The notion of strictly primitive recursive realizability is further investigated, and the realizable prenex sentences, which coincide with primitive recursive truths of classical arithmetic, are characterized as precisely those provable in transfinite progressions over a fragment of intuitionistic arithmetic. The progressions are based on uniform reflection principles of bounded complexity iterated along initial segments of a primitive recursively formulated system of notations for constructive ordinals. A semiformal system closed under a primitive recursively restricted -rule is described and proved equivalent to (...) the transfinite progressions with respect to the prenex sentences. (shrink)

We study a hierarchy of Kalmàr elementary functions on integers based on a classification of LOOP programs of limited complexity, namely those in which the depth of nestings of LOOP commands does not exceed two. It is proved that -place functions in can be enumerated by a single function in , and that the resulting hierarchy of elementary predicates (i.e., functions with 0,1-values) is proper in that there are predicates that are not in . Along the way the rudimentary predicates (...) of Smullyan are classified as. (shrink)

An elementary theory of concatenation,QT+, is introduced and used to establish mutual interpretability of Robinson arithmetic, Minimal Predicative Set Theory, quantifier-free part of Kirby’s finitary set theory, and Adjunctive Set Theory, with or without extensionality. The most basic arithmetic and simplest set theory thus turn out to be variants of string theory.

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 sets. (...) 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (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)

A realizability notion that employs only primitive recursive functions is defined, and, relative to it, the soundness of the fragment of Heyting Arithmetic (HA) in which induction is restricted to Σ 0 1 formulae is proved. A dual concept of falsifiability is proposed and an analogous soundness result is established for a further restricted fragment of HA.

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)

Kristiansen and Murwanashyaka recently proved that Robinson arithmetic, Q, is interpretable in an elementary theory of full binary trees, T. We prove that, conversely, T is interpretable in Q by producing a formal interpretation of T in an elementary concatenation theory QT+, thereby also establishing mutual interpretability of T with several well-known weak essentially undecidable theories of numbers, strings, and sets. We also introduce a “hybrid” elementary theory of strings and trees, WQT*, and establish its mutual interpretability with Robinson’s weak (...) arithmetic R, the weak theory of trees WT of Kristiansen and Murwanashyaka, and the weak concatenation theory WTCε of Higuchi and Horihata. (shrink)

The thesis critically examines the question of the philosophical coherence of finitism, the view which seeks to interpret mathematics without postulating an actual infinity of mathematical objects. It is argued that a widely accepted characterization of finitism, most recently expounded by Tait, is inadequate, and a new characterization based on the notion of elementary abstraction is proposed. It is further argued that the notion of elementary abstraction better explains the bearing of Godel's incompleteness theorems on the issue of the coherence (...) of finitism. By abstraction is meant a procedure by which one recognizes or establishes that some infinite process exhibits a distinctive uniformity. If the procedure does not require one to conceive of the integers in any other way than as the result of simple iterations, we call such abstraction elementary. Some six different formal models exploring a variety of different ways in which this notion can be made precise are proposed as possible formal characterizations of finitistic truth. It is proved that all these different models are equivalent with respect to finitistically meaningful sentences. This is taken as strong evidence that the notion of elementary abstraction is determinate enough to provide a basis for a coherent philosophical formulation of finitism. (shrink)

Deflationists about truth typically deny that truth is a causal-explanatory property. However, the now familiar 'success argument' attempts to show that truth plays an important causal-explanatory role in explanations of practical success. Deflationists have standardly responded that the truth predicate appears in such explanations merely as a logical device, and that therefore truth has not been shown to play a causal-explanatory role. I argue that if we accept Jackson and Pettit's account of causal explanations, the standard deflationist response is inconsistent, (...) for on this account even logical properties can be causally explanatory. Therefore the deflationist should remain neutral as to whether truth is a causal-explanatory property, and focus instead on the claim that truth, if it is a property, is a merely logical one. (shrink)

