The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

NOTE TO THE READER - December, 2021 ●●●●● -/- After a long period of time devoted to research in other areas, the author returned to the subject of this paper in a book-length study, CRITIQUE OF IMPURE REASON: Horizons of Possibility and Meaning. In this book (Chapter 11, “The Metalogic of Meaning”), the position developed in the 1982 paper, "Referential Consistency as a Criterion of Meaning", has been substantively revised and several important corrections made. It is recommended that readers (...) read the revised and corrected version that appears in the book, CRITIQUE OF IMPURE REASON. ●●●●● -/- The book is available in a printed edition, ISBN 978-0-578-88646-6, from online booksellers such as Barnes & Noble, Amazon, and through independent bookstores. The book is also available as a freely downloadable _corrected second edition_ eBook, DOI: 10.5281/zenodo.5458352, through PhilSci, PhilPapers, HAL, and other online archives. ●●●●● -/- In addition to the above-mentioned book, readers may find "A Primer on Bartlett's CRITIQUE OF IMPURE REASON" to be useful as a guide to the nearly 900-page CRITIQUE. The primer is available as a free download through PhilPapers. ●●●●● -/- "Referential Consistency as a Criterion of Meaning" describes a logically compelling criterion of meaning — that is, a necessary condition of meaning, one which is non-arbitrary and compelling. One cannot _not_ accept the proposed criterion without self-referential inconsistency. This “metalogical” variety of self-referential inconsistency is new, opening a third category beyond semantical and pragmatical forms of self-referential inconsistency. ●●●●● -/- It is argued that such a criterion of meaning can serve as an instrument of internal criticism for any theoretical framework that permits reference to a class of objects. The paper combines the concern of the logical empiricists to formulate a rigorous meaning criterion, with the analytical interest in identifying and eliminating self-defeating statements through an analysis of the referential structure of theories. ●●●●● -/- The paper is followed by a list of other publications by the author that further develop and extend the ideas presented here. (shrink)

We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely (...) combinatorial characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective (...) is more theoretical. Here, the invariance criterion is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force. (shrink)

In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is (...) to be identified with an infinite sequence of consequence relations holding between increasingly complex relata: formulae, inferences, metainferences, and so on. As a result, the present proposal allows not only to differentiate Classical Logic from ST, but also from other systems sharing with it their valid metainferences. Finally, we show how these results have interesting consequences for some topics in the philosophical logic literature, among them for the debate around Logical Pluralism. The reason being that the discussion concerning this topic is usually carried out employing a rivalry criterion for logics that will need to be modified in light of the present investigation, according to which two logics can be non-identical even if they share the same valid inferences. (shrink)

I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.

Philosophers are divided on whether the proof- or truth-theoretic approach to logic is more fruitful. The paper demonstrates the considerable explanatory power of a truth-based approach to logic by showing that and how it can provide (i) an explanatory characterization —both semantic and proof-theoretical—of logical inference, (ii) an explanatory criterion for logical constants and operators, (iii) an explanatory account of logic’s role (function) in knowledge, as well as explanations of (iv) the characteristic features of logic —formality, strong modal force, (...) generality, topic neutrality, basicness, and (quasi-)apriority, (v) the veridicality of logic and its applicability to science, (v) the normativity of logic, (vi) error, revision, and expansion in/of logic, and (vii) the relation between logic and mathematics. The high explanatory power of the truth-theoretic approach does not rule out an equal or even higher explanatory power of the proof-theoretic approach. But to the extent that the truth-theoretic approach is shown to be highly explanatory, it sets a standard for other approaches to logic, including the proof-theoretic approach. (shrink)

Physicists routinely claim that the fundamental laws of physics are 'time symmetric' or 'time reversal invariant' or 'reversible'. In particular, it is claimed that the theory of quantum mechanics is time symmetric. But it is shown in this paper that the orthodox analysis suffers from a fatal conceptual error, because the logical criterion for judging the time symmetry of probabilistic theories has been incorrectly formulated. The correct criterion requires symmetry between future-directed laws and past-directed laws. This criterion (...) is formulated and proved in detail. The orthodox claim that quantum mechanics is reversible is re-evaluated. The property demonstrated in the orthodox analysis is shown to be quite distinct from time reversal invariance. The view of Satosi Watanabe that quantum mechanics is time asymmetric is verified, as well as his view that this feature does not merely show a de facto or 'contingent' asymmetry, as commonly supposed, but implies a genuine failure of time reversal invariance of the laws of quantum mechanics. The laws of quantum mechanics would be incompatible with a time-reversed version of our universe. (shrink)

Relevant logics are a family of non-classical logics characterized by the behavior of their implication connectives. Unlike some other non-classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with (...) some questions for future research. (shrink)

The search for the extensions of sentences can be guided by Frege’s “principle of compositionality of extension”, according to which the extension of a composed expression depends only on its logical form and the extensions of its parts capable of having extensions. By means of this principle, a strict criterion for the admissibility of objects as extensions of sentences can be derived: every object is admissible as the extension of a sentence that is preserved under the substitution of co-extensional (...) expressions. The question is: what are the extensions of elementary sentences containing empty singular terms, like ‘Vulcan rotates’. It can be demonstrated that in such sentences, states of affairs as structured objects (but not truth-values) are preserved under the substitution of co-extensional expressions. Hence, such states of affairs are admissible (while truth-values are not) as extensions of elementary sentences containing empty singular terms. (shrink)

