non-mysterious processes? Is the interaction itself necessarily mysterious or not? If not@` then at what point does the mystery set in? But if so@` what prevents our necessary ignorance of mental processes from spreading to all causally related processes@` and from those on out@` until we are necessarily ignorant of everything? Can we have a non-mysterious theory of the process by which the capacity to carry out necessarily mysterious processes develops in the human fetus? Will the theory of the evolution of the brain be mysterious or non-mysterious? What mathematically definable mutations and selection pressures could be imagined to bring necessarily mysterious processes into being?
In this light we can see that@` at best@` naturalism has almost all the disadvantages of dualism@` as well as its own notorious difficulties with morality@` meaning@` freedom@` values and so forth@` there seems to be nothing left to attract us to it. Because of Gödel@` naturalism is in ruins.
Gödel and the Bayesian Confirmation of Theism The defeat which Gödel's theorem hands naturalism can be used to aid theism in several ways. In what follows@` I will show that the argument from Gödel can be of use in the rigorous program of confirmation of theism articulated by Richard Swinburne.
Swinburne's Bayesean argument Swinburne uses Bayes theorem and other elements of the calculus of probability to build a cumulative case for theism.28 His argument is that theism can be supported by using a variety of inductive arguments to build up a cumulative case for it@` in much the same way that we would for our more important large-scale scientific hypotheses. Using Bayesian techniques@` each bit of evidence can be judged to determine the approximate amount of confirmation or disconfirmation it lends to the theistic hypothesis. In his book@` The Existence of God@` Swinburne builds a case using versions of the cosmological and design arguments@` as well as arguments from consciousness and the apparent providence of God@` supplemented with a rather different kind of argument based on the testimony of experience of God by many witnesses. This case@` he claims@` makes the theistic hypothesis more probable than not.
The argument from Gödel aids Swinburne's case in two ways. It helps establish his claim that personal explanation is a separate@` irreducible category of explanation. This provides Swinburne a way to respond to an important criticism leveled by John Mackie. In addition@` the argument from Gödel provides another piece of evidence which counts in favor of theism@` namely the scientifically inexplicable existence of human rationality.
The Gödelian defense of Personal Explanation One of the crucial pieces in Swinburne's case for the probability of theism is the claim that personal explanation cannot be reduced to scientific explanation. Swinburne argues this on conceptual grounds@` showing that every attempt to reduce personal explanation to scientific explanation involves diminishing or altering the concept. Then he points out that we know perfectly well how to use the concept@` and so it can be accorded an independent status. This is important for Swinburne because theism relies on a special kind of personal explanation@` namely the action of God. For his Bayesian analysis to succeed@` Swinburne has to argue that the theistic form of personal explanation is not terribly unlikely. In this way@` the irreducibility of personal explanation is crucial for the success of Swinburne's case.
The late John Mackie attacks Swinburne on this point in The Miracle of Theism. Mackie claims that the prior probability of the theistic hypothesis is fatally lowered by the theistic appeal to directly fulfilled intentions.29 Since all of our experience is of persons whose intentions are fulfilled only indirectly through physical bodies operating according to natural laws@` the hypothesis that there exists a being whose intentions are fulfilled independently of such means must have an enormously low prior probability.
