We present a refinement ofthe bounded modified realizability which provides both upper and lower bounds for witnesses. Our interpretation is based on a generalisation of Howard/Bezem's notion of strong majorizability. We show how the bounded modified realizability coincides with our interpretation in the case when least elements exist . The new interpretation, however, permits the extraction of more accurate bounds, and provides an ideal setting for dealing directly with data types whose natural ordering is not well-founded.

We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov's principle but meshes well with some classical principles, including the lesser limited principle of omniscience and weak König's lemma. We discuss some applications, as well as some previous results in the literature.

Realizability notions in mathematical logic have a long history, which can be traced back to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations of intuitionistic logic. Kleene’s initial realizability laid the ground for more sophisticated notions such as Kreisel’s modified realizability and various modern approaches. In this context, our work aligns with the lineage of realizability strategies that emphasize the accumulation, rather than the propagation of precise witnesses. In this paper, (...) we introduce a new notion of realizability, namely herbrandized modified realizability. This novel form of (cumulative) realizability, presented within the framework of semi-intuitionistic logic is based on a recently developed star combinatory calculus, which enables the gathering of witnesses into nonempty finite sets. We also show that the previous analysis can be extended from logic to (Heyting) arithmetic. (shrink)

The classical forms of both modified realizability and relative realizability are naturally described in terms of the Sierpinski topos. The paper puts these two observations together and explains abstractly the existence of the geometric morphisms and logical functors connecting the various toposes at issue. This is done by advancing the theory of triposes over internal partial combinatory algebras and by employing a novel notion of elementary map.

Summary. A constructive realizablity interpretation for classical arithmetic is presented, enabling one to extract witnessing terms from proofs of 1 sentences. The interpretation is shown to coincide with modified realizability, under a novel translation of classical logic to intuitionistic logic, followed by the Friedman-Dragalin translation. On the other hand, a natural set of reductions for classical arithmetic is shown to be compatible with the normalization of the realizing term, implying that certain strategies for eliminating cuts and extracting a (...) witness from the proof of a 1 sentence are insensitive to the order in which reductions are applied. (shrink)

Goodman’s theorem states that HAω+AC+RDC is conservative over HA. The same result applies to the extensional case, that is, E-HAω+AC+RDC is also conservative over HA. This is due to Beeson. In this article, we modified the Goodman realizability and provide a new proof of the extensional case.

According to Kant's theory of thought or cognition, thoughts are rules for empirical reactions in the compass of spatial and temporal constructions. Theses rules function to represent our situation in relation to all the ways it is proper to interact with reality. After outlining Kant's theory, I present a modified version in which rules are identified with executive mechanisms for behavioural output. Following Kant, I show how such rules can pertain to the past in terms of mechanisms for being (...) beyond or past stages of temporal constructions. This identification of rules with mechanisms allows for a real definition of the truth of thoughts as the active realizability of the mechanisms that thoughts are. I show how this modified version can encompass the full scope of even relativistic spatio-temporal reality, and indicate why this theory deserves consideration as against rival descriptive and causal theories of cognition. (shrink)

It has been pointed out that Gettier case scenarios have deviant realizations and that deviant realizations raise a difficulty for the logical analysis of thought experiments. Grundmann and Horvath have shown that it is possible to rule out deviant realizations by suitably modifying the scenario of a Gettier-style thought experiment. They hypothesize further that the enriched scenario corresponds to the way expert epistemologists implicitly interpret the original one. However, no precise account of this implicit enrichment is offered, which makes the (...) proposal somewhat ad hoc. Drawing on pragmatic theory, I argue that the content of Grundmann and Horvath’s modified scenario corresponds to the default interpretation of the original scenario and that epistemological expertise is not required to access the deviance-proof interpretation. This Default Interpretation proposal offers thus a more general and independently motivated solution to the Problem of Deviant Realizations. (shrink)

