Logic and Philosophy of Logic, Misc

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or not (...) arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. -/- Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

Grice argues that indicative conditionals ‘if p then q’ have conventional, truth conditional meaning according to the material conditional ‘p  q’. In order to explain away the known paradoxes with this interpretation, he distinguishes between truth conditions and assertion conditions, attempting to demonstrate that the assumed connection between ‘p’ and ‘q’ (the Indirectness Condition) is a conversational implicature; hence a matter only relevant for the assertion conditions of a conditional. This paper argues that Grice fails to demonstrate i) that (...) the Indirectness Condition is cancellable, hence a conversational implicature, ii) that the Indirectness Condition is not part of the conventional, truth-relevant meaning of ‘if’, and accordingly, iii) semantic or logical equivalence between indicative and material conditionals. (shrink)

The conditional interpretation of general categorical statements like ‘All men are animals’ as universally quantified material conditionals ‘For all x, if x is F, then x is G’ suggests that the logical structure of law statements is conditional rather than categorical. Disregarding the problem that the universally quantified material conditional is trivially true whenever there are no xs that are F, there are some reasons to be sceptical of Frege’s equivalence between categorical and conditional expressions. -/- Now many philosophers will (...) claim that the material conditional interpretation of laws statements, dispositions ascriptions, or any causal claim is generally accepted as wrong and outdated. Still, there seem to be some basic logical assumptions that are shared by most of the participants in the debate on causal matters which at least stems from the traditional truth functional interpretation of conditionals. This is indicated by the vocabulary in the philosophical debate on causation, where one often speaks of ‘counterfactuals’, ‘possible worlds’ and ‘necessity’ without being explicit on whether or to what extent one accepts the logical-technical definition of these notions. To guarantee a non-Humean and non-extensional approach to causal relations, it is therefore important to be aware of the logical and metaphysical implications of the technical vocabulary. -/- In this paper we want to show why extensional logic cannot deal with causal relations. Via a logical analysis of law-like statements ‘All Fs are Gs’ we hope to throw some new light on interrelated notions like causation, laws, induction, hypotheticality and modality. If successful, our analysis should be of relevance for a deeper understanding of any type of causal relations, whether we understand them to be laws, dispositions, singulars or categoricals. (shrink)

Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying (...) claim to any notion of reality. This foundation begins with Ludwig Wittgenstein’s Tractatus Logico-Philosophicus and the relationship of language to formal logic. Ultimately, we arrive at an answer to the question of why people believe the things they do. This is effectively a modification of Alfred Tarski’s semantic theory of truth. The second major issue addressed is the ‘dreaded’ Hard Problem of Consciousness as first stated by David Chalmers in 1995. The solution is found in the unification of consciousness, information theory and notions of physicalism. The physical world is shown to be an isomorphic representation of the phenomenological conscious experience. New concepts in understanding how language operates help to explain why this relationship has been so difficult to appreciate. The inclusion of concepts from information theory shows how a digital mechanics resolves heretofore conflicting theories in physics, cognitive science and linguistics. Scientific orthodoxy is supported, but viewed in a different light. Mainstream science is not challenged, but findings are interpreted in a manner that unifies consciousness without contradiction. Digital mechanics and formal systems of logic play central roles in combining language, consciousness and the physical world into a unified theory where all can be understood within a single consistent framework. (shrink)

We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.

Forthcoming in Darren Bradley (ed.), Carnap and Contemporary Philosophy. -/- This paper is centered on Carnap’s views on rationality. More specifically, much of the focus is on a puzzle regarding Carnap’s view on rationality that Florian Steinberger has recently discussed. Not only is Steinberger’s discussion of significant intrinsic interest: his discussion also raises general questions about Carnap interpretation. As I have discussed in earlier work, there are two very different ways of interpreting Carnap’s talk of “frameworks” – and, relatedly, different (...) ways of interpreting Carnap’s principle of tolerance. Carnap can be interpreted as either a relativist or as what I call a language pluralist. Steinberger’s puzzle arises given the relativist interpretation; I believe the language pluralist interpretation is correct. Most of the discussion will concern the correct interpretation of Carnap, and what this means for Steinberger’s puzzle. While I will not here mount a full defense of the language pluralist interpretation, I will pause to discuss Vera Flocke’s recent criticism of it. Towards the end, I will describe a puzzle regarding rationality different from Steinberger’s. The puzzle that I describe does arise already for the language pluralist. (shrink)

By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be semantically (...) incorrect. (shrink)

