tIERBERT KEUTH

OBJECTIVE POPPER

KNOWLEDGE

ON BODY,

MIND,

OUT AND

OF IGNORANCE: THE

THIRD

WORLD

ABSTRACT. In the fifties, Popper defended an interactionistic version of body-mind dualism. It distinguished between the world of physical bodies and states and the world of "mental states". Later he added a third world of "objective thought contents". He claims the assumption that there is the third world is a necessary presupposition of problem-solving in general and of his philosophy of science in particular. The present article contains separate reasonings to the effect that this presupposition is neither necessary nor even possible. It is further argued that postulating the existence of entities makes sense only relative to a criterion of ontological commitment, which Popper does not mention and obviously does not have, and that in addition it presupposes a theory, which is tentatively accepted as true and which according to the criterion implies the existence of the entities. But as yet there is no testable theory involving terms like "mind", "intention" etc., which made the notion that itself or its terms are essentially different from what is already known in the empirical sciences at least plausible. Therefore the body-mind controversy is still pointless. Popper's stand on it seems to be but a reflex of his anti-behavioristic and anti-psychologistic attitude.

1. P o p p e r ' s ideas on the three worlds are closely connected with his p h i l o s o p h y o f science, "critical r a t i o n a l i s m " or, as he n o w calls it, " r a t i o n a l criticism". I n fact he says that it is " o n l y i n this third world, that the p r o b l e m s a n d standards of r a t i o n a l criticism can develop"A A brief sketch o f the core of his p h i l o s o p h y might therefore help to unders t a n d his views o n ontology. W h e n the idea o f the verifiability of scientific hypotheses h a d to be given up, two m a j o r substitutes were proposed, C a r n a p ' s idea of conf i r m a b i l i t y 2 a n d P o p p e r ' s idea o f falsifiabilityL While C a r n a p had to design new calculi, which never became so rich that they permitted to ascribe degrees o f c o n f i r m a t i o n to a n y interesting scientific hypothesis, P o p p e r relied o n deductive logic. I n addition, the logical theories, which he needs are decidable i n a n y finite universe and, as long as only oneplace-predicates occur, also in infinite universes. Therefore a n y o n e who accepts m a t h e m a t i c s has to accept the hard core o f the idea of falsifiability, which is simply that n o general statement m a y be logically derived f r o m a n y n u m b e r o f singular sentences, e.g. o b s e r v a t i o n statements, a n d that it is therefore n o t verifiable, whereas its n e g a t i o n m a y be derived Theory and Decision 5 (1974) 391-412. ,411Rights Reserved Copyright 9 1974 by D. Reidel Publishing Company, Dordrecht-Holland

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from only one singular sentence, so that the general statement itself is falsifiable. On the other hand Carnap's idea has greater scope. It covers not only universally quantified or deterministic hypotheses, which in the simplest case have the form "all A are B", in symbolic notation: (x)(Ax--.Bx), but also probabilistic hypotheses like P (B/A)= r : the probability to hit upon elements of B among elements of A is r. In addition a Carnapian might assign a degree of confirmation to a deterministic hypothesis which has not yet been falsified, while a Popperian has to suspend judgement until it is falsified. But Carnap's idea has remained a program of philosophy of science because until now there are neither sufficiently rich calculi of inductive logic, nor is there a generally acceptable reason to choose a specific one out of the continuum of inductive methods. 4 On the other hand, Popper's idea, though in its core indubitably true and acceptable for everyone, has never become a program of science. 5 Trying hard to crush a hypothesis, which one has laboriously developed, just in order to find out, if one is lucky, that is does not hold good and to be left in the dark otherwise seems to be too frustrating to make it a program. But it has to be admitted that the formalism applied in testing probabilistic hypotheses excludes any definite knowledge on how they fit reality, whereas the logic applied in testing deterministic hypotheses permits in principle to know that they are false. Both kinds of tests, however, presuppose the truth of the observation statements. But for reasons, which Popper has pointed out, 6 we cannot even know definitely whether they are true. Therefore we cannot have any certain empirical knowledge whatsoever. Carnap could accept this sad idea completely. But in contrast to Popper he also offered a consolation, namely the notion that it is possible to ascribe our hypotheses at least degrees of confirmation instead of the truth-values we would prefer to know. 2. In his "Language and the Body-Mind Problem" Popper defended an interactionistic body-mind-dualism. 7 It distinguished between the world of physical bodies and states and the world of "mental states". Later he added a third world of"objective thought contents", s Let us first consider his arguments for dualism. Should they not be tenable, his conception of