The provability logic of a theory $T$ is the set of modal formulas, which under any arithmetical realization are provable in $T$. We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$. We make an analogous modification for interpretability logics. We first study provability logics with restricted realizations and show that for various natural candidates of $T$ and restriction set $\Gamma$, the result is the logic of linear frames. However, for the theory Primitive (...) Recursive Arithmetic (PRA), we define a fragment that gives rise to a more interesting provability logic by capitalizing on the well-studied relationship between PRA and I$\Sigma_1$. We then study interpretability logics, obtaining upper bounds for IL(PRA), whose characterization remains a major open question in interpretability logic. Again this upper bound is closely related to linear frames. The technique is also applied to yield the nontrivial result that IL(PRA) $\subset$ ILM. (shrink)

This article systematically investigates so-called “truth variants” of several functional interpretations. We start by showing a close relation between two variants of modified realizability, namely modified realizability with truth and q-modified realizability. Both variants are shown tobe derived from a single “functional interpretation with truth” of intuitionistic linear logic. This analysis suggests that several functional interpretations have truth and q-variants. These variants, however, require a more involved modification than the ones previously considered. Following this (...) lead we present truth and q-variants of the Diller-Nahm interpretation, the bounded modified realizability and the bounded functional interpretation. (shrink)

This article presents a parametrized functional interpretation. Depending on the choice of two parameters one obtains well-known functional interpretations such as Gödel's Dialectica interpretation, Diller-Nahm's variant of the Dialectica interpretation, Kohlenbach's monotone interpretations, Kreisel's modified realizability, and Stein's family of functional interpretations. A functional interpretation consists of a formula interpretation and a soundness proof. I show that all these interpretations differ only on two design choices: first, on the number of counterexamples for A which became witnesses for ¬A (...) when defining the formula interpretation and, second, the inductive information about the witnesses of A which is considered in the proof of soundness. Sufficient conditions on the parameters are also given which ensure the soundness of the resulting functional interpretation. The relation between the parametrized interpretation and the recent bounded functional interpretation is also discussed. (shrink)

Five recursively axiomatizable theories extending Kleene's intuitionistic theory FIM of numbers and numbertheoretic sequences are introduced and shown to be consistent, by a modified relative realizability interpretation which verifies that every sequence classically defined by a Π11 formula is unavoidable and that no sequence can fail to be classically Δ11. The analytical form of Markov's Principle fails under the interpretation. The notion of strongly inadmissible rule of inference is introduced, with examples.

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$ sentence of a certain form is provable using E-HA ${}^\omega$ along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the (...) Dialectica interpretation. These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles in subsystems of constructive analysis. (shrink)

A notion of feasible function of finite type based on the typed lambda calculus is introduced which generalizes the familiar type 1 polynomial-time functions. An intuitionistic theory IPVω is presented for reasoning about these functions. Interpretations for IPVω are developed both in the style of Kreisel's modified realizability and Gödel's Dialectica interpretation. Applications include alternative proofs for Buss's results concerning the classical first-order system S12 and its intuitionistic counterpart IS12 as well as proofs of some of Buss's conjectures (...) concerning IS12, and a proof that IS12 cannot prove that extended Frege systems are not polynomially bounded. (shrink)

We show how two iterated products of selection functions can both be used in conjunction with systemTto interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated product is equivalent over systemTto Spector’s bar recursion, whereas the other isT-equivalent to modified bar recursion. Modified bar recursion itself is shown to arise directly from the iteration of a different binary product of ‘skewed’ selection functions. Iterations of the dependent binary products (...) are also considered but in all cases are shown to beT-equivalent to the iteration of the simple products. (shrink)

An axiomatic treatment of synthetic domain theory is presented, in the framework of the internal logic of an arbitrary topos. We present new proofs of known facts, new equivalences between our axioms and known principles, and proofs of new facts, such as the theorem that the regular complete objects are closed under lifting . In Sections 2–4 we investigate models, and obtain independence results. In Section 2 we look at a model in de Modified realizability Topos, where the (...) Scott Principle fails, and the complete objects are not closed under lifting. Section 3 treats the standard model in the Effective Topos. Theorem 3.2 gives a new characterization of the initial lift-algebra relative to the dominance. We prove that in the standard case it is not the internal colimit of the chain 0 → L → L 2 → ⋯ . The models in Sections 2 and 3 compare via an adjunction. Section 4 discusses a model in a Grothendieck topos. A feature here is that N is not well-complete , whereas 2 is. (shrink)