Ontological arguments like those of Gödel (1995) and Pruss (2009; 2012) rely on premises that initially seem plausible, but on closer scrutiny are not. The premises have modal import that is required for the arguments but is not immediately grasped on inspection, and which ultimately undermines the simpler logical intuitions that make the premises seem plausible. Furthermore, the notion of necessity that they involve goes unspecified, and yet must go beyond standard varieties of logical necessity. This leaves us little reason (...) to believe the premises, while their implausible existential import gives us good reason not to. (shrink)

Motivated by the urgency of making explicit "the laws of possible rational passage from one concept to another", which Professor F. William Lawvere brought into figural salience for all to see, here we begin to characterize the space of all mathematical concepts (whose kinship with ordinary concepts was highlighted by none other than Einstein) which determines all possible rational passages between concepts.

In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics and a set of logical constants (with specified arities). The first generator returns formulae of exactly the given depth, using all or some of the propositional letters. The second does the same but samples up-to the given depth. The third generator outputs formulae with exactly (...) the desired depth and all the atomics in the set. To make the generators uniform (i.e. to make them return every formula in their space with the same probability), we will prove various cardinality results about those spaces. (shrink)

Un libro de texto de lógica, argumentación y razonamiento probabilístico que he estado escribiendo durante los últimos años. Lo he usado para clases en bachillerato, licenciatura y posgrado. Está incompleto todavía, pero las primeras tres partes (argumentación, lógica proposicional, y cuantificación) están completas a un 85%, aproximadamente. Si lo usas, me ayudarías mucho mandándome comentarios, críticas y cualquier sugerencia.

Which premisses should we use to start our inquiries? Which transitions during inquiry should we take next? When should we switch lines of inquiry? In this paper, I address these open questions about inquiry, formulating novel norms for such decisions during deductive reasoning. I use the first-order predicate calculus, in combination with Carnap’s state description framework, to state such norms. Using that framework, I first demonstrate some properties of sets of sentences used in deduction. I then state some norms for (...) decisions made during deductive reasoning, establishing initial benchmarks for efficient deduction by ideal reasoners. When deciding which transition to make next, reasoners should choose the most informative transition, the one that maximally reduces uncertainty in the sense of ruling out the largest number of state descriptions relevant to their inquiry. Finally, inspired by optimal foraging theory, I show that, under certain assumptions of ignorance, reasoners should change premiss sets when their information intake drops below the global average information intake across premiss sets. (shrink)

In this article I offer an explicating interpretation of the procedure of content recarving as described by Frege in §64 of the Foundations of Arithmetic. I argue that the procedure of content recarving may be interpreted as an operation that while restricting the subject matter of a sentence, performs a generalization on what the sentence says about its subject matter. The characterization of the recarving operation is given in the setting of Yablo’s theory of subject matter and it is based (...) on the relation of determination between properties. The main advantage of the proposal is its generality, for it is applicable not just to the case of abstraction principles. (shrink)

In contemporary philosophy there is much focus on conceptual engineering: the enterprise of revising and replacing concepts. In this talk, I focus on a theoretical issue that has not yet received much attention. What principled limits are there to this sort of enterprise? Are there concepts that for principled reasons cannot or should not be revised or replaced? Examples discussed include logical concepts and normative concepts.

In this article, I apply Australian logician and ecofeminist philosopher Val Plumwood’s Feminism and the Mastery of Nature, specifically its alternative logic of “the dance of interaction,” to a controversial community-engagement program in my home state of Alabama. At Rural Studio, Auburn University students design free housing and public works for one of the poorest regions in the United States, known as the “Black Belt.” Through the lens of Plumwood’s ecofeminist dancing logic, the marginalized source of Rural Studio’s survival is (...) revealed to be the resilience of the disempowered majority-Black community. Inspired thereby, I sketch an ecofeminist choreography with three “dancing” concepts (namely Plumwood’s “the master model,” Vandana Shiva’s “nature’s logic,” and Ariel Salleh’s “holding”), acknowledging the resilience of the disempowered as a necessary step toward an ethically-sustainable aesthetics. (shrink)

I argue that logic is unlike science in its methodology, thus rejecting anti-exceptionalism about logic. Logic has a mathematical and a philosophical part. In its mathematical part, the methodology of logic is like that of mathematics, and no need to choose between theories arises in that part. In its philosophical part, the methodology of logic is like that of philosophy. Philosophy and mathematics are both unlike the empirical sciences in their methodology. So logic is unlike the empirical sciences in its (...) methodology. I end by looking at disagreements about the liar paradox as an example. (shrink)

The notion of strength has featured prominently in recent debates about abductivism in the epistemology of logic. Following Williamson and Russell, we distinguish between logical and scientific strength and discuss the limits of the characterizations they employ. We then suggest understanding logical strength in terms of interpretability strength and scientific strength as a special case of logical strength. We present applications of the resulting notions to comparisons between logics in the traditional sense and mathematical theories.