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three worlds would be called in question too. The key argument for Popper's stand on the body-mind problem is the impossibility of a physicalistic explanation of language. There are two ways to demonstrate the alleged impossibility. 2.1. Popper could show that every potential explanandum, i.e. in this case every conceivable description of the use of any language must be contradictory, if formulated in physicalistic terms. In this case the impossibility would be definitely proved. But he fails to produce a single contradictory statement, while counterexamples abound. Instead he asserts that in particular "doubts about the existence of other minds become self-contradictory if formulated in a language"P He does, however, not even report on any such contradiction. 2.2. Second Popper could produce a theory excluding all those theories on language, which are formulated in physicalistic terms, or even all theories, which might play a part in the derivation of explananda stated in physicalistic terms. But his theory in its turn could, for the reasons given above, not be proved and so the statement of the impossibility of a physicalistic explanation of language had to remain a conjecture, which admittedly could not at present be falsified, because there is still no physicalistic explanation of language. The existence of Popper's theory, however, would be an additional reason to try physicalistic explanations, just in order to test its assertion that they are impossible. 2.3. But Popper's "Language and the Body-Mind-Problem" does not contain either at least a sketch of a theory which excludes "physicalistic" explanations of language. So his statement that they are impossible flatly contradicts the philosophical credo he professed in his "Logic of Scientific Discovery". He simply extrapolates our present incapability to furnish such explanations. But he does not infer that a "mentalistic" explanation of language is impossible from the fact that we do not have one now. So either he is inconsistent or he thinks that there are no explanations except "physicalistic" ones. His argument would then be that language is in principle inexplicable. As we shall see, this would conform to his identification of "explanation by deterministic or probabilistic hypotheses" with "physicalistic explanation".

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What Popper in fact gives are criticisms of arguments intended to support the idea of physicalistic explanations of language and arguments of his own to the effect that physicalistic explanations are impossible, because they do not harmonize with our present prescientific habits of talking about language. 2.3.1. "As for the body-mind-problem, (Popper) wish(es) to reject the following two different theses of the language analyst." The first is: "the problem can be solved by pointing out that there are two languages, a physical and a psychological language, but not two kinds of entities, bodies and minds. 1~ He asserts that the two-language solution is no longer tenable, as it disappears with the idea that the statements of physics and of psychology are about the same facts and therefore translatable into one another. "But the idea of mutual translatability had to be given up long ago." 11 From this Popper concludes that the statements of physics and of psychology are about different facts and obviously also that they are therefore about different entities. 2.3.1.1. But it is not clear whether "the statements a and b are about the same facts" means (1) " a and b are true statements which have the same meaning" or (2) " a and b are true statements whose individual names denote the same entities". In order to get more manageable formulations we consider only singular statements and leave individual variables and their ranges aside. In case (2) the individual names could (2.1) denote states of affairs as in " c is temporary" where " c " is the name of the state of affairs that person d is of age, or they could (2.2) denote other entities as in "person d is of age". Let us therefore examine Popper's statement in each case with the help of a two-language model. For simplicity both languages only admit logical connectives, parentheses, individual names and one-place predicates. The individual names in both languages are the same, i.e. the languages not only use the same signs for names, but the signs also have the same meanings. On the other hand the languages have no common predicate, nor is any predicate of one language definable by any predicates of the other. This means that no sentence of one language may be translated into a sentence of the other. In case (1) the statements are not about the same facts, because they

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are not intertranslatable and therefore do not have the same meaning. B u t nevertheless their individual names have the same meaning and the

statements are therefore about the s a m e entities. This result is not due to the artificiality of our model as the sentences " a is of age" and " a is not of age" drastically show. Though they are not only not intertranslatable but contradictory, they are about the same person. In case (2) the languages deal with the s a m e entities and in so far with the s a m e f a c t s , because their individual names have the same meanings, though the sentences are not intertranslatable. While (2.2) does not pose any additional problems, (2.1) does. In this case the individual names refer to states of affairs, which therefore are the entities whose existence the use of the names prima facie implies. But the states may be characterized by phrases involving names of a different kind, e.g. names of h u m a n beings. So the question arises whether we are committed to assume their existence in addition to or instead of the existence of the states. But in the present context only one aspect of the question is relevant: are these entities the same, when the meanings of the names denoting the states of affairs are the same? They are, as the names cannot have the same meaning in case they may be substituted by expressions entailing different ontological commitment. F o r these reasons f r o m Popper's premiss that the languages of physics and of psychology are not intertranslatable it does not follow that the hypotheses of physics and of psychology are not about the s a m e entities. This does not even follow if we add the premiss that physics and psychology use different names, because the entities are the extensions of their names and names with different meanings or intensions may nevertheless have the same extensions, as Frege's famous "evening star" " m o r n i n g star" example shows. 12 The refutation of Popper's argument for the diversity of the entities which are the objects of physics and those which are the objects of psychology does not even presuppose that e.g. " a ' s b o d y " and " a ' s m i n d " have the same extensions, as " a ' s b o d y " and " a ' s heartbeat" do not have the same extension either and " a ' s heartbeat" is nevertheless a legitimate object of physics. 2.3.1.2. Of course there is no logical and no known factual reason to exclude the possibility of entities with properties, which according to a given definition of the field of physics no physical entity must have. Such