Gödel's dialectica interpretation of Heyting arithmetic HA may be seen as expressing a lack of confidence in our understanding of unbounded quantification. Instead of formally proving an implication with an existential consequent or with a universal antecedent, the dialectica interpretation asks, under suitable conditions, for explicit 'interpreting' instances that make the implication valid. For proofs in constructive set theory CZF-, it may not always be possible to find just one such instance, but it must suffice to explicitly name a set (...) consisting of such interpreting instances. The aim of eliminating unbounded quantification in favor of appropriate constructive functionals will still be obtained, as our ∧-interpretation theorem for constructive set theory in all finite types CZFω- shows. By changing to a hybrid interpretation ∧q, we show closure of CZFω- under rules that – in stronger forms – have already been studied in the context of Heyting arithmetic. In a similar spirit, we briefly survey modified realizability of CZFω- and its hybrids. Central results of this paper have been proved by Burr 2000a and Schulte 2006, however, for different translations. We use a simplified interpretation that goes back to Diller and Nahm 1974. A novel element is a lemma on absorption of bounds which is essential for the smooth operation of our translation. (shrink)

Gödel's dialectica interpretation of Heyting arithmetic HA may be seen as expressing a lack of confidence in our understanding of unbounded quantification. Instead of formally proving an implication with an existential consequent or with a universal antecedent, the dialectica interpretation asks, under suitable conditions, for explicit ‘interpreting’ instances that make the implication valid. For proofs in constructive set theory CZF‐, it may not always be possible to find just one such instance, but it must suffice to explicitly name a set (...) consisting of such interpreting instances. The aim of eliminating unbounded quantification in favor of appropriate constructive functionals will still be obtained, as our ∧‐interpretation theorem for constructive set theory in all finite types CZFω‐ shows. By changing to a hybrid interpretation ∧q, we show closure of CZFω‐ under rules that – in stronger forms – have already been studied in the context of Heyting arithmetic. In a similar spirit, we briefly survey modified realizability of CZFω‐ and its hybrids. Central results of this paper have been proved by Burr 2000a and Schulte 2006, however, for different translations. We use a simplified interpretation that goes back to Diller and Nahm 1974. A novel element is a lemma on absorption of bounds which is essential for the smooth operation of our translation. (shrink)

We show that the so-called weak Markov's principle which states that every pseudo-positive real number is positive is underivable in [MATHEMATICAL SCRIPT CAPITAL T]ω ≔ E-HAω + AC. Since [MATHEMATICAL SCRIPT CAPITAL T]ω allows one to formalize Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within the framework of Bishop-style mathematics . The underivability even holds if the ine.ective schema of full comprehension for negated formulas is added, which allows one to derive the law of excluded (...) middle for such formulas. (shrink)

This article argues that standard causal and functionalist definitions of realization fail to account for the realization of entities that cannot be individuated in causal or functional terms. By modifying such definitions to require that realizers also logically suffice for any historical properties of the entities they realize, one can provide for the realization of entities whose resistance to causal/functional individuation stems from their possession of individuative historical properties. But if qualia cannot be causally or functionally individuated, then qualia can (...) be physically realized only if the thesis that all things are physical or physically realized is insufficient for physicalism. (shrink)