The verifiability principle was the characteristic claim of a group of thinkers who called themselves the Vienna Circle and who formed the philosophical movement now known as logical positivism. The verifiability principle is an empiricist criterion of meaning which declares that only statements that are verifiable by —i.e., logically deducible from— observational statements are cognitively meaningful. -/- This essay is a short introduction to the philosophical movement of logical positivism and its formulation of the verifiability principle. Its primary aim (...) is to provide students of philosophy with an accessible first overview of this philosophical movement. -/- After pointing out some aspects of the philosophical background of logical positivism (section 1), I will comment on the reasoning that lead these authors to formulate the verifiability principle (section 2), and I will analyse the debate about how to understand observational language and how observational statements (the so-called ‘protocol statements’) are verified (section 3). I will also comment on the two main consequences of accepting the verifiability principle: the conception of philosophy as the task of logical analysis and the project of unified science (section 4), and I will explain the different views on ethical language defended by logical positivists (section 5). I will end this essay by identifying the main problems of the verifiability principle and I will explain the core ideas of Carnap’s confirmability criterion, which attempts to resolve these problems (section 6 and 7). (shrink)

This paper outlines a formal recursive wager resolution calculus (WRC) that provides a novel conceptual framework for sentential logic via bridge rules that link wager resolution with truth values. When paired with a traditional truth-centric criterion of logical soundness WRC generates a sentential logic that is broadly truth-conditional but not truth-functional, supports the rules of proof employed in standard mathematics, and is immune to the most vexing features of their traditional implementation. WRC also supports a novel probabilistic criterion (...) of logical soundness, the fair betting probability criterion (FBP). It guarantees that the conclusion of an FBP-valid argument is at least as credible as a conjunction of premises, and also that the conclusion is true if the premises are. In addition, WRC provides a platform for a novel non-probabilistic, computationally simpler criterion of logical soundness – the criterion of Super-validity - that issues the same logical appraisals as FBP, and hence the same guarantees. (shrink)

Due to their acceptance of the verifiability principle, the only way left for logical positivists to argue for the meaningfulness of religious language was to accept some sort of emotivistic conception of it or to reduce it to the description of religious attitude. The verifiability principle, however, suffers from some severe limitations that make it inadequate as a criterion for cognitive meaning. To resolve these problems, logical positivists gave up the requirement of conclusive verifiability and defended a sort of (...) ‘liberalization’ of the verifiability principle. Carnap’s confirmability criterion for cognitive meaning, which is a liberalized form of the verifiability principle, is compatible with an orthodox conception of religious language since, from a theistic perspective, the existence of God can be confirmed through our observational statements. (shrink)

This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the verdicts, hypotheses, or conjectures of any science. In work currently in progress, we argue for the unique suitability of LF for the formalization of logic, mathematics, syntax, and semantics. The present document specifies the language and rules (...) of LF, lays out some notational conventions, and states some basic technical facts about the system. (shrink)

Paraconsistent logics are logical systems that reject the classical principle, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is (...) paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate and invalidate both versions of Explosion, such as classical logic and Asenjo–Priest’s 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski’s and Frankowski’s q- and p-matrices, respectively. (shrink)

As known from the academic literature on Hinduism, the foreign, Persian word, “Hindu” (meaning “Indian”), was used by the British to name everything indigenously South Asian, which was not Islam, as a religion. If we adopt explication as our research methodology, which consists in the application of the criterion of logical validity to organize various propositions of perspectives we encounter in research in terms of a disagreement, we discover: (a) what the British identified as “Hinduism” was not characterizable by (...) a shared set of beliefs or shared outlook, but a disagreement or debate about basic topics of philosophy with a discourse on tenets of moral philosophy anchoring the debate; and (b), the Western tradition’s historical commitment to language as the vehicle of thought not only leads to the conflation of propositions with beliefs, but to interpreting (explaining by way of belief) on the basis of the Eurocentric tradition rooted exclusively in ancient Greek philosophy. Interpretation on the basis of the Western tradition leads to the Western tradition vindicating itself as the non-traditional, non-religious, rational platform—the secular—for explaining everything—the residua are what get called religions on a global scale. This serves the political function of insulating Western colonialism from indigenous moral and political criticism. Given that Western colonialism is the pivotal event, before which South Asians just had philosophy, and after which they had religion (the explanatory residua of Eurocentric interpretation), we can ask about Hindu religious belief. This only pertains to the period after colonialism, when Hindus adopted a Westcentric frame for understanding their tradition as religious because of colonization. Prior to this, the tradition the British identified as “Hindu” had a wide variety of philosophical approaches to justification, which often criticized propositional attitudes, like belief, as irrational. (shrink)

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of the “syllogism” (...) in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry. (shrink)

Ian Rumfitt (2000) developed a bilateralist account of logic in which the meaning of the connectives is given by conditions on asserted and rejected sentences. An additional set of inference rules, the coordination principles, determines the interaction of assertion and rejection. Fernando Ferreira (2008) found this account defective, as Rumfitt must state the coordination principles for arbitrary complex sentences. Rumfitt (2008) has a reply, but we argue that the problem runs deeper than he acknowledges and is in fact related to (...) the challenge of establishing proof-theoretic harmony. We motivate a distinctively bilateral criterion for harmony and show how the bilateralist can meet it. This also resolves Ferreira's complaint. (shrink)

Expressivism in logic is the view that logical vocabulary plays a primarily expressive role: that is, that logical vocabulary makes perspicuous in the object language structural features of inference and incompatibility (Brandom, 1994, 2008). I present a precise, technical criterion of expressivity for a logic (§2). I next present a logic that meets that criterion (§3). I further explore some interesting features of that logic: first, a representation theorem for capturing other logics (§3.1), and next some novel logical (...) vocabulary for expressing structural features of inference (§4). (shrink)