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entities might be called "minds" or "intentions" etc. But if science is asked to decide whether they are there, this can only be done by producing intersubjectively testable hypotheses. If such a hypothesis survives strict tests, permits explanations which no other theory permits, and, according to a given criterion of ontological committment (see below 2.3.2.3) commits to the~assumption that a certain entity exists, then this is a reason to assume the entity exists. But there simply is no well corroborated theory involving terms like "mind". Let us, however, suppose it were there. Then it would, like all theories, be constantly open to revision and so is the criterion of ontological commitment and the definition of the subject area of physics. Any scientific answer to the question whether such entities exist can therefore in principle be only preliminary. So even in this case the statement that physicalistic explanations of language or of other problems, which are supposed to be connected with "the mind", are not only now but in principle impossible, would not be justified. 2.3.2. The second thesis on the body-mind-problem, which Popper wants to reject, is: "the problem is due to a faulty way of talking about minds, i.e., it is due to talking as if mental states exist in addition to behaviour, while all that exists is behaviour of varying character, e.g. intelligent and unintelligent behaviour." 18 "Since (it) is so vague", Popper asks questions to illustrate it, among them: "Is there the signalman's understanding of the message (the stationmaster communicates to him about a train, H.K.) in addition to his understanding-like behaviour? It is possible that the signalman understood the message perfectly well but behaved (for some reason or other) as if he had misunderstood it?" 14 Popper considers three reactions to these questions which he obviously regards as the same. If, as he thinks, the answer is "yes", the bodymind problem arises in its classical Cartesian form. If it is "no", we are faced with a philosophical theory which may be called "physicalism" or "behaviorism". If they are regarded as "meaningless", because all that can be known e.g. on a person's toothache is known through observing his behaviour, we faced with the verifiability dogma of meaning. 2.3.2.1. As Popper's falsifiability criterion of demarcation between

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science and metaphysics 15 is a convincing substitute for the verifiability criterion of meaning and the latter is no longer seriously defended, we may, like Popper, accept the questions as meaningful. We may also concede that the answer to the question "is it possible that the signalman understood the message perfectly well but behaved as if he had misunderstood it?" is yes. This does, however, not imply, as Popper seems to presuppose, that there are the signalman's behaviour and his understanding and that therefore mental states exist in addition to behaviour. 2.3.2.2. If Popper wants to maintain that there are entities to which predicates like " x understands y " refer, e.g. x's understanding of y, he has to showfirst that this assumption is possible, that it does not entail antinomies. The plausibility of the notion of x's understanding of y is no guarantee, especially as the "mental" entities are supposed to be essentially different even from the abstract entities whose existence is assumed in physics and other empirical sciences. In set theory a similar assumption, Cantor's existence postulate, has led to Russell's well known antinomy. The postulate ( E y ) ( x ) ( x ~ y = P x ) states that to any predicate P there is a certain entity y, namely the set of all x which are P. The postulate is by no means implausible, nor is the idea that a set normally does not contain itself as an element. But if we substitute " x does not contain itself as an element" for Px, we can derive y ~ y - , , , y e y . So the attempt to define the set of all sets not containing themselves as an element leads to a contradiction. As the various successful attempts to eliminate Russell's antinomy from set theory show, 16 its derivability depends on the statements which are permitted in set theory. If we want to find out whether "Popper's existence postulate" that there are entities like x's understanding of y leads to antinomies, we have to inspect the system of psychological statements which he wants to permit. As there still is no such system, it is not possible to know now whether it is possible to assume that there are such entities. On the other hand an ad-hoc example of an antinomy "in the theory of the second world" is easily constructed. Take e.g. the statement: " a understands that he doesn't understand himself" or, ontologically speaking "a's understanding of the non-existence of his understanding

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himself exists". I f understanding that one understands something about one's understanding implies that one understands oneself, we have our second-world antinomy. O f course the danger of producing contradictions or antinomies is no reason to stop the production of new theories but it is good reason not to claim that an ontology is necessary before one has even examined whether it is possible. 2.3.2.3. Can we, however, as we did in 2.3.2.1. concede that the sentence "the signalman understood the message perfectly well, but behaved as if he had misunderstood it" is true, and nevertheless refuse the idea that the signalman's understanding of the message exists, or is it necessary to assume its existence? This depends on which other statements the "theory of the second world" contains and on which criterion of ontological commitment we apply. " N o discussion of an ontological question, in particular of the issue between nominalism and realism, can be regarded as intelligible unless it obeys a definite cJ:iterion of ontological commitment." 17 There is still but one such criterion, Quine's famous " t o be is to be the value of a variable". 18 According to this criterion we are committed to assume as existent what may fall into the ranges of the bound variables occurring in statements which we accept as true. A discussion of the criterion and its implications in terms of ranges of bound variables alone is probably not the approach which is most intelligible for readers who are not already familiar with the issue. Therefore I'll start with individual names. When we use individual names like " a " , we normally assume that there is what they purport to name. We tacitly made this assumption above in our two-language model. I f the language, to which the individual names belong, admits in:addition individual variables and quantifiers, we can in this case infer (Ex) Fx: there is an x which is F, from Fa: a is F. But this is not always so. Suppose " a " means "Pegasus" and F is a property which we think only Pegasus but nothing else has. Then we may be prepared to accept "Fa" but nevertheless reject " ( E x ) F x " , because we think that Pegasus does not "really exist". In this case we say that " a " doesn't "really" name, though it purports to do so. This is one reason not to make our ontological commitment dependent on the use of names but rather on the use of bound variables. Another one