This book consists of seven chapters containing multiple questions of the global socially epistemological situation in science and higher education. Despite the progress of techno-sciences, we are facing blind flaws in leading systems of knowledge and perception. The global era, in a paradox way, connects the new knowledge of economics, postpolitics, postdemocracy, and biopolitical regulation of live and unpresentable forms of the global geo-located violence. Techno-optimism and techno-dictatorship in the twenty-first century coincide with the ideology of market, biopolitics of mandatory (...) satisfaction, religious revivalism, and collapse of higher education. In order for sciences to recover, it is necessary to make a globally epistemological and moral turn toward the truth. The book shows that, when joint desires of the new economics of knowledge and technology erase epistemology (in a way to assign definitions of knowledge and rules and practices of the public usage of the mind), then the time for epistemology is on its way"--https://www.intechopen.com/books/epistemology-and-transformation-of-knowledge-in-global-age, accessed 06/07/2020. (shrink)

Departing from Levinas, this paper will address the significance of shame in contemporary discourse in order to approach what could be called its ethical intrigue. Focusing on its political, social and phenomenological implications, I intend to reconsider the experience of shame as it has been appropriated within the politics of affect and account for its relation to ethics, which alone can reveal its transformative possibilities. Shame will emerge as an affect of proximity whose basic structure of being exposed is an (...) attestation of our constitutive openness to others that towers above the politics of interest and the structures of economy that advance the drama of the Ego. (shrink)

Departing from what Levey and Sznaider (2002) in their seminal work ‘Memory Unbound’ refer to as ‘cosmopolitan memory’ that emerges as one of the fundamental forms ‘collective memories take in the age of globalization’, this article will consider the underlying ethical implications of global memory formation that have yet to be adequately theorized. Since global disseminations of local memory cultures and the implicit canonization of its traumas are intimately related to the concept of archive, I will first focus on what (...) Derrida (1996) in Archive Fever calls ‘archival violence’ and will show its inherent relation to the formation of cosmopolitan memory. Another related concept that I will use and that will problematize the transformation of living, embodied memory into archival, cultural memory upon which the formation of cosmopolitan memory depends is the witness. Using Agamben’s writing (2002) in this context that in Remnants of Auschwitz focuses on the foundational (im)possibilities of bearing witness, I will show that this transformation that determines the very possibility of cosmopolitan memory is far from unproblematic and readily accessible as Levy and Sznaider seem to assume. What will emerge as the most distinctive concern of global memory formation is the ethical material of difference as that which both makes its imperatives historically and politically exigent and that which signifies the difficulties of its unified articulation. Solidarity with the suffering of the other that mobilizes the very formation of cosmopolitan memory is also what should solicit vigilance against the universalistic ritualizations of its prerogatives. (shrink)

We’re tired of trees. We should stop believing in trees, roots, and radicles. They’ve made us suffer too much [ … ] Nothing is beautiful or loving or political aside from underground stems and aeri...

Revelation is the thesis that having an experience that instantiates some phenomenal property puts us in a position to know the nature or essence of that property. It is widely held that although Revelation is prima facie plausible, it is inconsistent with physicalism, and, in particular, with the claim that phenomenal properties are physical properties. I outline the standard argument for the incompatibility of Revelation and physicalism and compare it with the Knowledge Argument. By doing so, I hope to show (...) that on various plausible interpretations of Revelation it is in fact consistent with physicalism. Moreover, there is a robust reading of Revelation that a posteriori physicalists can, and should, accept. (shrink)

For many, the paradigm of a deflationary theory of truth is the redundancy theory, which is typically taken to consist of two claims: namely (i) that sentences containing the truth predicate are synonymous with sentences not containing the truth predicate (and so the truth predicate is redundant) and (ii) that there is no property of truth.1 The redundancy theory is not an attractive theory of truth since neither of its claims is particularly plausible on its own, and the combination of (...) the two claims is, if not actually inconsistent, at least uncomfortable.2 Very few deflationists nowadays endorse either part of the theory. (shrink)

Modern physics encompasses theoretical and experimental research divided in subfields with specific features. For instance, high energy physics (HEP) attracts significant funding and has distinct organizational structures, i.e., large laboratories and cross-institutional collaborations. Expensive equipment and large experiments create a specific work atmosphere and human relations. While the gender misbalance is characteristic for STEM, early-career researchers are inherently dependent on their supervisors. This raises the question of how satisfied researchers with working in physics are and how different subgroups – female (...) and early-career researchers – perceive their work environment. We empirically investigated job satisfaction and satisfaction with the academic system among physicists (N=123) working in large laboratories, universities, and independent institutes. The scale for measuring the satisfaction with the academic system in physics yielded three factors: experience of research autonomy, opportunities to use one's knowledge, and appreciation of the research by the general public. The results show that physicists are less satisfied with the academic system than with their work environment. Moreover, female scientists and junior researchers experience their jobs more negatively. The results emphasize the need for improving work and research conditions for underprivileged groups in physics. Interestingly, no significant effect was found between different types of academic institutions and general job satisfaction. Finally, physicists felt that their work has not been well understood by the public. (shrink)