The common use of Shannon’s information, specified for the needs of telecommunications, gives rise to many misunderstandings outside of this context. (e.g. in conceptions of such well-known theorists as C.F. Weizsäcker and J. A. Wheeler). This article shows that the terms of the general definition of information meet the structural information, and Shannon’s information is a special case of it. Similarly, complexity is misunderstood today as exemplified by the concepts of reputable computer scientists, such as S. Lloyd, S. Wolfram and (...) J. Schmidhuber. These theorists use an algorithmic definition of complexity and the so-called logical depth, neither of which meets the intuitive criterion of complexity. Hence, their misconceptions of beauty, art and the universe. It will be shown that the intuitive criterion is met by Abstract Complexity Definition. This definition also fulfils the criterion for a general complexity definition, as it defines complexity of the most general/abstract structure of our reality, that is, binary structure. It also explains such fundamental issues of information theory as the information–energy relationship and the value of information, which are still discussed and need to be clarified. (shrink)

1971. Discourse Grammars and the Structure of Mathematical Reasoning II: The Nature of a Correct Theory of Proof and Its Value, Journal of Structural Learning 3, #2, 1–16. REPRINTED 1976. Structural Learning II Issues and Approaches, ed. J. Scandura, Gordon & Breach Science Publishers, New York, MR56#15263. -/- This is the second of a series of three articles dealing with application of linguistics and logic to the study of mathematical reasoning, especially in the setting of a concern for improvement of (...) mathematical education. The present article presupposes the previous one. Herein we develop our ideas of the purposes of a theory of proof and the criterion of success to be applied to such theories. In addition we speculate at length concerning the specific kinds of uses to which a successful theory of proof may be put vis-a-vis improvement of various aspects of mathematical education. The final article will deal with the construction of such a theory. The 1st is the 1971. Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and Stratification of Language, Journal of Structural Learning 3, #1, 55–74. https://www.academia.edu/s/fb081b1886?source=link . (shrink)

Karl Popper (1902-1994) was one of the most influential philosophers of science of the 20th century. He made significant contributions to debates concerning general scientific methodology and theory choice, the demarcation of science from non-science, the nature of probability and quantum mechanics, and the methodology of the social sciences. His work is notable for its wide influence both within the philosophy of science, within science itself, and within a broader social context. Popper’s early work attempts to solve the problem of (...) demarcation and offer a clear criterion that distinguishes scientific theories from metaphysical or mythological claims. Popper’s falsificationist methodology holds that scientific theories are characterized by entailing predictions that future observations might reveal to be false. When theories are falsified by such observations, scientists can respond by revising the theory, or by rejecting the theory in favor of a rival or by maintaining the theory as is and changing an auxiliary hypothesis. In either case, however, this process must aim at the production of new, falsifiable predictions. While Popper recognizes that scientists can and do hold onto theories in the face of failed predictions when there are no predictively superior rivals to turn to. He holds that scientific practice is characterized by its continual effort to test theories against experience and make revisions based on the outcomes of these tests. By contrast, theories that are permanently immunized from falsification by the introduction of untestable ad hoc hypotheses can no longer be classified as scientific. Among other things, Popper argues that his falsificationist proposal allows for a solution of the problem of induction, since inductive reasoning plays no role in his account of theory choice. Along with his general proposals regarding falsification and scientific methodology, Popper is notable for his work on probability and quantum mechanics and on the methodology of the social sciences. Popper defends a propensity theory of probability, according to which probabilities are interpreted as objective, mind-independent properties of experimental setups. Popper then uses this theory to provide a realist interpretation of quantum mechanics, though its applicability goes beyond this specific case. With respect to the social sciences, Popper argued against the historicist attempt to formulate universal laws covering the whole of human history and instead argued in favor of methodological individualism and situational logic. Table of Contents 1. Background 2. Falsification and the Criterion of Demarcation a. Popper on Physics and Psychoanalysis b. Auxiliary and Ad Hoc Hypotheses c. Basic Sentences and the Role of Convention d. Induction, Corroboration, and Verisimilitude 3. Criticisms of Falsificationism 4. Realism, Quantum Mechanics, and Probability 5. Methodology in the Social Sciences 6. Popper’s Legacy 7. References and Further Reading a. Primary Sources b. Secondary Sources -/- . (shrink)

I construct a quantum-logical model of the type of situation that seems to be at the root of the problem of interpreting the projection postulate (Luders' rule) as a criterion of minimal disturbance. It is shown that the most natural way of characterizing minimal disturbance leads to contradictory conclusions concerning the final state.

Purpose. This article is devoted to the case study of relevant linguacultural stereotypes of the particular organization’s managerial culture and based on corresponding results the inquiry of the discourses formation features associated with the lexico-semantic meanings dispersion of (Foucault). -/- Methods and Procedure of Research. Top managers of a large Ukrainian enterprise (67 respondents) were asked to arbitrarily describe the following concepts – “manager”, “subordinate”, “managerial style”. Each concept was differentiated according to the principle of the lexico-semantic opposition (“productive – (...) counterproductive”). The obtained set of texts was lemmatized and a frequency analysis of the lemmas was carried out as well. Collocations were also evaluated, in particular, repeated n-grams were identified. In the further analysis were used all detected n-grams and those lemmas, the observed frequencies of which statistically significantly exceeded the expected ones. -/- Results. Discourse formation features are determined by the paradigmatic relations of lexico-semantic units (words) and their semantic linear compatibility. The paradigmatic dispersion of a discourse is represented by the quality of connections between lemmas according to the criterion of the paradigm types to be found. Also informative is the assessment of the lemmas number (granularity of the discourse) and the spectrum diversity of paradigmatic relations in the discourse. These parameters reflect the properties of homogeneity/complexity of discourse meanings dispersion. The syntagmatic dissemination of discourse is manifested by the features of the words semantic linear interrelationship in each n-gram. This parameter reflects the quality of rationalizations (verbal-logical chains) associated with the corresponding discourses. The length of n-grams (the number of words) is also indicative – the higher n, the more differentiated the discourse is and vice versa. Matching the words semantics in n-grams with lemmas allows one to draw a conclusion regarding the internal consistency (integration) of the discourse. -/- Conclusions. Psycholinguistic tools can be effectively used in an organizational phenomena study. In particular, the frequency analysis of lemmas, their lexico-semantic evaluation, as well as the qualitative analysis of n-grams in the problem-targeted texts of respondents allows one to solve applied research issues related to the assessment of current linguacultural trends in an organization and understanding their possible causes. Managerial culture, as a linguacultural phenomenon, is represented by a set of stably reproduced discourses in the process of the organization’s functioning. At the same time, discourses are constituted by the dispersion of meanings (words), which is being realized in two linguistic dimensions – paradigmatic and syntagmatic ones. (shrink)