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is that individual names may be substituted by expressions containing only individual variables, predicates and o p e r a t o r s : 9 A third reason is that the most interesting statements of science, general theories, contain individual variables, but only seldom names. Coefficients are constants, but they are names only of abstract entities called " n u m b e r s " . The universal quantifier "(x): for all x " in "(x) Fx: all x are F " and the existential quantifier " ( E x ) " are intersubstitutable, as (x) Fx =- ~ (Ex) ~ F x is a valid theorem. Therefore either of them alone is in principle sufficient. But for reasons, which we cannot discuss here and which are connected with the emptiness or non-emptiness of the ranges of variables and with limitations on the variety of such ranges, Church proposes the following alternative to Quine's criterion: " T h e assertion of ( E x ) M x carries ontological commitment to entities x such that M . " 2o Suppose we want to talk about human beings or physical bodies in general and make the set of human beings or of physical bodies the range of our variables. The ranges of variables are then not empty and denumerable. In this case (Ex) Fx is logically equivalent to Fa 1 v Fa2 v . . . v Fa,, where the ai are the names of the human beings or the individual physical bodies and n may be any natural number. Of course do not all physical bodies have names, but it is in principle though not actually possible to name them all if natural numbers are used. The equivalence can, however, only hold, if at least one of the ai, which purport to name, really name, or in other words, if the range of " x " is not empty. Otherwise we have to reject (Ex)Fx. So the criterion of ontological commitment is not as disconnected from the use of proper names as might appear, if one considers only Quine's or Church's formulation. Most important, however, is that it is a "criterion of logical coherence". zl It does not say what the extra-linguistic "reality" must be like, if we want to assert correctly that there is something. The empirical or philosophical interpretation of existential statements is left open. The criterion merely avoids contradictory statements asserting the existence of some entity and at the same time the non-existence of any such entities, which may arise from the use of " n a m e s " that do not "really" name. As there is no formal distinction between such names and "real" names, a formal criterion relying on proper names could not exclude these contradictions. On the other hand there is no such ambiguity in the use of existential statements. To say there is something and nevertheless main-

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tain that it does not exist is always considered to be a contradiction. Though " a understands b " implies ( E x ) ( E y ) ( x understands y), so that we are committed to assume that a and b exist, it does not imply any statement which in lieu of "understands" contains a variable bound by an existential quantifier. Consequently we are not committed to assume that there is something like " x ' s understanding o f y " . This does of course not prove that such entities do not exist. But the assumption that they exist is not gratuitous, as we cannot exclude that it implies antinomies. So we know that accepting the sentence "the signalman understood the message perfectly well but behaved as if he had misunderstood it" as true does not commit us to assume that his understanding exists, but we do not know whether the assumption that it exists will not involve us in antinomies. 2.2.3. The most incisive criticism Popper directs against his opponents, the empirical psychologists, is that "doubts about the existence of other minds become self-contradictory if formulated in a language", z2 His argument can not be that talking about something, e.g. somebody's mind, presupposes its existence, so that denying its existence becomes self-contradictory. This was an issue in the medieval discussion on universals. But, as we saw above, it has long since been recognized that some names do not "really" name, that is not do denote an entity. In addition predicates like " x understands y " are no longer supposed to be names of abstract entities but open sentences, a species of syncategorematic expressions like "this one", so that the use of predicates commits ontologically at most, if they themselves fall into the range of some "second order" variable. His argument cannot be either that, if somebody doubts the existence of minds and formulates hypotheses on the use of language, which do not contain terms seemingly referring to entities like minds or properties which minds might have, then these hypotheses will necessarily be selfcontradictory. Almost any behavioristic statement - true or false - on language would be a conterinstance. His argument in fact is that "in arguing with other people ... we cannot but attribute to them intentions, and this means, mental states". The "machine argument" 2~ is designed to show us why this is so. 2.3.3.1. " A wall-thermometer may be said not only to express its internal

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state but also to signal...". It does, however, not describe, as "we do not attribute the responsibility for the description to it; we attribute it to its maker". But why does Popper not also attribute the responsibility for its expressing and signalling to its maker and consequently deny that it expresses or signals? After all his maker made it according to known physical laws so that the position of its mercury column relative to its reading scale varies with the temperature of the surrounding medium. Popper claims that this situation "is fundamentally the same for all physical machines, however complicated". If we do not understand the mechanism of such a machine and its behaviour is very human, we may "wonder whether it does not, perhaps, act intentionally rather than mechanically (causally, orprobabilistically), i.e. whether it does not have a mind after all ...". "But once we realize completely how it is constructed, how it can be copied, who is responsible for its design etc., no degree of complexity will make it different in kind from an automatic pilot, or a watch, or a wallthermometer. 2.3.3.2. Popper contrasts "acting intentionally" with "acting mechanically" which he equalizes with "acting causally or probabilistieally". This in its turn obviously means "acting in such a way, that the action or a distribution of such actions can be explained or predicted by deterministic or probabilistic hypotheses". On the other hand hypotheses are deterministic or probabilistic according to their form (see above 1) but irrespective of the interpretation which a philosophical realist like Popper tends to give them. 2~ Otherwise an instrumentalist, who uses the formalism of probability theory, would not deal with probabilistic hypotheses. 2.3.3.3. What could "acting intentionally" in this case mean? The answer cannot be as simple as "acting in such a way that the action can be explained or predicted by a mentalistie hypothesis", because, once deterministic or probabilistic hypotheses are eliminated, only singular and existential statements like "Fa" and "(Ex) Fx" remain. They permit historical narratives of the actions of person a, of his mental states and among them his intentions. But there is an obvious difference between saying that at time t person a had intention I and at