When are logical theories equivalent? I discuss the notion of ground-equivalence between logical theories, which can be useful for various theoretical reasons, e.g., we expect ground-equivalent theories to have the same ontological bearing. I consider whether intertranslatability is an adequate criterion for ground-equivalence. Jason Turner recently offered an argument that first-order logic and predicate functor logic are ground-equivalent in virtue of their intertranslatability. I examine his argument and show that this can be generalized to other intertranslatable logical theories, which supports (...) the following: intertranslatability implies ground-equivalence. I also argue, however, that this ground-equivalence argument can be challenged as it faces a dilemma. The dilemma arises because the argument allows two distinct readings, the ‘internal’ and the ‘external’ reading. I argue that the argument turns out to be unsuccessful in both readings. The upshot of this dilemma in both philosophy of logic and metaphysics is considered. (shrink)

The article recapitulates what logic is about traditionally and works out two roles it has been playing in philosophy: the role of an instrument and of a philosophical discipline in its own right. Using Tarski’s philosophical-logical work as case study, it develops a logical reconstructionist methodology of philosophical logic that extends and refines Rudolf Carnap’s account of explication and rational reconstruction. The methodology overlaps with, but also partially diverges from, contemporary anti-exceptionalism about logic.

In reasoning, we draw conclusions from multiple premises. But thinkers can be fragmented. And if there is no single fragment of the agent that thinks all of the premises, then the agent cannot draw any conclusions from them. It follows that reasoning from multiple premises depends on their being thought together. But what is it to think premises together? What is the condition that contrasts with fragmentation? This paper provides an answer to this question that is simple but compelling: to (...) think premises together is to attribute those very thoughts to one and the same self. The ability to reason depends on the ability to attribute the thoughts from which one reasons to oneself. Reasoning—at least the sort of reasoning that we do—requires de se thought. (shrink)

Burgess (1997), building on Quine (1953), convincingly argued that claims in quantified modal logic cannot be understood as synonymous with or logically equivalent to claims about the analyticity of certain sentences. According to modal normativism, metaphysically necessary claims instead express or convey our actual semantic rules. In this paper, I show how the normativist can use Sidelle’s (1992a, 1995) neglected work on rigidity to account for two important phenomena in quantified modal logic: the necessity of identity and the substitutivity of (...) identicals into modal contexts. (shrink)

I provide a new way of thinking of questions using an expanded space of FDE worlds. This allows both for non-exclusive and non-exhaustive answers to questions concerning one’s gender identity. Further, and most crucially for the purposes of this paper, it allows for a new, more general definition of question-inclusion that makes it possible to identify a new form of hermeneutical injustice. This form of injustice, I argue, affects trans people by keeping them in a prolonged state of gender questioning (...) and confusion in which they only grasp the part of the question Am I a member of gender G? that corresponds to the question Do I want to be a member of gender G?. (shrink)

This is to appear in a Festschrift for Hilary Putnam on his 85th birthday. This is a pre-publication, not final, version.

There has been a long history of tension between feminists and feminist philosophy, on the one hand, and logic, on the other hand. This tension expresses itself in many ways, including claims that logic is a tool of the patriarchy, that logic/rationality/analytical tools in philosophy need to be rejected if women are to fully participate, that women = body and man = mind, that to do feminist philosophy one must do it as a situated, embodied person, not as an impersonal, (...) disembodied mind, that logic is “a masculine subject”. However the tension is expressed, it is women in logic and women logicians who are caught in between. The goal of my paper is to explore a conception of logic that not only is not inconsistent with being a feminist, but is actively welcoming of women as logicians. (shrink)

