Multiple realizability has been at the heart of debates about whether the mind reduces to the brain, or whether the items of a special science reduce to the items of a physical science. I analyze the two central notions implied by the concept of multiple realizability: "multiplicity," otherwise known as property variability, and "realizability." Beginning with the latter, I distinguish three broad conceptual traditions. The Mathematical Tradition equates realization with a form of mapping between objects. Generally speaking, (...) x realizes (or is the realization of) y because elements of y map onto elements of x. The Logico-Semantic Tradition translates realization into a kind of intentional or semantic notion. Generally speaking, x realizes (or is the realization of) a term or concept y because x can be interpreted to meet the conditions for satisfying y. The Metaphysical Tradition views realization as a species of determination between objects. Generally speaking, x realizes (or is the realization of) y because x brings about or determines y. I then turn to the subject of property variability and define it in a formal way. I then conclude by discussing some debates over property identity and scientific theory reduction where the resulting notion of multiple realizability has played a central role, for example, whether the nonreductive consequences of multiple realizability can be circumvented by scientific theories framed in terms of narrow domain-specific properties, or wide disjunctive properties. (shrink)

Multiply realizable properties are those whose realizers are physically diverse. It is often argued that theories which contain them are ipso facto irreducible. These arguments assume that physical explanations are restricted to the most specific descriptions possible of physical entities. This assumption is descriptively false, and philosophically unmotivated. I argue that it is a holdover from the late positivist axiomatic view of theories. A semantic view of theories, by contrast, correctly allows scientific explanations to be couched in the most perspicuous, (...) powerful language available. On a semantic view, traditional notions of multiple realizability are thus very hard to motivate. At best, one must abandon either the idea that multiple realizability is an interesting scientific notion, or else admit that multiply realizable properties do not automatically block scientific reductions. (shrink)

The argument from multiple realizability is that, because quite diverse physical systems are capable of giving rise to identical psychological phenomena, mental states cannot be reduced to physical states. This influential argument depends upon a theory of reduction that has been defunct in the philosophy of science for at least fifteen years. Better theories are now available.

In the literature on multiple realizability and the identity theory, cases of neural plasticity have enjoyed a very limited role. The present article attempts to remedy this small influence by arguing that clinical and experimental evidence of quite extensive neural reorganization offers compelling support for the claim that psychological kinds are multiply realized in neurological kinds, thus undermining the identity theory. In particular, cases are presented where subjects with no measurable psychological deficits also have vast, though gradually received, neurological (...) damage. Common objections and concerns are also discussed and rejected. 1 Introduction2 The GRP, Serial Lesion Effect, and Multiple Realizability2.1 A case study of the serial lesion effect2.2 Evaluating the case study’s evidence for multiple realizability3 The GRP More Generally4 Objections to the GRP as Evidence for Multiple Realizability4.1 Small plastic effects and neurological taxonomies4.2 But do neural regions and locations even matter at all?4.3 But are there not other options besides location?5 Conclusion. (shrink)

We critically analyze Alexander Rosenberg’s argument based on the multiple realizability of biological properties that there are no biological laws. The argument is intuitive and suggestive. Nevertheless, a closer analysis reveals that the argument rests on dubious assumptions about the nature of natural selection, laws of nature, and multiple realizability. We also argue that the argument is limited in scope, since it applies to an outmoded account of laws and the applicability of the argument to other more promising (...) accounts of laws is questionable. Another concern of ours is that the relation between multiple realizability and natural selection is more complex than Rosenberg acknowledges. Finally, we claim that an explanation for why Rosenberg’s argument appears persuasive and appealing is that the argument is based on an inflated concept of multiple realizability that rests on unreliable intuitions concerning what counts as a different realization of the same property. Consequently, we argue that the argument is at best inconclusive and at worst false insofar as its implications for the existence of biological laws are concerned. (shrink)