This paper provides a critical exploration of the capability approach to human rights (CAHR) with the specific aim of developing its potential for achieving a synthesis between “humanist” or “naturalistic” and “political” or “practical” perspectives in the philosophy of human rights. Section II presents a general strategy for achieving such a synthesis. Section III provides an articulation of the key insights of CAHR (its focus on actual realizations given diverse circumstances, its pluralism of grounds, its emphasis on freedom of choice, (...) its demand for public reasoning, its context-sensitive universalism, and its broad view of obligations). These insights go some way toward the achievement of the desired synthesis. But, as explained in IV.1, in its current form CAHR faces two serious objections by the defenders of the political perspective: the Gap Between Capabilities-Interests and Rights Objection and the Disconnect From Practice Objection. Answering these criticisms requires some amendments to CAHR. Section IV.2 suggests a response to the first objection based on the introduction of a contractualist framework of justification. Sections IV.3 and IV.4 tackle the second objection by introducing a re-characterization of the cosmopolitan standard underlying the humanist perspective and by identifying the differences and relations between various dimensions of a conception of human rights and their significance for actual political practice. The paper illustrates the practical implications of CAHR, in its modified form, for the pursuit of some important rights. (shrink)

In Zhong (Philos Phenomenol Res 83:129–147, 2011; Analysis 72:75–85, 2012), I argued that, contrary to what many people might expect, the counterfactual theory of causation will generate (rather than solve) the exclusion problem. Recently some philosophers raise an incisive objection to this argument. They contend that my argument fails as it equivocates between different notions of a physical realizer (see Christensen and Kallestrup in Analysis 72:513–517, 2012). However, I find that their criticism doesn’t threaten the central idea of my view. (...) In this paper, I make two separate responses that appeal to two unequivocal notions of physical realizers, respectively. I aim to show that a modified argument that uses either notion would work. (shrink)

Despite the fact that the nature of the properties of causation is rarely discussed within the mental causation debate, the implicit assumption is that they are universals as opposed to tropes. However, in recent literature on the problem of mental causation, a new solution has emerged which aims to address the problem by appealing to tropes. It is argued that if the properties of causation are tropes rather than universals, then a psychophysical reductionism can be advanced which does not face (...) the problem of multiple realizability. However, the 'trope solution' rests upon the assumption that one can combine a trope monism with a type dualism. I argue that such a combination cannot be allowed. Given a plausible interpretation of types within a trope ontology, trope monism in fact entails type monism. Consequently, if one identifies mental tropes with physical tropes, one must also identify mental and physical types and in doing so face a modified version of the multiple realizability argument. (shrink)

Tononi has proposed a fundamental theory of consciousness he terms Integrated Information Theory (IIT). IIT purports to explain the quantity of conscious experience by linking it with integrated information: information shared by the system as a whole and quantified by adopting a modified version of Shannon's definition of information. Since the fundamental aspect of IIT is information the theory allows for the multiple realizability of consciousness. While there are several concepts within IIT that need further theoretical development, the (...) main failings of the theory are an absence of a link between conscious experience and awareness and the use of Shannon's limited data based definition of information. These limitations prevent the theory from satisfying Chalmers' principles of structural coherence and organizational invariance which any functionalist theory should obey. It is not clear whether IIT can be repaired without simply reducing the theory to a general statement of computational functionalism. (shrink)

Court interpreting in Croatia is a very unregulated field especially regarding the training and the skills that are to be acquired in order to pro- vide accurate translation at courts. One of the prerequisites according to the Regulations on Court Interpreters in Croatia is knowledge of the structure of judicial power, state government and legal terminology. Although the Regulations prescribe that the training should last no longer than two months, the organisations providing such training shorten this to three or four (...) days. Taking into account all that has been said one realizes that in such short time a per- son cannot be properly qualified to practice as a court interpreter. According to the EU Directive on the right to interpretation and translation in criminal proceedings member states should provide adequate training in order to ensure the quality of interpretation and to avoid that suspected or accused persons complain that the quality of interpretation was not good enough to secure the fairness of the proceeding, which according to Article 2 of the Directive they have the right to. Since Croatia joined the European Union on 1 July 2013, it will have to change its Regulations on Court Interpreters in order to com- ply with this Directive. This paper will try to analyze the problems within the scope of court interpreter’s profession in Croatia both in civil and in criminal proceedings. Several examples will be suggested as the possible model for modifying court interpreting in Croatia. Since this profession is often underrated by the national courts, the paper will suggest ways to prevent such views and point out the importance of good court interpretation. (shrink)