Swinburne has responded directly to Mackie on this point. His primary complaint is that Mackie has failed to give due attention to his intention of judging the prior probability of the theistic hypothesis on the basis of tautological background knowledge alone.30 Swinburne claims the right to proceed in this way because the distinction between background knowledge and evidence is largely a matter of choice and he wants to use the existence of the universe as one bit of evidence in his cumulative case. This leaves nothing but logical truth as background knowledge. But@` Swinburne urges@` when we try@` on the basis of tautological background knowledge alone@` to judge the prior probability of an all-inclusive hypothesis like theism@` the primary factor is its simplicity. The simplicity of a hypothesis will have some inverse relation to the number of entities and kinds of entities the hypothesis postulates@` and the complexity of the properties the hypothesis attributes to the entities it postulates.31 The crucial point of this in answer to Mackie is that the simplicity of a hypothesis can be evaluated apart from its familiarity or fit with our ordinary experiences and expectations. Therefore@` it does not matter so much whether we are familiar with the direct fulfillment of intentions as long as the concept is a simple one. Swinburne's claim is that it is simple@` and that this is made obvious by the fact that we learn to use this concept in our own case long before we become aware of the complexities of the processes which actually connect our intentions with their fulfillments.32
I certainly think Swinburne's response to Mackie is defensible@` but the argument from Gödel means that even if we@` incorrectly@` accept Mackie's claim that the prior probability of the theistic hypothesis must be assessed on the basis of our ordinary expectations@` we can still resist his criticism. For Mackie's doubt about direct fulfillment of intentions is clearly a corollary of his confidence that there can be@` in principle at least@` a complete scientific explanation of human thought processes@` and the argument I have developed shows that this confidence is misplaced. Mackie says "any personal explanations that we can actually give@` as applied to ordinary actions@` constitute@` when properly spelled out@` a sub-class of causal explanations@` not a rival mode of explanations to the causal one."33 Later in the same paragraph@` he adds:
Teleological description may be distinct from anything involving causation; but teleological explanation of anything's coming about is@` in all ordinary cases@` only a special kind of explanation in terms of efficient causes. For example@` to explain an action as purposive is to indicate that it is causally brought about by the agent's desires@` beliefs and decisions. If we say that a plant or an animal has such and such organs@` or behaves in a certain way@` because this serves some function or tends to produce some result@` this is shorthand for a causal account of how these features have been developed by natural selection.34
By 'causal explanation@`' Mackie means an explanation in terms of laws and initial conditions.35 And Mackie has argued elsewhere what he here assumes@` that teleological causation@` of which causation by human action is one type@` can be seen as a sub-type of this single type of causation by laws and initial conditions.36 Explanations by laws and initial conditions are what I have been calling scientific explanations. Therefore@` it is clear that Mackie's objection depends upon the assumption that we can@` in principle at least@` complete a scientific explanation of human action. But the argument from Gödel shows that this assumption is false. In view of apparently unavoidable interdependence of human rationality and human action@` it is implausible to suggest that we could find a complete scientific explanation of the second when we are prevented from finding a complete scientific explanation of the first. Therefore@` Mackie is simply wrong when he claims that our ordinary personal explanations are@` when properly spelled out@` really just special cases of causal explanations. We are permanently unable to complete the 'spelling out' he has in mind. Consequently@` the personal explanations which we give in relation to ordinary actions cannot be abbreviated or promissory causal explanations. Indeed@` we must now regard most of the events for which we give personal explanations every day to be scientifically inexplicable. It is plausible to suppose that we will continue to believe that most of these personal explanations are correct. And it is plausible to suppose that we are unjustified in asserting the presence of natural laws where we know that no coherent theory can be constructed@` even in principle. On these suppositions@` we must conclude that in every correct personal explanation@` the causal story of the connection of the intention with its fulfillment will stop short at some point. That is@` after science has said everything it can about the events which take place in muscles@` nerves@` neurons and so forth@` it will not have shown the link between the intention and its fulfillment. The connection will only be completed if the intention of the agent has some direct result which begins the scientifically explicable process leading to the fulfillment of the intention. We must posit that such direct results of intentions take place in every instance of correct personal explanation. But this conclusion is devastating to Mackie's objection. For it means that we have daily experience of the kind of direct connection between intentions and physical results@` which is what Mackie actually finds so improbable in the theistic hypothesis.
Furthermore@` my argument leaves science unable to complete any account of the origin (either evolutionary or in terms of individual growth and learning) of the capacities humans have to act intentionally as they do. Nevertheless@` our daily experience confirms that humans do act intentionally. So against Mackie's doubts@` we can say that we are entirely familiar with beings whose intentions bring about physical results@` and yet for whose development we can give no complete causal account.
Viewed from a slightly different angle@` these same considerations answer Mackie's doubts about the category of personal explanation as something separate from causal or scientific explanation. We have seen that true explanations in terms of the intentional actions of humans are scientifically inexplicable. Therefore it is not just that we are faced with a lot of gaps in what it is possible for science to explain it is that we already know and use an alternate scheme to fill a great many of those gaps@` and that scheme is the scheme of personal explanation. Therefore Mackie has no right to complain that Swinburne is doing something irregular when he appeals to the category of personal explanation in theism as something separate from scientific explanation. For this reason and for the ones Swinburne has pressed@` we can see that Mackie's criticisms give us no ground to reject Swinburne's Bayesian methodology.