Multiple realizability says that the same kind of mental states may be manifested by systems with very different physical constitutions. Putnam ( 1967 ) supposed it to be “overwhelmingly probable” that there exist psychological properties with different physical realizations in different creatures. But because function constrains possible physical realizers, this empirical bet is far less favorable than it might initially have seemed, especially when we take on board the richer picture of neural and brain function that neuroscience has been (...) uncovering over the past forty years, in which all sorts of brain activities play crucial roles beyond all-or-nothing electrical signaling. Because of its evolutionary history, the brain’s metabolic and informational processes are inextricably intertwined. The resulting complex integrated functions impose more constraints on possible realizers than the clean, single-purpose functions usually cited as examples in discussions of multiple realizability—with ramifications for the functionalist and computationalist foundations of cognitive science, artificial intelligence, and the philosophy of mind. (shrink)

The claim of the multiple realizability of mental states by brain states has been a major feature of the dominant philosophy of mind of the late 20th century. The claim is usually motivated by evidence that mental states are multiply realized, both within humans and between humans and other species. We challenge this contention by focusing on how neuroscientists differentiate brain areas. The fact that they rely centrally on psychological measures in mapping the brain and do so in a (...) comparative fashion undercuts the likelihood that, at least within organic life forms, we are likely to find cases of multiply realized psychological functions. (shrink)

The neural vehicles of mental representation play an explanatory role in cognitive psychology that their realizers do not. In this paper, I argue that the individuation of realizers as vehicles of representation restricts the sorts of explanations in which they can participate. I illustrate this with reference to Rupert’s (2011) claim that representational vehicles can play an explanatory role in psychology in virtue of their quantity or proportion. I propose that such quantity-based explanatory claims can apply only to realizers and (...) not to vehicles, in virtue of the particular causal role that vehicles play in psychological explanations. (shrink)

A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church's Thesis and a variant of a modal set (...) theory due to Goodman and Scedrov, (ii) a model of a modal version of Troelstra's generalized continuity principle together with a fragment of second-order arithmetic, and (iii) a model based on Scott's graph model (for the untyped lambda calculus) which witnesses the failure of the stability of non-identity. (shrink)

This article examines the multiple realizability thesis within a causal framework. The beginnings of this framework are found in Elliott Sober’s “Multiple Realizability Argument against Reduction,”...

Multiple Realizability (MR) must still be regarded as one of the principal arguments against type reductionist accounts of higher-order properties and their special laws. Against this I argue that there is no unique MR but rather a multitude of MR categories. In a slogan: MR is itself “multi-realized”. If this is true then we cannot expect one unique reductionist strategy against MR as an anti-reductionist argument. The main task is rather to develop a taxonomy of the wide variety of (...) MR cases and to sketch possible reductionist answers for each class of cases. The paper outlines some first steps in this direction. (shrink)

A variant of realizability for Heyting arithmetic which validates Church’s thesis with uniqueness condition, but not the general form of Church’s thesis, was introduced by Lifschitz (Proc Am Math Soc 73:101–106, 1979). A Lifschitz counterpart to Kleene’s realizability for functions (in Baire space) was developed by van Oosten (J Symb Log 55:805–821, 1990). In that paper he also extended Lifschitz’ realizability to second order arithmetic. The objective here is to extend it to full intuitionistic Zermelo–Fraenkel set theory, (...) IZF. The machinery would also work for extensions of IZF with large set axioms. In addition to separating Church’s thesis with uniqueness condition from its general form in intuitionistic set theory, we also obtain several interesting corollaries. The interpretation repudiates a weak form of countable choice, ACω,ω, asserting that a countable family of inhabited sets of natural numbers has a choice function. ACω,ω is validated by ordinary Kleene realizability and is of course provable in ZF. On the other hand, a pivotal consequence of ACω,ω, namely that the sets of Cauchy reals and Dedekind reals are isomorphic, remains valid in this interpretation. Another interesting aspect of this realizability is that it validates the lesser limited principle of omniscience. (shrink)

The multiple-realizability argument has been the mainstay of anti-reductionist consensus in philosophy of mind for the past thirty years. Reductionist opposition to it has sometimes taken the form of the Disjunctive Move: If mental types are multiply-realizable, they are not coextensive with physical types; they might nevertheless be coextensive with disjunctions of physical types, and those disjunctions could still underwrite psychophysical reduction. Among anti-reductionists, confidence is high that the Disjunctive Move fails; arguments to this effect, however, often leave something (...) to be desired. I raise difficulties for one anti-reductionist response to the Disjunctive Move, the Explanatory Response. (shrink)