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time t + 1 he acted A and saying that his intention at time t contributed to - f o r obvious reasons we cannot say "caused" - his action at time t + 1. 2.3.3.4. Connections or associations between what are in empirical science, but not always as well in logic, called "variables" are expressed either by deterministic or by probabilistic hypotheses. But the hypotheses are not always formulated in a symbolism which makes their logical character apparent in their syntax. Often predicates are used as in " x caused y ' . The logical character of the hypotheses is then hidden in the interpretation of the predicates. But it can always be made explicit " by inquiring under which conditions a sentence containing such a predicate is considered true. The situation is the same for predicates expressing probabilistic connections, and a thought-experiment will show that it is the same also for all linguistic signs expressing connections like the contribution of intentions to actions. 2.3.3.5. Suppose we were given a sentence with such a sign asserting a connection between a's intention 1 at t and his action A at t + 1 and suppose it were true that a had intention 1 at t and acted A at t + 1. Should in this case the sentence asserting the connection only be true, if A and 1 were at least not statistically independent, then "acting intentionally would nevertheless mean "acting probabilistically" or, if A always or never followed o n / , even "acting deterministically". Should the sentence, however, also be true in case of statistical independence, then "a's intention 1 at t influenced a's action A at t + 1" would be logically equivalent to "'a had intention I at t and a acted A at t + t " . The assertion of an influence would then be completely empty. Suppose now there is also a rule on the use of the sign which asserts the association or influence we have been talking about. Being a rule it demands a regularity in the use of the sign. This would also be the case, if it ruled that the sign be only applied to assert the statistical independence of I and A. Were the use of the sign and the kind of association between I and A statistically independent of each other, the sign would not inform in any way about the association, and were its use statistically independent of everything, it had no meaning at all. Therefore, if' 'acting intentionally" cannot be"acting probabilistically" or "acting deterministically" the descriptive use of language, which has to

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be at least probabilistic, if it is to transmit any information, cannot be

intentional. 2.3.3.6. In addition, Popper's machine argument does not contain any reason why "we cannot but attribute intentions" to human beings with whom we argue, nor why we cannot attribute intentions to something of which we know how it works and how it can be copied. The machine argument merely states that we do or else do not do so. This is a report not even on our present knowledge, but on our present habits, which of course may be formed to some extent by our present knowledge. But like all human knowledge it is fallible. So we have to consider the possibility that some day we may know in which way our organism is composed of molecules or even of subatomic particles and how to copy a human being exactly. Would Popper then be prepared to assume we are not different in kind from wall-thermometers ? 2.3.4. Popper presents yet another argument for body-mind dualism, which he even considers to be stronger than the previous one, though one can hardly imagine how this could be possible, as the previous one was that the negation of dualism is self-contradictory. The new argument is on "the causal-theory of naming". 25 Popper thinks that no causal physical theory of the descriptive and argumentative functions of language is possible, since no causal realization of the name relation is possible and naming is by far the simplest case of a descriptive use of words. We already mentioned that names may in principle be completely dispensed with, but let us for the sake of argument suppose, that name relations are indispensable with descriptions. How does Popper show that there can be no physicalistic causal theory of naming? He constructs a causal model of the name relation. It consists in " a machine which, every time it sees a (certain individual, H.K) ginger cat, says 'Mike'". This model is deficient because though the machine may be said to realize "what we may loosely call a 'causal chain' of events joining Mike (the cat) with 'Mike' (its name)", "we cannot accept this causal chain as a representation or realization of the relation between a thing and its name, for it is not the 'objective' physical situation which makes Mike and 'Mike' the beginning and the end of the causal chain, but our interpretation".

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2.3.4.1. This argument provokes two objections. First, Popper concludes from the impossibility to furnish a machine model of naming that a causal theory of naming is also impossible. This conclusion would only be correct, if to any causal theory or at least to any causal physical theory machine models could be constructed which adequately simulate all relevant aspects of the facts which the theory explains. Popper must have tacitly presupposed that once we have a causal theory, we can also manipulate whatever the theory declares to be the initial conditions of the effect it explains. But a theory only says what happens if the initial conditions are there, not that or even how they can be brought about. This information may be contained in another theory. With it the same problem arises again and so on. We can now state a formal condition for the constructability of machine models at least one of which corresponds to each theory. The causal theories have to form a closed system with respect to their initial conditions. There must be no theory whose antecedent which characterizes the initial conditions - is not implied by the consequent - which characterizes the predicted effect - of at least one other theory. But this formal condition is not sufficient. There is still a material condition concerning the content of the theories. To each theory there has to be a chain of theories starting with a theory which contains in its antecedent only the description of a human action which can always be performed and ending with the theory in question. Only then do we know that we can start a process leading to effects predicted by any theory. I cannot imagine Popper to pretend this were the case. If, however, we do not know how to start such a process, or if our theories even exclude it, we cannot construct a machine performing it. 2.3.4.2. Second, Popper argues that, even if there were a chain of causal theories connecting an object and the use of its name, it would not be a realization of the name-relation, as the beginning and the end of the chain are not determined by the "objective" physical situation but by our interpretation. Elsewhere 26 he himself pointed out that nature does not present us with ready made facts-by-themselves to be described in protocol-sentences, but that we always interpret nature in the light of our theories. If this is a general feature of a// descriptions and explanations, it cannot be turned against some of them. 3. Popper's conjectures on the "third world" 27 are centered around his