The Existence of Human Rationality as Confirmation of Theism In this section@` I will use Swinburne's Bayesian methodology to assess the extent to which the existence of human rationality confirms theism. I will argue that the existence of human rationality@` that is@` the human ability@` given finite time and resources@` to recognize true propositions@` raises the probability of the theistic hypothesis.
The first condition which must be met if the existence of human rationality is going to raise the probability of theism is that human rationality must be scientifically inexplicable. As we have seen@` the argument from Gödel satisfies this condition. Human rationality is scientifically inexplicable@` since every attempt has scientific explanation can be show to be incomplete by the Gödelian method.
The second condition which must be met for a Swinburne style inductive argument is that the existence of human rationality must be epistemically more probable on the hypothesis of theism than on the hypothesis that it exists uncaused@` (i.e. with no explanation at all.) Of course@` we can see that the probability of human rationality existing uncaused@` as a brute fact of the universe@` is very@` very low. Human rationality is an extremely complex and orderly phenomenon. It unites the bewildering array of markings@` noises and conscious episodes with which we are continually faced. The propositions signified by these markings@` noises and conscious episodes have intricate relationships@` many of which are perceived through our rationality. Such ordered diversity is just not to be expected unless there is some reason for its existence. So human rationality is very@` very unlikely to exist uncaused.
But we can also see that there is more reason to expect the phenomenon of human rationality if God exists as described in Swinburne's theistic hypothesis37. First@` if God exists@` then there exists a being with the power to bring human rationality into existence. Second@` as Swinburne has already shown in his argument from consciousness@` God has good reason to bring about the existence of agents of limited power and knowledge who have the ability to increase their power and knowledge.38 But beings will only be able to move from limited knowledge to greater knowledge if they are in some sense rational. So God has good reason to bring about the existence of rational beings.
Furthermore@` we can see that God might have good reason for choosing to create our particular type of rationality. One of the important features of our rationality is our ability to create and use algorithms and recognize truths about them. We can imagine having@` and often wish to have@` a more immediate grasp of complex logical points and a greater capacity to remember all the relevant issues of some problem. But our inadequacies in these areas can be overcome to a certain extent by our ability to construct rules for reasoning. With our rules for logic and arithmetic and so forth@` we can use the limited memory and reasoning ability we have to solve intricate and lengthy problems. And often@` when we find and train ourselves in largely automatic procedures in some domain@` we achieve a level of speed and accuracy that closely approximates what we would expect from beings with far more internal processing power.
Now@` there may well be good reasons for God to bring about beings with far more unconscious reasoning power and brute memory than we have@` who for these reasons would not have to rely as heavily on algorithmic reasoning as we do. But we can see that he also has good reason to bring about beings like us. For constructing algorithms in any domain requires effort@` and therefore requires a choice on our part. While algorithmic reasoning can impart great power and knowledge@` these benefits do not come automatically. If we do not make the effort@` we remain ignorant and weak@` but with effort@` we are able to create algorithmic structures which tremendously expand our knowledge and power. So by creating beings who must depend on algorithmic procedures@` God creates beings with a wide range of choice concerning the amount of knowledge and power they achieve. It seems to be true@` as Swinburne argues@` that it is good thing that there be at least some beings in a largely do-it-yourself world. Consequently@` it is a good thing that there should be beings with our kind of rationality. Therefore@` we can see that God has good reason to bring about human rationality.
Thus@` if God exists@` it is not all that unlikely that he will choose to create human rationality. Since we said that human rationality is very@` very unlikely to exist uncaused@` the probability that something like human rationality will exist is increased by the hypothesis that God exists. By Bayesian analysis it follows that the existence of human rationality raises the probability of the theistic hypothesis.
Gödel's theorems have been called the most important logical theorems of this century. I concur with this assessment@` and would add that their significance for wider areas of thought has not yet been fully appreciated by the philosophical world. As I showed in my first section@` they clearly reduce naturalism to a position which is@` at best@` too weak to be tenable. Further@` as I showed in my second section@` they strengthen Swinburne's rigorous Bayesian case for theism in two ways. First@` one implication of Gödel's theorems is that personal explanation is not reducible to scientific explanation. This raises the plausibility of theism@` which relies on the special case of personal explanation by God's action. Second@` since Gödel's theorems show that human rationality is scientifically inexplicable@` and since there seem to be clear reasons why God might well create beings with our kind of rationality@` human rationality is more to be expected with the theistic hypothesis than without it. In this way@` the existence of human rationality becomes further confirmation of the existence of God.