Multiple realizability (MR) is traditionally conceived of as the feature of computational systems, and has been used to argue for irreducibility of higher-level theories. I will show that there are several ways a computational system may be seen to display MR. These ways correspond to (at least) five ways one can conceive of the function of the physical computational system. However, they do not match common intuitions about MR. I show that MR is deeply interest-related, and for this reason, (...) difficult to pin down exactly. I claim that MR is of little importance for defending computationalism, and argue that it should rather appeal to organizational invariance or substrate neutrality of computation, which are much more intuitive but cannot support strong antireductionist arguments. (shrink)

This paper concerns what Jerry Fodor calls a 'metaphysical mystery': How can there by macroregularities that are realized by wildly heterogeneous lower level mechanisms? But the answer to this question is not as mysterious as many, including Jaegwon Kim, Ned Block, and Jerry Fodor might think. The multiple realizability of the properties of the special sciences such as psychology is best understood as a kind of universality, where 'universality' is used in the technical sense one finds in the physics (...) literature. It is argued that the same explanatory strategy used by physicists to provide understanding of universal behavior in physics can be used to explain how special science properties can be heterogeneously multiply realized. (shrink)

The claim of the multiple realizability of mental states by brain states has been a major feature of the dominant philosophy of mind of the late 20th century. The claim is usually motivated by evidence that mental states are multiply realized, both within humans and between humans and other species. We challenge this contention by focusing on how neuroscientists differentiate brain areas. The fact that they rely centrally on psychological measures in mapping the brain and do so in a (...) comparative fashion undercuts the likelihood that, at least within organic life forms, we are likely to find cases of multiply realized psychological functions. (shrink)

Framed within the dialectic of the causal exclusion argument (Kim 2005), this paper does two things. One, it clarifies some properties of multiple realizability based on its true origin (Turing 1950). And two, it challenges a form of argument Noordhof (1997), Clarke (1999), and Whittle (2007) employ to support the idea that the mental has causal powers not had by its physical realization base (Novel). The paper challenges Novel with ideas derived from multiple realizability, among others.

In [17], we introduced an extensional variant of generic realizability [22], where realizers act extensionally on realizers, and showed that this form of realizability provides inner models of $\mathsf {CZF}$ (constructive Zermelo–Fraenkel set theory) and $\mathsf {IZF}$ (intuitionistic Zermelo–Fraenkel set theory), that further validate $\mathsf {AC}_{\mathsf {FT}}$ (the axiom of choice in all finite types). In this paper, we show that extensional generic realizability validates several choice principles for dependent types, all exceeding $\mathsf {AC}_{\mathsf {FT}}$. We then (...) show that adding such choice principles does not change the arithmetic part of either $\mathsf {CZF}$ or $\mathsf {IZF}$. (shrink)

We present the model construction technique called Linear Realizability. It consists in building a category of Partial Equivalence Relations over a Linear Combinatory Algebra. We illustrate how it can be used to provide models, which are fully complete for various typed λ-calculi. In particular, we focus on special Linear Combinatory Algebras of partial involutions, and we present PER models over them which are fully complete, inter alia, w.r.t. the following languages and theories: the fragment of System F consisting of (...) ML-types, the maximal theory on the simply typed λ-calculus with finitely many ground constants, and the maximal theory on an infinitary version of this latter calculus. (shrink)

LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If (...) the machinery of justifications is to be applied to artificial intelligence, or better yet, to everyday reasoning, we will need to work with whatever justifications we may have at hand—one version may not be interchangeable with another, even though they realize the same S4 formula. In this paper we begin the process of providing tools for reasoning about justifications directly. The tools are somewhat complex, but in retrospect this should not be surprising. Among other things, we provide machinery for combining two realizations of the same formula, and for replacing subformulas by equivalent subformulas. The results are algorithmic in nature—semantics for LP plays no role. We apply our results to provide a new algorithmic proof of Artemov’s Realization Theorem itself. This paper is a much extended version of [M.C. Fitting, Realizations and LP, in: S. Artemov, A. Nerode , Logical Foundations of Computer Science—New York ’07, in: Lecture Notes in Computer Science, vol. 4514, Springer-Verlag, 2007, pp. 212–223]. (shrink)

b>: This article explains the concept of multiple realizability and its role in the philosophy of mind. In particular, I consider what is required for the multiple realizability of psychological kinds, the relevance of multiple realizability to the reducibility and autonomy of psychology, as well as further refinements of the concept that would prove helpful.