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conception of " a general schema of problem solving by the method of imaginative conjectures and criticism or, as I have often called it, by the method of conjecture and refutation. The schema (in its simplest form) is this:

P1 ~ TT ~ EE ~ P2. Here P1 is the problem from which we start, TT (the 'tentative theory') is the imaginative conjectural solution which we first reach .... EE ('error elimination') consists of a severe critical examination of our conjecture, ... : it consists, e.g. of the critical use of documentary evidence (or empirical tests, H.K.) and, if we have at this early stage more than one conjecture at our disposal, it will also consist of a discussion and comparative evaluation of the competing conjectures. P2 is the problem situation as it emerges from our first attempt to solve our problem. It leads up to our second attempt (and so on)." 28 The merits of the scheme, which sums up his philosophy of science, have been discussed elsewhere. 29 Most important in our context is Popper's claim that problem-solving according to this scheme presupposes a "linguistic third world" 30 of"objective contents of thought" 81 and involves direct interactions between first- and second-world entities and between second- and third-world entities, whereas interactions between first- and third-world entities are indirect. So we have what we did not have when discussing the second world, a sketch of a theory. If we accept the theory as true we may be committed to assume the existence of the entities which Popper calls "inmates of the third world ''z2 and possibly also the partition of the set of all entities into three "worlds". 3.1. Before examining whether we are in fact ontologically committed let me conjecture which reasoning led Popper to his statements on the third world. His major contribution to philosophy, on which also the above scheme relies, was his proposal to substitute Wittgenstein's verifiability criterion of meaning by a falsifiability or testability criterion of demarcation between science and metaphysics. 33 The "'objectivity of scientific statements (however) lies in the fact that they can be intersubjectively tested". 3~ But hypotheses which we hold "in our minds" and which therefore exist in the second world cannot be intersubjectively tested, as minds are essentially subjective. Of course hypotheses can be

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written down. It is, however, not their physicalfirst-world manifestation, printing-ink on paper, which is intersubjectively tested. So there has to be something else, which is in fact tested. This is their "objective content". As it neither belongs to the first, nor to the second world, there has to be another world of the products of the human mind to which it belongs. 3.1.1. Popper's above proposition is on scientific statements in general. In symbolic notation it contains a universally quantified variable ranging (at least) over scientific statements. Therefore anyone, who accepts the proposition as true, is according to the logician's criterion of ontological commitment bound to suppose that scientific statements exist. But there is an exception to this commitment, which we have not yet mentioned. If the proposition containing the variables may be substituted by a logically equivalent one not containing them, we are not ontologically committed though for linguistic convenience we use the bound variables, because we know how their use can be avoided. So we are not committed to assume that in addition to what we called the first world manifestation of a sentence there is in the third world the sentence itself or its objective content, if everything, which we said by means of variables ranging among other things over " t h e " sentence or "its content", can as well be said e.g. by means of predicates expressing properties of the physical strings of signs on paper. Let us now examine whether this is the case. 3.1.1. A scientific statement or another sentence may be reproduced thousands of times from the same printing-plate. It may be rephrased in different words and translated in various languages. Nevertheless we (and Popper) say that it is always the same sentence and that it always has the same content. According to Leibniz' definition of identity x = y - iF) (Fx - Fy)

x and y are identical, if they have all properties F in common. So what is here called "sentence" (sentence1) cannot be identical with any and a fortiori not with all of the strings of signs on paper which are called "sentences" (sentence2) as well, because the strings of signs differ as to the spatiotemporal location of the individual copies of the book in which they are contained. Also the paper on which they are printed is not the