In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose (...) an alternative of our own. After that, we consider a number of objections to our account and evaluate a substantially different approach to the same problem. (shrink)

This paper examines the work of Immanuel Kant in the light of a new theory on the nature of truth, knowledge and falsehood (the Inversion Theory of Truth). Kant’s idea that knowledge could be absolutely certain, and that its truth must correspond with reality, is discredited by a dissection of the Correspondence Theory of Truth. This examination of the nature of truth, as well as knowledge and falsehood, is conducted with reference to Sir Karl Popper’s writings on regulative ideas, the (...) criterion of demarcation and the principle of falsifiability. It is argued that if truth is to be regarded as certain, it should be used to describe objects and events in the objective (noumenal) state, and that subjective knowledge must contain (and is improved by) falsehood. Perceptions and knowledge are obtained by the biological and evolutionary process of Active Subjectivism. Ideas we have knowledge of can be metaphysical or scientific, according to Popper’s Criterion of Demarcation. Kant’s “Copernican revolution” claim that our intellect imposes absolutely true laws on nature could not allow for the possibility that ideas might be constructed from fallible perceptions, and hence that all knowledge is uncertain. Instead, he developed a Critique of Practical Reason in which religion, though not provable through logical reasoning, could be proved by our innate moral sense, giving us a Categorical Imperative that could lead to perverse results. By rejecting the absolute certainty of a priori knowledge, and admitting a degree of essential falsehood, we arrive at a more reasonable grounding for moral behavior. (shrink)

In this article, I argue that G. A. Cohen’s defense of the feminist slogan, “The personal is political”, his argument against Rawls’s restriction of principles of justice to the basic structure of society, depends for its intelligibility on the ability to distinguish—with reasonable but perhaps not perfect precision—between those situations in which what Nancy Rosenblum has called “the logic of congruence” is validly invoked and those in which it is not. More importantly, I suggest that the philosophical shape of Cohen’s (...) critique makes it difficult for him to supply the required criterion, and that the methodological “intuitionism” he claims to be committed to is at odds with his larger argument against Rawls concerning the subject of justice. (shrink)

In his Encyclopaedia Logic, Hegel affirms that truth is ‘usually’ understood as the agreement of thought with the object, but that in the ‘deeper, i.e. philosophical sense’, truth is the agreement of a content with itself or of an object with its concept. Hegel then provides illustrations of this second sort of truth: a ‘true friend’, a ‘true state’, a ‘true work of art’. Robert Stern has argued that Hegel's ‘deeper’ or ‘philosophical’ truth is close to what Heidegger labelled ‘material’ (...) truth, namely a property attributed to a thing on the basis of the accordance of that thing with its essence. It has since been common to think of Hegel's concept of ‘philosophical’ truth as ‘ontological’, ‘objective’ or ‘material’ in contrast to ‘epistemological’ or ‘propositional’ definitions. In this paper, I wish to add an important nuance to the existing literature on this subject: even though things have a truth-value for Hegel, the latter is always negative. I argue that Hegel's criterion of ‘philosophical’ truth, which is best formulated as ‘agreement with self’, is first and foremost intended to examine the truth-value of thought-determinations. I then argue that even though this criterion may also be applied to examine the truth-value of things (namely, even though things have a truth-value), things never fall under this definition. After reviewing several of Hegel's explicit remarks on the matter, I provide an alternative explanation to those features of Hegel's ‘philosophical’ truth which have led scholars to view it as a truth in things. Especially, I argue that what are generally seen as Hegel's examples (‘true friend’, ‘true state’, ‘true work of art’) are not intended as examples but only as imperfect illustrations of ‘philosophical’ truth. (shrink)

The purpose of this article is to support the logical incompatibility of the opposing views as a criterion for characterizing disagreements as genuinely metaphysical. That is, I intend to argue that a specific dispute is a metaphysical disagreement only when the conflicting views are governed by different logics. If correct, this criterion would not only help to separate merely verbal from genuine metaphysical debates, but it also would ground an argument against deflationism, guaranteeing the substantiality and relevance of (...) metaphysics. I intend to clarify the criterion, to present its basic foundations and commitments, to give some logical and metaphysical motivations for its adoption and some examples of its application. (shrink)

Neil Tennant was the first to propose a proof-theoretic criterion for paradoxicality, a framework in which a paradox, formalized through natural deduction, is derived from an unacceptable conclusion that employs a certain form of id est inferences and generates an infinite reduction sequence. Tennant hypothesized that any derivation in natural deduction that formalizes a genuine paradox would meet this criterion, and he argued that while the liar paradox is genuine, Russell's paradox is not. -/- The present paper delves (...) into Tennant's conjecture for genuine paradoxes and suggests that to validate the conjecture, one of two issues must be addressed. The first issue is the need for a philosophical consensus on the identification of a genuine paradox in an informal sense. The second issue is the requirement for a uniform approach to formalize paradoxes in natural deduction. If either of these issues is addressed, the conjecture could be validated, or at the very least, it could hold philosophical importance in delineating the proof-theoretic features of paradoxicality. (shrink)

This paper compares several models of formalization. It articulates criteria of correct formalization and identifies their problems. All of the discussed criteria are so called “semantic” criteria, which refer to the interpretation of logical formulas. However, as will be shown, different versions of an implicitly applied or explicitly stated criterion of correctness depend on different understandings of “interpretation” in this context.