Critics of multiple realizability have recently argued that we should concentrate solely on actual here-and-now realizations that are found in nature. The possibility of alternative, but unactualized, realizations is regarded as uninteresting because it is taken to be a question of pure logic or an unverifiable scenario of science fiction. However, in the biological context only a contingent set of realizations is actualized. Drawing on recent work on the theory of neutral biological spaces, the paper shows that we can (...) have ways of assessing the modal dimension of multiple realizability that do not have to rely on mere conceivability. (shrink)

Realizabilities are powerful tools for establishing consistency and independence results for theories based on intuitionistic logic. Troelstra discovered principles ECT 0 and GC 1 which precisely characterize formal number and function realizability for intuitionistic arithmetic and analysis, respectively. Building on Troelstra's results and using his methods, we introduce the notions of Church domain and domain of continuity in order to demonstrate the optimality of “almost negativity” in ECT 0 and GC 1 ; strengthen “double negation shift” DNS 0 to (...) DNS 1 and use it with GC 1 and Markov's Principle MP to characterize the classically provably realizable formulas of analysis; and show that intuitionistic analysis with GC 1 , MP and DNS 1 is consistent and satisfies Troelstra's and Church's Rules. We end with a discussion of semi-intuitionistic theories and a conjecture. (shrink)

A popular argument supporting functionalism has been what is commonly called the “multiple realizability” argument. One version of this argument uses thought experiments designed to show that minds could be composed of different types of material. This article offers a metaphilosophical analysis of this argument and shows that it fails to provide a strong case for functionalism. The multiple realizability argument is best understood as an inference‐to‐the‐best‐explanation argument, whereby a functionalist account of our mental concepts serves to explain (...) our multiple realizability intuitions. I show that the argument is inadequate because alternative accounts of our mental concepts exist that provide equally plausible explanations for these intuitions. Moreover, in the case of our qualia concepts, a nonfunctionalist account explains several other intuitions that functionalism cannot explain. Thus, despite its popularity, the intuition‐based version of the multiple realizability argument is a poor reason for accepting functionalism. (shrink)

This thesis presents a proof theoretical investigation of some constructive set theories with restricted set induction. The set theories considered are various systems of Constructive Zermelo Fraenkel set theory, CZF ([1]), in which the schema of $\in$ - Induction is either removed or weakened. We shall examine the theories $CZF^\Sigma_\omega$ and $CZF_\omega$, in which the $\in$ - Induction scheme is replaced by a scheme of induction on the natural numbers (only for  formulas in the case of the first theory, (...) for arbitrary formulas in the second theory). Of particular interest is the system CZF− + INAC, which is obtained by removing $\in$ - Induction and by adding an axiom, INAC, for inaccessible sets. The main outcome is that CZF− + INAC is a predicative set theory with inaccessible sets, its proof theoretic ordinal being $\Gamma_0$. The proof theoretic strength of these theories, has been determined by means of proof theoretical reductions. The upper bounds have been obtained by interpreting the set theories in classical theories of (iterated) inductive definitions with ordinals. A significant feature of these interpretations is that they are realizability interpretations, which make an indirect use of Aczel’s interpretation of CZF in Martin Löf type theory, and, in the case of CZF− + INAC, also employ a maximum bisimulation relation to represent equality between sets. The lower bounds are obtained by interpreting appropriate subsystems of intuitionistic second order arithmetic in the set theories. At the conclusion of the thesis we present work unrelated to the previous chapters. It is a preliminary study of the constructible hierarchy in CZF. We begin by formalizing the notion of definability in constructive set theory and then introduce Gödel’s L in CZF. We prove that intuitionistic L is a model of a subsystem of CZF strong enough to include intuitionistic Kripke-Platek set theory, and also that L is a model of the axiom of constructibility, provably in CZF. (shrink)