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same though it m a y be taken from the same charge, and there are minute typographical peculiarities hardly recognizable to the unarmed eye. In different languages completely different strings of signs are used etc. But if we subtract what is different in the individual strings of signs, there remains something common. It is some other typographical properties and above all the properties which characterize the use made of these strings of signs. O f course the use differs from person to person and f r o m context to context, but if the strings of signs are to be effective means of communication, some properties characterizing their use must be the same with some persons in some contexts. Let us for the sake of argument first suppose that all properties of the strings of signs, which we call their use are the same with all persons in all contexts. Which would then be the difference between sentence 1 and the use of the sentences2 and which would be the difference between sentencel and its objective content? We need not investigate the use of "sentence" in the first sense or of "objective content", for, should there be a difference, then, as a consequence of our suppositions, it cannot concern the c o m m o n use or meaning of the sentences2. So, as long as we are only interested in the use or meaning of the latter, the distinction between (1) their use, (2) sentence 1 and (3) its content does not make sense. The distinction between individual sentences, on the one hand and their c o m m o n use or meaning or objective content or sentencel on the other hand of course does make sense. I f the properties of the strings of signs, which we called their use, are not the same with all persons and in all contexts, the situation is more complex. We then have to do with different "uses" and possibly different sentencesl. But our reasonings, as to the use of the single sentence I apply in this case to any of the uses of the different sentencesl. In any case what we called " u s e " or "objective content" can be completely described with predicate constants and therefore does not commit to the assumption that there is anything like "the use", "the meaning", "the objective content" of sentence 1 or even like "sentencel" itself. Consequently the problem to which w o r m the entity belongs does not arise. In the context of formulating and testing hypotheses the third world is therefore completely superfluous. 3.1.1.2. N o w we can also afford a less strict but possibly more plausible

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argument. Suppose, somebody (1 st world) has an idea (subjective knowledge, 2rid world) and lays it down in a string of signs on paper (1 st world). The strings can be copied (lst world) and somebody else (lst world) with the same disposition to use the signs (2nd world) may read it and acquire subjective knowledge (2nd world). He may perform experiments (lst world) and draw his conclusions as to the tenability of the newly acquired subjective knowledge (2nd world). He may also communicate his results to his colleagues (see above). According to Popper's "Logic of Scientific Discovery" there is nothing more objective to "objective knowledge". So even if we grant Popper his stand on the body-mind problems we do not need his third world in order to have the kind of objective knowledge, which plays a central part in his earlier writings on epistemology. But as Popper has not produced any valid reason in support of his stand on the body-mind problem, we may well have "objective knowledge" and at the same time avoid his affluent ontology completely. 3.1.2. Let us for the sake of argument now suppose that Popper's statements about what interacts with what in problem solving are true and that in addition they cannot be replaced by other statements entailing less ontological commitment, so that we are bound to accept the existence of all entities which Popper postulates. This does, however, not imply that the "the world (which contains them all, H.K.) consists of at least three ontological categories: or as (Popper) shall say, there are three worlds".35 Of course Popper is free to subdivide "the world" according to any convention he likes and to call the results "ontological categories". But if the subdivision were rather arbitrary, it would not make sense to defend it as vigorously as he does. Unfortunately Popper does not only seem not to know the logician's criterion of ontological commitment, he also fails to furnish a substitute for it and in addition a criterion of the difference of ontological categories. So we have to make do with his examples. But they are hopelessly ambiguous. 3.2.1. Take e.g. the borderline of the first "world of physical objects or of physical states". 38 Let us leave as well abstract entities as physical states or processes out of consideration and start with a very "safe" definition: The physical world is the world of physical bodies.

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Does an electron now belong to the first world? It has particle- as well as wave-characteristics. So we have to reformulate the definition: the physical world is the world of all entities which - at least also - have particle-characteristics. All such definitions depend on the actual state of our theories, but with the present one this becomes particularly evident. Suppose wave theory could be modified so that it accounted as well for those characteristics of the electron, which are now explained as particle characteristics. It would then no longer be necessary to assume that the electron belongs to the first world. Let us assume also that something of the kind were true of protons, neutrons etc. Further atoms can be regarded as sets of what are today called subatomic particles. The sets are structured by certain physical laws. Therefore we need even today not assume that atoms are physical bodies which exist in addition to the subatomic particles. The same holds for molecules with respect to atoms and for macroscopic physical bodies - the paradigms of physical bodies - with respect to molecules. So, in case our presuppositions are true, we need not assume there is any physical body. In this case the first world is empty and the classical abstract-concrete distinction collapses. Suppose now that the "worlds" are the sets or classes of the entities which they allegedly contain. As there is but one empty set and the empty set is a subset of all sets, the first world would as well be contained in the second and third worlds. But even at the present state of our physical theories we may regard only subatomic particles as "really" existing physical bodies and all the rest as abstract entities or, as is more often done vice versa. So even now the abstract-concrete distinction is extremely arbitrary and so is the border of the "first world" with - probably - the third. 3.1.2.2. As there is no theory on "the mind", which is in any way comparable at least to present quantum-physics, the attempt at a demarcation of the second world is hopeless. Even Popper can, as we have seen, not contribute more on the mind than some prescientific notions, or shall we say prejudices ? 3.2. Last not least the assumption that there is something which corresponds to Popper's characterization o f " t h e third world" is inconsistent.