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11-CA0. Ordinal analysis and the (Schwichtenberg-Wainer) subrecursive hierarchies play a central role and are (...) used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11-CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic. (shrink)

THIS PAPER IS THE CO-WINNER OF THE FRED BERGER PRIZE IN PHILOSOPHY OF LAW FOR THE 1999 AMERICAN PHILOSOPHICAL ASSOCIATION FOR THE BEST PUBLISHED PAPER IN THE PREVIOUS TWO YEARS. -/- The conflict between liberal legal theory and critical legal studies (CLS) is often framed as a matter of whether there is a theory of justice that the law should embody which all rational people could or must accept. In a divided society, the CLS critique of this view is overwhelming: (...) there is no such justice that can command universal assent. But the liberal critique of CLS, that it degenerates into an unpalatable moral relativism on which there is no non-arbitrary basis between a justice that underwrites forms of domination such as slavery and a justice that condemns such forms of domination is equally powerful and compelling. I show that there is a way to harmonize both views that is subject to empirical test. -/- First I show that the most widely accepted and influential formulation of liberal justice, John Rawls' Justice as Fairness, in. e.g, A Theory of Justice, cannot avoid the relativistic challenge because it would not be accepted, as a matter of sociological fact, by real people in a divided society once the "veil of Ignorance" is removed and real people step out from the Original Position. To put it differently, different reflective equilibria are inevitable in a divided society. Given the weight that Rawls properly puts on the realizability of a conception of justice and its stability in practice, this is a fatal objection. There can be no divided society that is "well ordered" in Rawls' sense, governed by a shared conception of justice and known to be so governed. -/- I then turn to the most powerful statement of the CLS view, Milton's Fisk's relativistic account in The State and Justice. For Fisk, justice is a compromise between what the dominant groups can compel and what the the subordinate groups will acquiesce to., There is no one such compromise in any given situation, so the account is in that sense relativistic, but more deeply, it is relativistic in that it offers no non-arbitrary, non-question begging way to choose between the official justice of, e.g., a slaveholding society and and the radical justice of the slaves, which has no place for slaveholders as a group or slavery as an institution.All that Fisk can offer is an arbitrary existential choice: I'm with the slaves. (Or the slaveowners.) Most of us would find this disconcerting or even unacceptable. -/- I show that Fisk's general sort of account can be modified to allow for an non-arbitrary choice. Given general facts about human nature, societies based on domination will produce resistance that over the long run will diminish or eliminate various forms of domination. Through a sort of ratchet effect, rights won will be hard if not impossible to reverse. Societies embodying forms of domination can therefore be compared on dimensions of stability: the more domination, the more resistance, and the less stability. Such societies are inferior on the dimension of justice to more emancipatory society on the terms of both kinds of justice, official and radical. -/- This is not question begging because regimes of domination incorporate stability no less than more emancipatory social orders. The choice between official justice embodying domination and radical justice that does not is not arbitrary because it is based on a shared commitment to long term stability. This offers an empirical test of which social orders are more justice, and a prediction that over time, domination will tend to decrease. (shrink)

Aiming at the problem of inaccurate classification of big data information in traditional English teaching ability evaluation algorithms, an English teaching ability evaluation algorithm based on big data fuzzy K-means clustering and information fusion is proposed. Firstly, the author uses the idea of K-means clustering to analyze the collected original error data, such as teacher level, teaching facility investment, and policy relevance level, removes the data that the algorithm considers unreliable, uses the remaining valid data to calculate the weighting factor (...) of the modified fuzzy logic algorithm, and evaluates the weighted average with the node measurement data and gets the final fusion value. Secondly, the author integrates the big data information fusion and K-means clustering algorithm, realizes the clustering and integration of the index parameters of English teaching ability, compiles the corresponding English teaching resource allocation plan, and realizes the evaluation of English teaching ability. Finally, the results show that using this method to evaluate English teaching ability has better information fusion analysis ability, which improves the accuracy of teaching ability evaluation and the efficiency of teaching resources application. (shrink)