The multiple-realizability argument has been the mainstay ofanti-reductionist consensus in philosophy of mind for the past thirty years. Reductionist opposition to it has sometimes taken the form of the Disjunctive Move: If mental types are multiply-realizable, they are not coextensive with physical types; they might nevertheless be coextensive with disjunctionsof physical types, and those disjunctions could still underwrite psychophysical reduction. Among anti-reductionists, confidence is high that the Disjunctive Move fails; arguments to this effect, however, often leave something to be (...) desired. I raise difficulties for one anti-reductionist response to the DisjunctiveMove, the Explanatory Response. (shrink)

This work is a step toward the development of a logic for types and computation that includes not only the usual spaces of mathematics and constructions, but also spaces from logic and domain theory. Using realizability, we investigate a configuration of three toposes that we regard as describing a notion of relative computability. Attention is focussed on a certain local map of toposes, which we first study axiomatically, and then by deriving a modal calculus as its internal logic. The (...) resulting framework is intended as a setting for the logical and categorical study of relative computability. (shrink)

Recently, several critics of the multiple realizability thesis have argued that philosophers have tended to accept the thesis on too weak grounds. On the one hand, the analytic challenge has problematized how philosophers have treated the multiple realization relation itself, claiming that assessment of the sameness of function and the relevant difference of realizers has been uncritical. On the other hand, it is argued that the purported evidence of the thesis is often left empirically unverified. This paper provides a (...) novel strategy to answer these worries by introducing a role for multiple realizability in the context of biological engineering. In the field of synthetic biology, bioengineers redesign the evolutionary realizations of biological functions, even constructing artificial chemical surrogates in the laboratory. I show how in the rational design approach to biological engineering, multiple realizability can function as a design heuristic in which the sameness of function and difference of realizers can be controlled. Although practically motivated, this engineering approach has also a theoretical, exploratory component that can be used to study the empirical limitations of multiple realizability. Successful realization of the engineering designs would amount to a concrete demonstration of multiple realizability, taking evidence for MRT beyond what is readily found in nature. (shrink)

V. Lifschitz defined in 1979 a variant of realizability which validates Church's thesis with uniqueness condition, but not the general form of Church's thesis. In this paper we describe an extension of intuitionistic arithmetic in which the soundness of Lifschitz' realizability can be proved, and we give an axiomatic characterization of the Lifschitz-realizable formulas relative to this extension. By a "q-variant" we obtain a new derived rule. We also show how to extend Lifschitz' realizability to second-order arithmetic. (...) Finally we describe an analogous development for elementary analysis, with partial continuous application replacing partial recursive application. (shrink)

A close examination of Kim's argument in "Multiple Realization and the Metaphysics of Reduction" for the claim that if a kind is multiply realizable in a way that blocks identification with more fundamental properties it is also a kind unlikely to appear as an appropriate kind in a theory in the first place. Ultimately, I argue that there is one reasonably promising argument of this sort, but its success turns on explanatory questions the answers to which are far from obvious.

Metaphysical semantics is supposed to connect the nonfundamental to the fundamental in a distinctively “linguistic” way, explaining how nonfundamental truths can be grounded in fundamental facts , and so inducing a radically eliminative vision of the nonfundamental as mere talk. I wonder how the story goes when a single nonfundamental truth can be grounded in many different fundamental facts. For instance, the truth that Moore has hands can presumably be grounded in many different distributions of fields, arrangements of particles, vibrations (...) of strings, or whatnot. I am asking how metaphysical semantics can accommodate this sort of multiple realizability. (shrink)

A realizability notion that employs only Kalmar elementary functions is defined, and, relative to it, the soundness of EA-(Π₁⁰-IR), a fragment of Heyting Arithmetic (HA) with names and axioms for all elementary functions and induction rule restricted to Π₁⁰ formulae, is proved. As a corollary, it is proved that the provably recursive functions of EA-(Π₁⁰-IR) are precisely the elementary functions. Elementary realizability is proposed as a model of strict arithmetic constructivism, which allows only those constructive procedures for which (...) the amount of computational resources required can be bounded in advance. (shrink)