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

This paper develops a criterion for sameness of Fregean senses. I consider three criteria: logical equivalence, intensional isomorphism, and epistemic equipollence. I reject the first two and argue for a version of the third.

The aim of the paper is to sketch a principle of individuation that is intended to serve the Fregean notion of a proposition, a notion I take for granted. A salient feature of Fregean propositions, i.e. complexes of modes of presentation of objects, is that they are fine-grained items, so fine-grained that even synonymous sentences might express different Fregean propositions. My starting point is the principle labelled by Gareth Evans the Intuitive Criterion of Difference for Thoughts, which states that (...) it is impossible coherently to take different mental attitudes to the same proposition. As a logical truth, this is a synchronic principle, the application of which is restricted to attitudes held at a single time. I argue that such a restriction might be reasonably lifted and, on the basis of an adequate notion of attitude-retention, I propose an admissible diachronic extension of the principle. (shrink)

I argue against the skeptical epistemological view exemplified by the Groarkes that “all theories of informal argument must face the regress problem.” It is true that in our theoretical representations of reasoning, infinite regresses of self-justification regularly and inadvertently arise with respect to each of the RSA criteria for argument cogency (the premises are to be relevant, sufficient, and acceptable). But they arise needlessly, by confusing an RSA criterion with argument content, usually premise material.

If there is an area of discourse in which disagreement is virtually absent, it is mathematics. After all, mathematicians justify their claims with deductive proofs: arguments that entail their conclusions. But is mathematics really exceptional in this respect? Looking at the history and practice of mathematics, we soon realize that it is not. First, deductive arguments must start somewhere. How should we choose the starting points (i.e., the axioms)? Second, mathematicians, like the rest of us, are fallible. Their ability to (...) recognize whether a putative proof is correct is not infallible. In most cases, disagreement over the correctness of a putative proof is, however, evanescent. Once an error is spotted and communicated, the disagreement disappears. But this is not always the case. Sometimes it is recalcitrant; that is, it persists over time. In order to zoom in on this type of disagreement and explain its very possibility, we focus on a single case study: a decades-long (1921-1949) controversy between Federigo Enriques and Francesco Severi, two prominent exponents of the Italian school of algebraic geometry. We suggest that the instability of the mathematical community to which they belonged can be explained by the gap between an abstract criterion of rigor and local criteria of acceptability. It is this instability that made the existence of recalcitrant disagreement over putative proofs possible. We do not condemn speculative mathematics but rather its pretense of being rigorous mathematics. In this respect, we show that the overly self-confident Severi and the more intuitive, visionary Enriques had a completely different attitude. (shrink)

The precondition of any feminist politics – a usable category of ‘woman’ – has proved to be difficult to construct, even proposed to be impossible, given the ‘problem of exclusion’. This is the inevitable exclusion of at least some women, as their lives or experiences do not fit into the necessary and sufficient condition(s) that denotes group membership. In this paper, I propose that the problem of exclusion arises not because of inappropriate category membership criteria, but because of the presumption (...) that categories can only be organised by identity relations or shared properties among their members. This criterion of sameness as well as the characterisation of this exclusion as essentialism attests to a metaphysics that is not conducive to resistance and liberatory projects. Following a strain of hybrid thinking in feminist and post-colonial theory, I outline an alternative pluralist logic that confronts oppressive binaries that impede theory work in gender, sexuality, and race theory, and limit political action and resistance. The problem of exclusion is neither irresolvable nor is it essentialism. Instead it is a denial of subjectivity due to pseudodualistic self/Other dichotomies that can be resisted by adopting a new categorial logic. While this paper focuses on the specific problem of formulating a category of ‘woman’, it has implications for other areas of gender, critical race, and postcolonial theory. Rather than working toward an inclusive category founded on sameness, theorists need to develop independent and positive categories grounded in difference. Our current categorial logic does not permit such a project, and therefore a new metaphysics must be adopted. (shrink)

Bioethics, neuroscience, medicine are contributing to a debate on the definition and criteria of death. This topic is very controversial, and it demonstrates clashing views on the meaning of human life and death. Official medical and legal positions agree upon a biological definition of death as irreversible cessation of integrated functioning of the organism as a whole, and whole-brain criterion to ascertain death. These positions have to face many criticisms: some scholars speak of logical and practical inconsistency, some others (...) of invalid scientific theory about the supreme integrator. In this paper some criticisms are exposed and discussed in order to reconstruct the state of the art in bioethical debate. -/- . (shrink)