In the last 30 years repeated attempts have been made to develop a proof-sketch Kripke gave for essentialism about material origins into a cogent argument. I argue that there are general reasons that all such attempts have failed, and so we should likewise expect future attempts to fail.

When Donald Davidson published his influential article ‘Actions, Reasons and Causes’ [1963], many of his contemporaries were convinced that reasons for action could not be causes of anything, so that even an explanation such as ‘Gilbert knelt because he had decided to propose to Gertrude’ did not work by citing Gilbert’s decision as a cause of his kneeling. Davidson was mainly responsible for demolishing that consensus and reinstating causalism—the thesis that psychological or rationalizing explanations of human behaviour are a species (...) of event-causal explanation—as the dominant view in the philosophy of action, so that it is now often regarded as an obvious truth. (shrink)

‘The Unity of the Proposition’ is a label for a problem which has intermittently intrigued philosophers but which for much of the last century lay neglected in the sad, lightless room under the stairs of philosophical progress, along with other casualties and bugaboos of early analytic philosophy such as the doctrine of internal relations, the identity theory of truth, and Harold Joachim. Yet it was while struggling with this problem (among others), that Bertrand Russell built one of the first steps (...) on the staircase by creating what came later to be called the theory of descriptions.1 According to that theory, statements containing definite descriptions are true only if there exists a unique thing satisfying the description. So nothing one says about ‘The Problem of the Unity of the Proposition’, for example, can be true unless there is one and only one such problem. Yet, as we shall explain below (§1), on the one hand it is unclear that there is any such problem at all, while, on the other, if there is a problem, there seem to be several. One might conclude, then, that everything we say in this paper is likely to be false. But perhaps the paper could be, in the context, appropriately treated as a ladder, to be kicked away after climbing. For Wittgenstein, too, was concerned with the problem: ‘At the centre of Wittgenstein’s project was the task of explaining the unity of the proposition’, says Michael Potter, for example.2 Wittgenstein had inherited the task from two of his philosophical mentors, Russell and Frege. Yet while Russell’s series of failed accounts of propositions, and then judgments, each of which was meant to resolve the problem, seemed ultimately to serve only as a sort of negative inspiration for him,3 Frege’s response to the problem proved a deep influence. We will outline Frege’s position as a backdrop to Wittgenstein’s below (§§2 and 3). As we will argue, one of the most important ways in which Wittgenstein’s position resembles Frege’s is precisely that his (Wittgenstein’s) solution to the problem of unity required treating his own book as an attempt to say the unsayable.. (shrink)

Although its use is not universal, there is a map of the logical space of theories of truth that is widely applied. According to this map, the most foundational divide amongst theories of truth is that between deflationary and inflationary theories, where, roughly, the former hold that truth is an insubstantial, logical property of little philosophical interest and the latter that it is a substantial property suitable for philosophical attention. Amongst the inflationary theories, there are other fundamental divisions. For example, (...) on the one hand, correspondence theorists hold that the truth of a proposition is a matter of the proposition’s standing in a relation to something else which is not a proposition, such as a fact. On the other hand, coherence theorists hold that the truth of a proposition is a matter of its relations to other propositions. And again, pragmatists hold that the truth of a proposition is a matter of its being useful to believe. Throughout the twentieth century, philosophers used one or other version of this map to orient themselves and their students in the often complex and confusing debates about truth, even while acknowledging that the map may be incomplete in crucial respects (it does not include functionalist and pluralist views, for example). Our objection to the map is not that it is incomplete—although it obviously is—, but that it needs to be radically redrawn. In particular, the familiar division between coherence theories and correspondence theories needs to be rethought. The coherence theory is so often glibly dismissed as absurd that labelling someone as a coherence theorist is often seen as reason enough to ignore them.1 While none of the philosophers usually so labelled should be ignored, we shall argue (§3) that none of them actually held this view anyway. The difficulty—perhaps impossibility—of finding a genuine coherence theorist of truth strikes us as more than just an indication that this is a rare animal. Rather, it suggests the possibility of something significant, namely, that the only occupant of this position in historical space is a set of slogans; this would give us some reason to suppose that the logical space of theories is just as empty at this point.. (shrink)

Australasian Journal of Philosophy, Volume 89, Issue 4, Page 735-738, December 2011.