It has been debated what implications multiple realizability has for reductionism. I claim that more explicit attention needs to be paid to the distinction between multiple realizations of kinds and diverse implementations of laws. In this paper, I distinguish two different theses on the relations between multiple realization and diverse implementation: one thesis states that multiple realizations imply diverse implementations and the other states the converse. I claim that although antireductionism might turn out to be false if the first (...) thesis is accepted, this “realization‐based” antireductionism is not the only option for antireductionism. For the antireductionists who accept the second thesis, multiple realizations only provide evidence for diverse implementations. I defend this “implementation‐based” antireductionism again Shapiro's dilemma. I argue that one horn of the dilemma does not pose any problem and that the other horn simply begs the question. (shrink)

Two straightforward “extensionalisations” of Kleene's realizability are considered; denoted re and e. It is shown that these realizabilities are not equivalent. While the re-notion is a subset of Kleene's realizability, the e-notion is not. The problem of an axiomatization of e-realizability is attacked and one arrives at an axiomatization over a conservative extension of arithmetic, in a language with variables for finite sets. A derived rule for arithmetic is obtained by the use of a q-variant of e- (...) class='Hi'>realizability; this rule subsumes the well-known Extended Church's Rule. The second part of the paper focuses on toposes for these realizabilities. By a relaxation of the notion of partial combinatory algebra, a new class of realizability toposes emerges. Relationships between the various realizability toposes are given, and results analogous to Robinson and Rosolini's characterization of the effective topos, are obtained for a topos generalizing e-realizability. (shrink)

A variant of the notion of symmetric constructive realizability is introduced where the information about the symmetric constructive truth or falsity of an arithmetical formula is expressed by a single natural number. The methods of transformations of such a realization to the realizations of known kinds and those of reverse transformations are given. The formal arithmetical system based on such a realizability is investigated.

In this paper it is argued that the multiple realizability argument and Kripke's argument are based on schemas of identifications rather than identification. In fact, "heat = molecular motion" includes a term "molecular motion" that does not capture a natural kind, nor has a unique referent. If properly framed, this schema suits also for the type identity theory of mind. Some consequences of this point are evaluated.

In tone languages, some case studies showed that the word-level tonal representation was closely related to the underlying metrical pattern. Based on different tonal patterns in prosodic units, the metrical structures could generally be divided into the left- and right-dominant types in Chinese dialects. Yet the cross-dialectal phonetic realizations (e.g., duration and pitch) between or within these two metrical structures were still unrevealed. The current study investigated the duration and pitch realizations of disyllabic prosodic words in Changsha and Chengdu dialects (...) (the left-dominant structure), and in Fuzhou and Xiamen dialects (the right-dominant structure). Results showed that not all the duration patterns across four Chinese dialects were sensitive to different metrical structures, indicating that the duration might not be the universal cue for metrical prominence in Chinese dialects. In terms of pitch realization across all the four Chinese dialects, level tones (sometimes falling tones) generally appeared in the metrically weak unit, while underlying pitch forms appeared in the metrically strong unit. Compared with duration, pitch might be more robust for prosodic realizations of metrical structures in Chinese dialects. Furthermore, there was an interaction between duration and pitch patterns in Chinese dialects, which could shed new light on the phenomenon of “metrical tone sandhi”. Meanwhile, this study also provides some references for the judgment of the metrical stress and prosodic realizations in other Chinese dialects. (shrink)

It has been noted in recent literature (e.g., Ross & Spurrett 2004, Kim 2006, McLaughlin 2006 and Cohen 2005) that functionalism can be separated into two varieties: one that emphasizes the role state, the other that emphasizes the realizer state. The former is called “role functionalism” while the latter has been called “realizer functionalism” (Ross & Spurrett 2004, Kim 2006, Cohen 2005) or “filler functionalism” (McLaughlin 2006). The separation between role functionalism and realizer functionalism mars the distinction traditionally made between (...) functionalism and the identity theory, because realizer functionalism can be seen as the synthesis of functionalism and the identity theory. In this paper, I begin with an analysis of the distinction between role and realizer functionalism. I shall further develop realizer functionalism as a viable, or arguably the best, explanatory model for the mind-brain relation. Finally, I will argue that under realizer functionalism, we can give an account of how mind is placed in the material world without at the same time giving up on the autonomy of psychology. The autonomy of psychology is tantamount to the thesis that mental properties are not type-identical with, nor type-reducible to, physical properties of the brain. In the philosophical debate on reductive and nonreductive physicalism, reductivism seems to be gaining the upper hand these days. In the final section of this paper, Ishall sketch my defense of nonreductive physicalism. I believe that the current enthusiasm for reductionism is misguided, and I shall show that under realizer functionalism, reductionism in the sense of reductive explanation, i.e., providing explanation of the psychological in terms of the underlying physical properties, is not a feasible project. (shrink)