This article has been written about the explanation of the scientific affair. There are the philosophical circles that a philosopher must consider their approaches. Postmodern thinkers generally refuse the universality of the rational affair. They believe that the experience cannot reach general knowledge. They emphasize on the partial and plural knowledge. Any human being has his knowledge and interpretation. The world is always becoming. Diversity is an inclusive epistemological principle. Naturally, in such a state, the scientific activity is a non-sense (...) process. The postmodern world is a post-scientific world. Another collection of approaches to science belongs to the analytical philosophy. The main part of analytical philosophy context centers around language. Language is the center of the world. We can study the world through language. Language is the possibility of knowledge. If we overcome the language games, we can study the world accurately. Generally, at present, it seems that the rational thoughts are marginal points in the sea of irrationality. We can probably talk about an anarchistic epistemological situation. Another issue is the role of observation to form a scientific activity. In this situation, the question is whether the observation is the technique of gathering information or the final reference of original scientific analysis. In relation to this issue, the confrontation of science with the families and the categories of the objects is the main problem. For more than two thousand years, the totalitarian heritage of the Aristotelian logic has been the guideline of categorizations for the human being. In order to reach an inclusive and applicable result, we should categorize everything; but it is not really known that if the method of the world categorization is the same or not. The accordance of the conceptual categories with their extensions in the world is one of the main problems which has malfunctioned the scientific system. It is better to say that it has deactivated science. Moreover, there are many interpretations for each event based on its occurrence conditions. For example, consider a fever; In order to diagnose its cause, the most significant factor is the role of a physician. There is no sense in saying that the observation has diagnosed the cause of the fever. This is the observer that plays a determinative role. Another problem is the disputes between realism and instrumentalism. Instrumentalists believe that to form a theory, the concepts are just the tools of scientific researches. Based on realism, but we confront the concepts in the original way. This chaos causes the scientific system to collapse. Now the question is what the solution is. I would like to propose my scheme that is constructed based on a main principle: there is no occurrence in the world unless we can trace the effect of consciousness back in that occurrence. In other words, there is no accident in the world. One can argue that it is the main problem that the effects of consciousness ---if there is such a concept--- is not traceable in the world. An immediate response to this problem is an inefficient technique . The observation is a technique . It is not the method of interpretation. Some people argue that the empirical approach cannot lead us to an authentic criterion to know the world. Because there is no criterion for truth, and if there is probably such a criterion, we can obtain it via several ways. The solution to the first problem is simple. Any occurrence is a truth; even we suppose it as a partial truth. Therefore we can say we face a multi-facial world. It can be the solution of the second problem: if consciousness is essentially the origin of the world and all occurrences, we face consciousness as a unique truth; even its creations contradict each other. If there is no consciousness as a creator of the world and we cannot trace it back in all existents, then what should we do? If there is consciousness, why its creations contradict each other. Since consciousness is a will, it is able to decide in any situation it intends. The issue of contradictory consciousness intentions has a teleological aspect. We cannot judge its teleological substance at present. If we are able to believe that there is no consciousness at all, it will contradict the main practical principle in our lives. Every action that we take in our lives is conjoined with consciousness. We learn many things from many sources. The substance of our instincts and emotions can be questioned. It is true that, infact we cannot analyze our instincts and emotions, but we can discuss explicitly about the rational elements of the instincts. What are these elements? These elements are the quality of their appearance. The quality of instinct appearance is different among beings. The strength and the depth and length of these irrational qualities are different in all beings. What factors or factor cause the differences among these aspects? There is certainly a determinative factor. The same factor which determines the occurrence of any event. Even if we believe in partial knowledge, we must accept the confrontation of the occurrences. Thus it is not possible to refuse the occurrences as the reference unit of knowledge. In spite of the difference, every occurrence, even as a single occurrence, happens and we can regard it as the reference unit of knowledge. Then we can consider every occurrence as an occurred object. When an occurrence happens, then it is a determined object. Everywhere there is a determination, there is certainly a determiner. Why do not we encounter a multi-determinative consciousness? Because there are a few aspects of the unique super-consciousness. These aspects are motion and growth and the amount of constituent material in every being. In all over the world, the difference in these factors creates all differences. Thus we do not encounter the plural consciousness. Is the world birth accidental? Infact, there is no accident. The accident has no meaning in the world. As explained above, the constructing element of the world is the occurrence. An occurrence can be analyzed. Therefore, we should not talk about the accident until we are not able to analyze all phenomena. We can look at every subject from different points of view at present. Thus there is theoretically no possibility to say that a certain matter is the consequence of the accident. The accident is a popular and inexact concept that has no philosophical content. Moreover, the definition of consciousness versus its contradiction causes the collapse of all epistemological axioms. We can ask why we must not define other logical principles against their contradictions. Thinkers who deny the role of logic usually ignore the role of logic. They have not been able to deny the logical function to form an epistemological system because it is not an easy task. In this article some other issues were discussed, such as the consideration of restriction as a stable and firm foundation of knowledge instead of the Descartes cogito. In addition to these philosophical points some other issues were propounded such as the role of instrumental mechanism to form the new science and the great alterations in philosophy and history of Europe. Many issues threaten human civilization. The only way to deal with such threats is certainly to use scientific facilities. The scientific possibilities undoubtedly come from a complete and inclusive scientific theory. The present article is an attempt to explain the scientific affair in order to develop human achievement, however small. -/- . (shrink)