In a famous footnote in Naming and Necessity, Kripke offered “something like a proof” of the thesis that material things have their material origins essentially (EMO). Although the sketch of a proof Kripke gave was incomplete in important respects, many philosophers have since endeavoured to develop Kripke’s style of argument so that it reaches its intended conclusion.1 In particular, a number of philosophers have attempted to complete Kripke’s argument sketch by appealing to some sort of “sufficiency principle” – a principle (...) that gives sufficient conditions for the identity of objects across possible worlds. These developments of Kripke’s argument face a number of problems, as pointed out by Mackie (1987, 2002), Robertson (1998, 2000) and others.2 Recently, however, Rohrbaugh and deRosset (2004, 2006) have offered a new route to origin essentialism that develops a Kripke-style argument without appeal to a sufficiency principle. While this argument has also not escaped criticism3, the argument suffers from a crucial flaw which has not been noticed. More interesting, though, is that the problem the argument faces is the same problem facing the arguments that appeal to sufficiency principles, and indeed Kripke’s original “proof” – all these arguments over-generalize. This strongly suggests that there is no Kripkestyle route to origin essentialism. (shrink)

Is it time for politics and political theory to face the challenge of artificial intelligence (AI)? It seems to be the case that political theory constantly lags behind technological developments. With rapid developments in the field of AI, a common estimate is that technological singularity will probably happen in the next 50 to 200 years. Even regardless of the time frame, the very possibility of superhumanly smart AIs poses serious political questions and calls for some serious political decisions. Luckily, some (...) scenarios are already provided by science fiction. The most common trope is that of a hostile AI taking over and destroying/enslaving humanity. Yet there is another path—AI takes over and makes itself a ruler (openly or behind the scenes), but rules in the genuine best interest of humanity. Such a turn of events, as described in Neal Asher’s Polity novels, may be an improvement compared to present political arrangements. It will, however, probably rob us of politics as such. (shrink)

The most important contemporary debate in the theory of truth is that between inflationists and deflationists.1 But although the debate is of fundamental importance, we do not have a clear, unproblematic formulation of the difference between the two camps. Part of the reason for this is that contemporary deflationists have given up many of the distinctive positions that their predecessors endorsed: typically, they no longer claim that the truth predicate is redundant, that there is no property of truth, or that (...) ‘true’ is not a predicate.2 While the desire to eschew these claims is understandable, doing so has made it more difficult to identify any difference between deflationists and inflationists, and the debate, particularly between deflationists and correspondence theorists, sometimes appears to evaporate. Perhaps in response to this worry, contemporary deflationists have adopted a range of new and distinctive deflationary claims about truth. Yet, as a number of critics have pointed out, many of these new positions are equally as implausible as those of earlier deflationists. (shrink)

Book Information The Compositionality Papers. The Compositionality Papers Jerry A. Fodor and Ernest Lepore , Oxford: Clarendon Press , 2002 , viii + 212 , US$65.00 ( cloth ), US$19.95 ( paper ) By Jerry A. Fodor. and Ernest Lepore. Oxford: Clarendon Press. Pp. viii + 212. US$65.00 (cloth:), US$19.95 (paper:).

In several publications Graeme Forbes has developed and defended one of the strongest arguments for essentialism about biological origins. I attempt to show that there are deep, as yet unrecognized, problems with this argument. The problems with Forbes’s argument suggest that a range of other arguments for various forms of origin essentialism are also likely to be flawed, and that we should abandon the seemingly plausible general metaphysical thesis that concrete entities that share all intrinsic properties are identical.

Australasian Journal of Philosophy, Volume 90, Issue 1, Page 199-202, March 2012.