: A hallmark of Dogen's legacy is his introduction of Chinese Ch'an koan literature to Japan in the first half of the thirteenth century and his unique and innovative style of interpreting dozens of koan cases, many of which are relatively obscure or otherwise untreated in the annals. What constitutes the distinctiveness of Dogen's approach? According to Hee-Jin Kim's seminal study, Dogen shifts from an instrumental to a realizational model of koan interpretation. While this essay agrees with some features of (...) Kim's approach, especially his emphasis on the importance of language, it is argued that Kim overlooks the diversity of aims and intentions in Dogen's use of rhetorical and narrative strategies to highlight diverse doctrinal and ritual themes. There is no single underlying view of koans for Dogen, who continually modifies his interpretive approach to particular cases in order to articulate specific themes. (shrink)

Prominent in Hellenistic philosophy is the debate over whether the sage is really always happy even if tortured. This doctrine that the tortured sage is happy is important because the Hellenistic philosophers used this case to debate the power of moral virtue in a person's life. Modern pain research shows that it is indeed possible to be happy while being tortured because pain is not purely a sensory phenomenon. Based on this modern research, I investigate the positions of Epicurus, the (...) Cynics, the Aristotelians, the Neoplatonists, the Skeptics and the Stoics concerning the sage's complete happiness even if tortured. I show that the Stoics' position agrees with modern pain research and the Stoics are right that the tortured sage could still be happy. ;This does not show that the Stoic sage is always happy, though. While the common objection to Stoicism, that the Stoic sage is unemotional, is a misinterpretation of Stoic ethics, nevertheless Stoic philosophy cannot prove that the sage is always happy. For the Stoics claim that the sage is happy because of her oneness with God, but the Stoics are unable to demonstrate how a sage realizes this oneness and why this oneness makes a sage happy. ;Indian philosophy, through Pyrrho's visit to India, influenced Greek philosophy about the doctrine of the tortured sage who is indifferent to pain. Furthermore, Indian philosophy is able to modify Stoic philosophy so that we can show how the sage is always happy. For through the Indian technique of meditation a person can realize her oneness with God and experience deep joy and happiness. Modified by Indian philosophy with its technique of meditation, Stoic philosophy is right that the sage is always happy even if tortured. ;Stoic philosophy has two more contributions to our ethical concerns. First, Stoic ethics is a very interesting synthesis of impartialism and partialism. Second, the Stoics' understanding of the emotions and anger is better than our current understanding. (shrink)

It is shown that the program of naturalizing of epistemology, that is, the program of the whole substitution of epistemology for sciences or for the humanities is not realizable. Naturalized epistemology includes metaphysical (in Kant’s sense: synthetic, speculative, a priori) claims which save its partly autonomous philosophical status. The result presented in the paper does not exclude the naturalizing program. It leads, instead, to a modified, attenuated version of it—such one which permits to open epistemology by transferring it in (...) multi-facet vivid philosophical investigations juxtaposed with science and the humanities. The postulated attenuated version of naturalizing does not result in destroying epistemology as a special philosophical domain of investigations, not substitutable for sciences. (shrink)

It is shown that the program of naturalizing of epistemology, that is, the program of the whole substitution of epistemology for sciences or for the humanities is not realizable. Naturalized epistemology includes metaphysical (in Kant’s sense: synthetic, speculative, a priori) claims which save its partly autonomous philosophical status. The result presented in the paper does not exclude the naturalizing program. It leads, instead, to a modified, attenuated version of it—such one which permits to open epistemology by transferring it in (...) multi-facet vivid philosophical investigations juxtaposed with science and the humanities. The postulated attenuated version of naturalizing does not result in destroying epistemology as a special philosophical domain of investigations, not substitutable for sciences. (shrink)