Science was not far from philosophy in ancient thought, but the two were one thing. I do not know whether the ancient philosophers considered themselves the issue of the relationship between them, as the modern and contemporary philosophers did. But the sure thing is that the natural sciences became independent from philosophy in the modern era, and most of the scientific departments in universities were divided into two parts: sciences, literature, and humanities. At the end of the nineteenth century and (...) what followed, there were attempts to link them. Charles Peirce wrote on the scientific method and scientific metaphysics. The Vienna Circle presented a scientific conception of the world and the logical empiricists and Popper was concerned with the problem of distinguishing science from pseudoscience. The logical empiricists provided the criterion of verifiability, and Popper proposed the falsification principle. Quine defended a natural epistemology that asserts that philosophy is part of natural science. Bunge offered his own criteria for distinguishing science in the context of scientific philosophy. In this article, I want to refute the claim that philosophy has died and that science does not need it. I proved that the notion that philosophy is useless to science is not only wrong but also harmful to society, education, and science itself. This comes in a broader context, which is the moderate scientific tendency that I have defended in some of my writings. -/- لم يكن العلم بعيدًا عن الفلسفة في الفكر القديم، بل كان الاثنان شيئًا واحدًا. ولست أدرى أكان الفلاسفة القدماء يلقون على أنفسهم مسألة العلاقة بينهما مثل ما ألقاها الفلاسفة المحدثون والمعاصرون أم لا. ولكن الشيء المحقق أن العلوم الطبيعية استقلت عن الفلسفة في العصر الحديث، وانقسمت معظم الأقسام العلمية في الجامعات إلى قسمين: العلوم، والآداب والإنسانيات. وظهرت في أواخر القرن التاسع عشر وما تلاه محاولات لربطهما. كتب تشارلز بيرس عن المنهج العلمي والميتافيزيقا العلمية. وقدمت جماعة فيينا تصورًا علميًّا للعالم، واهتم التجريبيون المنطقيون وبوبر بمشكلة تمييز العلم من العلم الزائف؛ قدم التجريبيون المنطقيون معيار القابلية للتحقق، واقترح بوبر مبدأ التكذيب. ودافع كواين عن إبستمولوجيا طبيعية تؤكد أن الفلسفة جزء من العلم الطبيعي. وقدم بونجي معاييره الخاصة لتمييز العلم في سياق الفلسفة العلمية. (shrink)

In the first of the Insolubles in Chapter 8 of his Sophismata, Buridan contends that the inference Omnis propositio est affirmativa; ergo, nulla propositio est negativa (PS) is valid, even though it appeals to the self-reference in the conclusion to show that what we (following Read 2001) call the classical conception of validity (CCV) fails. This requires that we accept that there are good inferences in which a false conclusion follows from true premises. Partially following Hughes’ proposal (1982), we argue (...) that the First Sophism (PS) involves three different notions of validity. Two of them correspond to the ones described by Hughes (1982, 80–86), who calls them Theory A and Theory B. The third one—that will we call Theory C—is not mentioned by Hughes; instead, it is suggested by Buridan himself in the first three arguments in favor of the validity of PS. We show that: a) from what Buridan says in his Theory C it follows that PS is a formal and material consequence, and hence, a valid one. Then we show that: b) the rejection of CCV and the acceptance of Nulla propositio est negativa (NPN) as a (formal) consequence of Omnis propositio est affirmativa (OPA) leads to a paradox that bears similarities with the one put forward by Pseudo Scotus—which has been studied by Read (2001) and is related to Curry’s paradox. However, there are enough differences to merit considering this paradox separately, especially in relation to the so-called validity paradoxes. Interestingly, our work suggests that Buridan was aware of these problems, which explains why he introduced a new criterion for validity, one that is not based on truth-preservation but on what Spade (1988) calls firmness, and Klima (2016) correspondence. (shrink)

Explanations in behavioural neuroscience are often said to be mechanistic in the sense that they explain an organism’s behaviour by describing the activities and organisation of the organism’s parts that are “constitutively relevant” to organism behaviour. Much has been said about the constitutive relevance of working parts (in debates about the so-called “mutual manipulability criterion”), but relatively little has been said about the constitutive relevance of the organising relations between working parts. Some New Mechanists seem to endorse a simple (...) causal-linking account: organising relations are constitutively relevant to organism behaviour if and only if (and because) they are causal relations that link the working parts that are constitutively relevant to organism behaviour. In this paper, I argue that the causal-linking account is inadequate because it neglects the constitutive relevance of anatomical relations that organise the working parts of a behaving organism. I demonstrate this by considering a case study where the anatomical organisation of the barn owl (Tyto alba) is constitutively relevant to their mechanism for sound localization. The anatomical organisation of this mechanism is best understood as the back-and-forth flow of task information across 7 “levels of anatomy” (a notion that I distinguish from levels of mechanism). A further implication, I conclude, is that at least some of the interlevel structure of neuroscientific explanation is accounted for by levels of anatomy, not levels of mechanism. (shrink)

I argue against the skeptical epistemological view exemplified by the Groarkes that “all theories of informal argument must face the regress problem.” It is true that in our theoretical representations of reasoning, infinite regresses of self-justification regularly and inadvertently arise with respect to each of the RSA criteria for argument cogency (the premises are to be relevant, sufficient, and acceptable). But they arise needlessly, by confusing an RSA criterion with argument content, usually premise material.

I confront arbitrariness of the sign to a criterion assessing the quality of language, logical system, psychometrics and art.

We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals are (...) Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

Nelson Goodman observed that we use only certain ‘good’ (viz. projectible) predicates during reasoning, with no obvious demarcation criterion in sight to distinguish them from the bad and gruesome ones. This apparent arbitrariness undermines the justifiability of our reasoning practices. Inspired by Quine’s 1969 paper on Natural Kinds, Peter Gärdenfors proposes a cognitive criterion based on his theory of Conceptual Spaces (CS). He argues the good predicates are those referring to natural concepts, and that we can capture naturalness (...) in terms of similarity. In contrast to Quine, he does not primarily rely on logic, but geometry. He frames his account as a descriptive project, however, and it is not obvious how it addresses the normative dimension of Goodman’s Riddle. This paper develops a charitable reconstruction of his argument, based on the idea that the instrumental success of our projectible concepts is grounded in their cognitive-pragmatic naturalness. It then explores three lines of reasoning against the argument: Evolutionarily motivated skepticism, the miracles argument, and the relation between instrumental and pragmatic success. I conclude that in its current form, the CS account fails to provide any justification of reasoning beyond appealing to its instrumental success, and that a metaphysically robust notion of naturalness helps to achieve the desired goal. (shrink)