Some of the more prominent contributions to the last fifty years of scholarship on Aristotle’s syllogistic suggest a conceptual framework under which the syllogistic is a logic, a system of inferential reasoning, only if it is not a theory, a system concerned with ontology or general facts. I argue that this a misleading interpretative framework. I begin by noting that the syllogistic exhibits one mark of contemporary logics: syllogisms are inferences and not implications. The debate on this question has focused (...) on the interpretation of indirect proof. But I argue that this evidence is neutral on the question. Instead, I offer new considerations in favour of the interpretation of syllogisms as inferences. I next note that the syllogistic exhibits one mark of theories: it employs a distinct underlying logic so to derive derivative structures from primitive structures. So the syllogistic is something sui generis: by our lights, it is arguably neither clearly a logic, nor clearly a theory, but rather exhibits certain characteristic marks of logics and certain characteristic marks of theories. I conclude with a few remarks on the status of Aristotle as a founder of logic, and the use of modern systems to represent historical logics. (shrink)

When Aristotle introduces the perfect moods, he refers back to the dictum de omni et nullo, a semantic condition for universal affirmations and negations. There recently has been renewed interest in the question whether the dictum validates the assertoric syllogistic. I rehearse evidence that Aristotle provides a mereological semantics for universal affirmations and negations, and note that this semantics entails a nonstandard reading of the dictum, under which the dictum, in the presence of a minimal logical apparatus, indeed validates the (...) assertoric syllogistic. I argue that this mereological validation offers advantages over recent discussions in Morison, Malink, Ebert and Vlasits. (shrink)

Discussion of the Aristotelian syllogistic over the last sixty years has arguably centered on the question whether syllogisms are inferences or implications. But the significance of this debate at times has been taken to concern whether the syllogistic is a logic or a theory, and how it ought to be represented by modern systems. Largely missing from this discussion has been a study of the few passages in the Prior Analytics where Aristotle provides explicit guidance on how to individuate syllogisms. (...) I argue that syllogisms are individuated by unordered premise pairs and so may be fruitfully thought of as multiple-succedent sequents. I conclude by drawing a few consequences for the representation of the syllogistic. (shrink)

Āptamīmāṃsā – Deep Reflection On The Omniscient Lord – known also as Devāgama or Devāgamastotra, by Ācārya Samantabhadra (2nd century CE) is the cornerstone of Philosophy and Nyāya. It starts with a discussion, in a philosophical-cum-logical manner, on the concept of omniscience and the attributes of the Omniscient. Ācārya Samantabhadra questions the validity of the attributes that are traditionally associated with a praiseworthy deity and goes on to establish the logic of accepting the Omniscient as the most trustworthy and praiseworthy (...) Supreme Being. Employing the doctrine of conditional predication (syādvāda) – the logical expression of reality in light of the foundational principle of non-absolutism (anekāntavāda) – he faults certain conceptions based on absolutism: existence (bhāvaikānta) and non-existence (abhāvaikānta), non-dualism (advaita-ekānta) and separateness (pŗthaktva-ekānta), and permanence (nityatva-ekānta) and momentariness (kṣaṇika-ekānta). He elucidates the important concept of the ‘seven-nuance system’ (saptabhaṅgī). It embraces the seven limbs (saptabhaṅga) of assertion, the one-sided but relative method of comprehension called the standpoint (naya), and also the acceptance and rejection of the assertion. Ācārya Samantabhadra finally elucidates correct perspective on issues including fate (daiva) and human-deed (pauruṣa), and the bases of merit (puṇya) and demerit (pāpa). The book includes a comprehensive Index of Sanskrit terms. (shrink)

This book develops a new approach to plural arbitrary reference and examines mereology, including considering four theses on the alleged innocence of mereology. The authors have advanced the notion of plural arbitrary reference in terms of idealized plural acts of choice, performed by a suitable team of agents. In the first part of the book, readers will discover a revision of Boolosʼ interpretation of second order logic in terms of plural quantification and a sketched structuralist reconstruction of second-order arithmetic based (...) on the axiom of infinite, a la Dedekind, as the unique non-logical axiom. The work goes on to analyse the pros and cons of the new interpretation, also with respect to Linneboʼs objections to the thesis that second order logic is genuine logic. A theory of concepts that can be labelled as a theory of logical concepts is expounded. In the second part of the book, the authors consider grounding megethology on plural arbitrary reference and argue that the arguments for the ontological innocence of mereology are not conclusive and that – for a certain use of mereology – a thesis of innocence, similar to that of plural arbitrary reference, is defensible. The work proposes a virtual theory of mereology in which the role of individuals is played by plural choices of atoms. This considered work will appeal to scholars from branches of analytic philosophy, logic and the philosophy of mathematics in particular. (shrink)