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"... the third world is the world of intelligibles, or of ideas in the objective sense; it is the world of possible objects of thought." z7 It is not completely clear whether " t o belong to the third world" means " t o be its element" in the set-theoretical sense as we supposed above, or what else. Be that as it may. As the third world contains all possible objects of thought and sets are possible objects of thought, it contains all sets. But the set of all sets is a set. So the third world contains the set of all sets. N o w the statement (Ey) ~x)(x~ y) that this set exists has to be considered true, if the sets postulated by Quine's approach to set theory "new foundations ''3s are to be contained in the third world. However the negation ~(Ey)(x) (x~y) of this statement has to be considered true as well, or else expressions asserting the existence of sets in other set-theories, e.g. the axiom schema of separation (Ey)(x)(x~y=x~z.Px) in Zermelo-Fraenkel's set theory cannot be maintained. So the assumption that all sets, whose existence may consistently be postulated in some set theory, exist, leads to a contradiction. But, if it cannot be consistently assumed that they exist together, it cannot either be consistently assumed that there is something in which they together are contained. So they cannot all be assumed to be contained in Popper's third world. Therefore Popper's third world cannot contain all possible objects of thought. But this is what he asserts.

Faculty of Social Sciences, University of Mannheim NOTES 1 Popper [13], 346. 2 Carnap [11, (2). a Popper [9]. 4 Carnap [2]. 5 Kuhn [7] and Lakatos and Musgrave [8]. 6 Popper [9]. 7 Popper [10], [I1]. a Popper [13], 14[]. 9 Popper [10], 297. lo Popper [10], 294, my italics. 11 Popper [10], 294. 12 Frege [5]. xa Popper [10], 294, all quotations in 2.3.2 from this page, italics mine. 14 Popper [I0], 294, my italics.

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15 Popper [9]. 16 Quine [17]. For an exposition of various axiom systems of set theory see: Part Three. Axiom Systems. 17 Church [4]. 18 Quine [16], 15; [15], 225. 19 Quine [16]; [15], Section 37. Elimination of singular terms. 2o Church [4], 1014. 21 Church [4], 1009. 22 Popper [10], 297, my italics. 2a Popper [10], 296, 297, my italics. 24 Popper [9], appendix X; [12]. 25 Popper [10], 297, 298. 26 Popper [9]. 27 Popper [13], [14]. 28 Popper [14], 32. 29 Lakatos and Musgrave, eds. [8]. ao Popper [13], 346. al Popper [13], 333. a2 Popper [13], 334. 3a Popper [9]; Carnap [3]; Kraft [6]. a4 Popper [9], Ch. 8, p. 44. as Popper [14], 26, my italics. a6 Popper [13], 333. a7 Popper [14], 26, my italics. a8 Quine [17], Ch. 40. BIBLIOGRAPHY [1] Rudolf Carnap, Logical Foundations of Probability, Chicago 1950 and later editions. [2] Rudolf Carnap, The Continuum of lnduetive Methods, Chicago 1952. [3] Rudolf Carnap, 'K. R. Popper on the Demarcation Between Science and Metaphysics', in Arthur Schilpp (ed.), The Philosophy of Rudolf Carnap, La Salle, London 1963. [4] Alonzo Church, 'Ontological Commitment', The Journal of Philosophy LV (1958) 1008-1014. [5] Gottlob Frege, 'Uber Sinn und Bedeutung', Zeitschriftfiir Philosophic undPhilos. Kritik 100 (1892); English translation 'On Sense and Nominatum' by Herbert Feigl, in H. Feigl and W. Sellars, Readings in PhtTosophicalAnalysis, New York 1949, p. 85 iT. [6] Viktor Kraft, Der Wiener Kreis, Wien, New York 1968. [7] Thomas S. Kuhn, The Structure of Scientific Revolutions, Chicago 1962 and later editions. [8] Imre Lakatos and Allen Musgrave (eds.): Criticism and the Growth of Knowledge, Cambridge, G. B. 1970. [9] K. R. Popper, 'The Logic of Scientific Discovery', London-New York 1959, German edition Logik der Forschung, Wien 1935, and later editions both of the German and the English Editions. [10] K. R. Popper, 'Language and the Body-Mind Problem', in Proceedings of the XI

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International Congress of Philosophy 7, 1953; reprinted in: Popper: Conjectures and Refutations, London 1963, p. 293 ft. [11] K. R. Popper, 'A Note on the Body-Mind Problem', in Analysis, N.S., 15 (1955); reprinted in: Conjectures and Refutations, p. 299 ft. [12] K. R. Popper, 'Truth, Rationality and the Growth of Scientific Knowledge', in Conjectures and Refutations, London 1963. [13] K. R. Popper, 'Epistemology without a Knowing Subject', in Rootselaar and Stahl (eds.): Proceedings of the Third International Congress for Logic, Methodology, and Philosophy of Science; reprinted in: K. R. Popper, Objective Knowledge. An Evolutionary Approach, Oxford 1972, pp. 106-152. [14] K. R. Popper, 'On the Theory of the Objective Mind', in Proceedings of the XIV International Congress of Philosophy o. O. 1968; reprinted with stylistic modifications in K. R. Popper, Objective Knowledge, pp. 153-190. [15] W. v. O. Quine, Methods of Logic, London 1952, 1958, 1962, 1966, 1972. [16] W, v. O. Quine, 'On What There Is', in From a Logical Point of View, New York, 1953, 1961. [17] Willard van Orman Quine, Set Theory andits Logic, Cambridge, Mass. 1963, 1970.