The paper replies to Matthew Rellihan’s recent criticism of Thomas Kroedel’s simple argument for downward causation. Rellihan argues that the simple argument equivocates between two notions of realizers of mental properties, namely total realizers and core realizers. According to Rellihan, one premise of the argument is false on each disambiguation. In response, this paper argues that the version of the argument in terms of total realizers is sound after all if we evaluate counterfactual conditionals about the non-occurrence of total realizers (...) correctly. (shrink)

I will discuss two possible options how a defender of the type identity-theory with respect to mental properties can avoid the conclusion of Putnam's Multiple Realizability Argument. I begin by offering a rigorous formulation of Putnam's argument, which has been lacking so far in the literature (section 2). This rigorous formulation shows that there are basically two possible options for avoiding the argument's conclusion. Contrary to current mainstream, I reject the first option?Kim's 'local reductionism'?as untenable (section 3). I endorse (...) the second option, which has been brought into discredit by being too closely associated with disjunctive properties. I first show that many of the criticisms of disjunctive properties miss their target or beg the question against their opponent view (sections 4 & 5). Then I argue that it is not necessary to tie the second option closely to disjunctive properties. Hence, even if we deny the legitimacy of disjunctive properties, the identity-theorist still need not accept the conclusion of the Multiple Realizability Argument since there is an alternative, though related, way to spell out the second response (section 6). (shrink)

J. L. Krivine developed a new method based on realizability to construct models of set theory where the axiom of choice fails. We attempt to recreate his results in classical settings, i.e., symmetric extensions. We also provide a new condition for preserving well ordered, and other particular type of choice, in the general settings of symmetric extensions.

Functionalism argues that since any mental state can be realized by different physical systems, it is therefore wrong to define or identify a mental state of an organism by the corresponding physical-chemical state of its body . In this paper, I argue that since a single mental state can also be realized in different functional patterns, multiple realizability creates the same problem for functionalism. This means that it is wrong to implicitly define a mental state by its causal role (...) in an interconnected network of inputs, outputs and internal states. It is discussed that the functionalists’ responses to this criticism are as plausible as the physicalists’ responses to the problem. It is concluded that in dealing with the multiple realizability problem, functionalism has no advantage over its rival, type physicalism. (shrink)

We present a realizability interpretation for classical analysis–an association of a term to every proof so that the terms assigned to existential formulas represent witnesses to the truth of that formula. For classical proofs of Π2 sentences ∀x∃yA(x,y), this provides a recursive type 1 function which computes the function given by f(x)=y iff y is the least number such that A(x,y).

We introduce a new model construction for Martin-Löf intensional type theory, which is sound and complete for the 1-truncated version of the theory. The model formally combines, by gluing along the functor from the category of contexts to the category of groupoids, the syntactic model with a notion of realizability. As our main application, we use the model to analyse the syntactic groupoid associated to the type theory generated by a graph G, showing that it has the same homotopy (...) type as the free groupoid generated by G. (shrink)

A new method of "minimal" realizability is proposed and applied to show that the definable functions of Heyting arithmetic (HA)--functions f such that HA $\vdash \forall x\exists!yA(x, y)\Rightarrow$ for all m, A(m, f(m)) is true, where A(x, y) may be an arbitrary formula of L(HA) with only x, y free--are precisely the provably recursive functions of the classical Peano arithmetic (PA), i.e., the $ -recursive functions. It is proved that, for prenex sentences provable in HA, Skolem functions may always (...) be chosen to be $ -recursive. The method is extended to intuitionistic finite-type arithmetic, HA ω 0 , and elementary analysis. Generalized forms of Kreisel's characterization of the provably recursive functions of PA and of the no-counterexample-interpretation for PA are consequently derived. (shrink)