Compare two conceptions of validity: under an example of a modal conception, an argument is valid just in case it is impossible for the premises to be true and the conclusion false; under an example of a topic-neutral conception, an argument is valid just in case there are no arguments of the same logical form with true premises and a false conclusion. This taxonomy of positions suggests a project in the philosophy of logic: the reductive analysis of the modal conception (...) of logical consequence to the topic-neutral conception. Such a project would dispel the alleged obscurity of the notion of necessity employed in the modal conception in favour of the clarity of an account of logical consequence given in terms of tractable notions of logical form, universal generalization and truth simpliciter. In a series of publications, John Etchemendy has characterized the model-theoretic definition of logical consequence as truth preservation in all models as intended to provide just such an analysis. In this paper, I will argue that Aristotle intends to provide an account of a modal conception of logical consequence in topic-neutral terms and so is engaged in a project comparable to the one described above. That Aristotle would be engaged in this sort of project is controversial. Under the standard reading of the Prior Analytics, Aristotle does not and cannot provide an account of logical consequence. Rather, he must take the validity of the first figure syllogisms (such as the syllogism known by its medieval mnemonic ‘Barbara’: A belongs to all B; B belongs to all C; so A belongs to all C) as obvious and not needing justification; he then establishes the validity of the other syllogisms by showing that they stand in a suitable relation to the first figure syllogisms. I will argue that Aristotle does attempt to provide an account of logical consequence—namely, by appeal to certain mereological theorems. For example, he defends the status of Barbara as a syllogism by appeal to the transitivity of mereological containment. There are, as I will discuss, reasons to doubt the success of this account. But the attempt is not implausible given certain theses Aristotle holds in semantics, mereology and the theory of relations. (shrink)

In constructional ontology, entities emerge by construction, that is, from the application of constructors to objects. We explore this approach to ontology, focusing on three modules: the constructors, the inputs to the constructors, and the constructional process. Our aim is to identify and assess some key theoretical choices arising in an ontology of this kind.

The aim here is to investigate assertion and inference as notions of logic. Assertion will be explained in terms of its purpose, which is to give interlocutors the right to request the assertor to do a certain task. The assertion is correct if, and only if, the assertor knows how to do this task. Inference will be explained as an assertion equipped with what I shall call a justification profile, a strategy for making good on the assertion. The inference is (...) valid if, and only if, correctness is preserved from the premiss assertions to the conclusion assertion. Most of this is a spelling out of views on assertion and inference presented by Per Martin-Löf in lectures since 2015. (shrink)

An inference is valid if it guarantees the transferability of knowledge from the premisses to the conclusion. If knowledge is here understood as demonstrative knowledge, and demonstration is explained as a chain of valid inferences, we are caught in an explanatory circle. In recent lectures, Per Martin-Löf has sought to avoid the circle by specifying the notion of knowledge appealed to in the explanation of the validity of inference as knowledge of a kind weaker than demonstrative knowledge. The resulting explanation (...) is the main topic of this article. (shrink)

According to the iterative conception of set, sets are formed in stages. According to the purely iterative conception of set, sets are formed by iterated application of a set-of operation. The cumulative hierarchy is a mathematical realization of the iterative conception of set. A mathematical realization of the purely iterative conception can be found in Peter Aczel’s type-theoretic model of constructive set theory. I will explain Aczel’s model construction in a way that presupposes no previous familiarity with the theories on (...) which it is based. (shrink)

Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...) connectives) and one for “universal” consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators. (shrink)

Many results in logic and mathematics rely on techniques that allow for concrete, often visual, representations of abstract concepts. A primary example of this phenomenon in logic is the distinction between syntax and semantics, itself an example of the more general duality in mathematics between algebra and geometry. Such representations, however, often rely on the existence of certain maximal objects having particular properties such as points, possible worlds or Tarskian first-order structures. -/- This dissertation explores an alternative to such representations (...) known as possibility semantics. Its core idea is to replace maximal objects with ordered systems of partial approximations. Although it originates in the semantics of modal logic and the representation of abstract ordered structures, I argue that it has far-reaching mathematical, foundational and philosophical significance, especially in the context of semiconstructive mathematics, a foundational framework that does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. -/- The dissertation is divided in two main parts. The first part explores various applications of the mathematical framework underlying possibility semantics to lattice theory and non-classical propositional logics. A major theme is the development of constructive dualities for various categories of lattices, which are related to standard non-constructive dualities via Vietoris constructions. -/- The second part of the dissertation explores the alternative foundational setting of semi-constructive mathematics, focusing on three applications of possibility semantics for classical first-order logic to the philosophy of the mathematical infinite. In particular, we introduce generic powers, a semi-constructive analogue of ultrapowers in classical model theory, and we explore the merits of these structures from a foundational, conceptual and historical viewpoint. (shrink)