It is shown that the program of naturalizing of epistemology, that is, the program of the whole substitution of epistemology for sciences or for the humanities is not realizable. Naturalized epistemology includes metaphysical (in Kant’s sense: synthetic, speculative, a priori) claims which save its partly autonomous philosophical status. The result presented in the paper does not exclude the naturalizing program. It leads, instead, to a modified, attenuated version of it—such one which permits to open epistemology by transferring it in (...) multi-facet vivid philosophical investigations juxtaposed with science and the humanities. The postulated attenuated version of naturalizing does not result in destroying epistemology as a special philosophical domain of investigations, not substitutable for sciences. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Reinhold Niebuhr and Paul Ramsey: Idealist and Pragmatic Christians on Politics, Philosophy, Religion, and WarBradley BurroughsReinhold Niebuhr and Paul Ramsey: Idealist and Pragmatic Christians on Politics, Philosophy, Religion, and War Kevin Carnahan Lanham, Md.: Lexington Books, 2010. 302 pp. $75.00.In a time when the “war on terror” and the polarization of American political culture have raised acute questions about politics, war, and the use of power, Kevin Carnahan (...) believes ethicists could benefit from the legacies of Reinhold Niebuhr and Paul Ramsey. During a similarly vexed period, Niebuhr and Ramsey found themselves at odds over the morality of the Vietnam War. Carnahan’s project seeks to elucidate the underlying sources of this disagreement, examining in turn how each thinker construes the task of moral theology, the nature of political society, and the moral status of war. Throughout these treatments, Carnahan illustrates how Niebuhr and Ramsey elaborated “overlapping but divergent” positions profoundly influenced by their respective encounters with pragmatism and idealism.Even as he shows how Niebuhr modified the pragmatist inheritance and Ramsey the idealist, Carnahan highlights how both were shaped especially by the way in which these traditions sought to counter specific moral dangers. For pragmatists, the key danger lay in the kind of moral fanaticism that blithely assumes its own righteousness. Sensitized to this threat, Niebuhr articulated a moral theology centered upon an understanding of love as an ideal that is always relevant yet never fully realizable in history, a construal that subverts all pretensions to righteousness. Idealism, on the other hand, sets itself against the danger of atomistic individualism, which Ramsey opposed by depicting social institutions in their essential forms as “‘garments of skin’... with which God... clothed naked human relations” (129) and by characterizing love as fundamentally a matter of upholding the covenants implied in such institutions. Ultimately, Niebuhr’s opposition to fanaticism predisposed him to focus upon the idolatries at play in political society and war and allowed him rather early on to descry the pretentiousness of the Vietnam War. Meanwhile, Ramsey’s thought included a presumption in favor of supporting the policies developed by social and political leaders that led him to defend American intervention in Vietnam until sometime around 1973. [End Page 218]The book’s expository work is generally surefooted and illuminative, although it at times falls into redundancy, baldly reiterating its thesis. Nonetheless, it complements existing scholarship on Niebuhr and Ramsey with an investigation of the philosophical premises of their ethical thought that each was eager to conceal. Such work will benefit scholars of Niebuhr and Ramsey as well as advanced students seeking to grasp the general architecture of their thought. Moreover, many will find Carnahan’s interpretations of Niebuhr and Ramsey impressive. For example, Carnahan portrays Niebuhr as a more Barthian and ecclessially minded thinker than most accounts. Although Carnahan understandably does not treat such indictments in detail, his rendering undercuts charges leveled by many of Niebuhr’s critics, including Bennett, Yoder, and Hauerwas. Unfortunately, though, Carnahan’s arguments on some of these disputed points are predicated upon a relatively narrow selection of essays. Still, the book unsettles assumptions and suggests further possibilities for inquiry.In addition to his expository work, Carnahan also makes a further contribution as he subjects both Niebuhr and Ramsey to constructive criticism that exposes—and identifies ways of reinforcing—some of the weaknesses of pragmatism and idealism. Eschewing a synthesis, Carnahan instead offers a mutually constructive dialogue capable of helping thinkers of both stripes think through the issues that confront contemporary America. Even if he does not elaborate on a more precise application of his insights to contemporary politics, he offers advice helpful to pragmatists and idealists alike and leaves many of us hoping that he has more to say on such matters. [End Page 219]Bradley BurroughsEmory UniversityCopyright © 2012 Society of Christian Ethics... (shrink)

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)

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)

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 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)

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)

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,”...

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)

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)

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 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.

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)

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.

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)