Traditionally, consistency is the only criterion for the quality of a theory in logic-based approaches to reasoning about actions. This work goes beyond that and contributes to the metatheory of actions by investigating what other properties a good domain description should have. We state some metatheoretical postulates concerning this sore spot. When all postulates are satisfied we call the action theory modular. Besides being easier to understand and more elaboration tolerant in McCarthy’s sense, modular theories have interesting properties. We (...) point out the problems that arise when the postulates about modularity are violated, and propose algorithmic checks that can help the designer of an action theory to overcome them. (shrink)

Gödel’s slingshot-argument proceeds from a referential theory of definite descriptions and from the principle of compositionality for reference. It outlines a metasemantic proof of Frege’s thesis that all true sentences refer to the same object—as well as all false ones. Whereas Frege drew from this the conclusion that sentences refer to truth-values, Gödel rejected a referential theory of definite descriptions. By formalising Gödel’s argument, it is possible to reconstruct all premises that are needed for the derivation of Frege’s thesis. For (...) this purpose, a reference-theoretical semantics for a language of first-order predicate logic with identity and referentially treated definite descriptions will be defined. Some of the premises of Gödel’s argument will be proven by such a reference-theoretical semantics, whereas others can only be postulated. For example, the principle that logically equivalent sentences refer to the same object cannot be proven but must be assumed in order to derive Frege’s thesis. However, different true (or false) sentences can refer to different states of affairs if the latter principle is rejected and the other two premises are maintained. This is shown using an identity criterion for states of affairs according to which two states of affairs are identical if and only if they involve the same objects and have the same necessary and sufficient condition for obtaining. (shrink)

Application of the reliability of repairable systems on solving problems from constructing production systems takes an important place in the process of finding the optimal solution among the suggested system choices. The basic hypothesis when using the reliability of the repairable systems is that every machine is representing a component, a fact that is debatable when talking about technical sciences. However, considering the second assumption of the stationary process, the function of the availability is introduced. It represents the measure between (...) the reliability and the benefit of maintaining the components and the system as a whole one. An additional and the last reason for analyzing constructing machine as a whole one has an economic reason. From the aspect of the total cost and the capacity of the system, the function of the availability is catching more and more impact in the process of determinating the total cost in bill of quantities as the most important part of tender documents. Until former works, techno-economic optimisation usually ran over when choosing the system of the construction machines. In the work, there are shown the methodologies for gathering and analyzing the indicators of availabilities per unit of a company's machine park. The time of demission and reparation have been investigated among 34 components in the period of 6 years. Based on the obtained result for different conditions of machine exploitation and facilities, it is suggested the methodology of the future behaviour of the corresponding within the model optimization availability of constructing production system with the aim of eliminating extra criterion. The suggested model takes in consideration the total cost of the components when they are functional, and when they are not. This kind of approach enables the one who take choices decision of the height of profits, in the lenght of work in function of the projection of cash flow and managing with real indicators of functioning the system at the project level. Given the fact that the maintanance policy of machines is based on availability, and not on reliability of components, with the aim of maximizing the availability of different budget scenarios, a logical approach to the selection of the objective function in the terms of management of construction production systems is to minimize costs for a given availability of system constructing machinery is based on the use of historical data base with the values of the operational availability of components, conditions in which they function, in the process of forecasting the project availability for projects that follow. Ranking variant solutions is the result of the adopted function of the aim as a consequence due to enlargement methods of availability for serial parallel systems with the associated restrictions. For optimal system availability is taken a value that belongs to minimal total cost. However, it is predicted that after the end of the financial year, the real and projected indicators of system functions get compared to each other. Informational support to the proposed model is informational company system, which was built in the PHP programming language on the Linux software platform, and with data based in My SQL. The suggested model is tested on the system for the production and embedding bitumen bound materials on the specific project. Obtained results confirm the assumptions used in work. (shrink)

W. V. Quine’s criterion of ontological commitment is commonly presented as the slogan: “to be is to be the value of a variable”. More specifically, to be is to be in the domain of values of a bound variable attached to a existential quantifier in the body of a theory. If a sentence of our best available theory quantifies over bachelors, so we conclude that, according to it, there are bachelors. Simplicity and the use of logical apparatus for determining (...) this criterion are responsible for many philosophers to adhere to this standpoint within analytical metaphysics. I will argue that despite this strong influence of the Quinean criterion of ontological commitment in many debates, we find at least three interlinked problems in its original formulation: (1) The criterion depends of a clear definition of theory for the determination of the quantifications counting as entailers of ontological commitments. However, Quine does not present such clear concept of what would be a theory and of how to formalize it. Quine develops this notion under just the metaphor of the knowledge fabric, in which we have a group of sentences, which does not suffice for the required account of ontological commitment. (2) There are distinct possibilities of quantifying over given sentences, which leaves room for different ontological commitments associated with the same statement. In that sense, someone could argue that the Quinean solution would be to endorse just the first order predicate logic. Nonetheless, the Quinean should explain why we ought to be restricted to this logic. (3) The previous problems lead to a possible explosion of the Quinean criterion of ontological commitment, making it trivial, because it permits the quantification over any supposed entities and, hence, that anything can exist. Thus, I will discuss Quine’s criterion of ontological commitment in the light of the abovementioned problems, showing that, unless the Quinean presents a more specific definition of theory beyond just a group of sentences, he leads to an explosion of commitments with different entities. I will conclude that, if you understand ‘theory’ as Alonzo Church’s concept of ‘formalized language’, this knot can be undone. However, Church’s concept is much more akin to Carnap’s linguistic framework than to a notion of knowledge fabric “without borders” as the one proposed by Quine. (shrink)