Aristotle counts as the founder of formal logic. The logic he develops dominated until Frege and others introduced a new logic. This new logic is taken to be more powerful and better capable of capturing inference patterns. The new logic differs from Aristotelian logic in significant respects. It has been argued by Fred Sommers and Hanoch Ben-Yami that the new logic is not well equipped as a logic of natural language, and that a logic closer to Aristotle's is better suited (...) for this task. Each of them developed their own formalism - Sommers in form of term logic, Ben-Yami in form of his Quantified Argument Calculus (QUARC). I discuss Aristotle's logic - a term logic - and attempt a comparison between Aristotelian logic and (i) the new logic, (ii) Sommers' term logic, and (iii) Ben-Yami's QUARC. I consider differences between the systems, and show how they are related to and diverge from the new logic. (shrink)

The gender spectrum, a continuum ranging from “male” to “female,” is a huge improvement over the traditional binary model, according to which one can be either one or the other, and no degrees are allowed. However, the model still suffers from some inadequacies, most notably the inability to represent other genders and agender identities. This is accounted for in the new “spectral” models of gender, which use independent scales to measure the degree to which a person identifies with a given (...) gender category. However, by conceiving the amounts on gender dimensions to be mutually independent, these models invite other difficulties, most notably the inability to account for agender identities in a straightforward fashion. In this paper, I argue that a way to solve the problems with the new models (and not to have the old problems re-appear) is to take a step back, of sorts, towards the initial gender spectrum. I explore from a perspective of philosophical logic the types of relations among gender categories in the spectral models of gender and argue that the initial spectrum construes gender categories to be in the logical opposition of “fuzzy contradiction,” while the models with more than one spectrum do not construe gender categories to be in any kind of logical opposition. I propose a weaker opposition (namely, “fuzzy contrariety”) between gender categories, as well as the “fuzzy gender hexagon”—an application of a particular abstract logical diagram to gender terms—as a model of gender identity. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence according (...) to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space of (...) FDE worlds (Berto and Jago, 2019) with a Lewisian (1988) understanding of subject matters as partitions. By doing so, I show how subject matters impose some order in the anarchic space of FDE worlds, while the worlds allow for distinctions between contents which would not otherwise be available. Combining the two approaches, then, brings us closer to the desired closure principles for knowledge of minimally rational agents. (shrink)

Developments in truthmaker semantics for the most part stay clear of the metaphysical issue of what sort of entities serve as the truthmakers and falsitymakers for sentences. It is assumed that perhaps facts or states of affairs (Fine, 2017a; Jago, 2020), with these taken sometimes as concrete particulars (Hawke, 2018) could serve for the job, but nonetheless that some such entities would do. In this paper I take a closer look at the issue of what entities could or could not (...) play the role of truthmakers and falsitymakers in standard truthmaker semantics (Fine, 2016, 2017a,b; Fine and Jago, 2019), based on desiderata imposed by metaphysical and semantic considerations. (shrink)

It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the same conclusion would have to be identified. In this paper it will be shown that the question, which reductions we accept in our system, is not only important if we see them as generating a theory of proof identity but is also (...) decisive for the more general question whether a proof has meaningful content. There are certain reductions which would not only force us to identify proofs of different arbitrary formulas but which would render derivations in a system allowing them meaningless. To exclude such cases, a minimal criterion is proposed which reductions have to fulfill to be acceptable. (shrink)

Formalizations in first-order logic are standardly used to represent logical forms of sentences and to show the validity of ordinary-language arguments. Since every sentence admits of a variety of formalizations, a challenge arises: why should one valid formalization suffice to show validity even if there are other, invalid, formalizations? This paper suggests an explanation with reference to criteria of adequacy which ensure that formalizations are related in a hierarchy of more or less specific formalizations. This proposal is then compared with (...) stronger criteria and assumptions, especially the idea that sentences essentially have just one logical form. (shrink)

Prior’s puzzle is standardly taken to be the puzzle of why, given the assumption that that-clauses denote propositions, substitution of “the proposition that P” for “that P” within the complements of many propositional attitude verbs is invalid. I show that Prior’s puzzle is much more general than is ordinarily supposed. There are two variants on the substitutional form of the puzzle—a quantificational variant and a pronominal variant—and all three forms of the puzzle arise in a wide range of grammatical positions, (...) rather than merely in the complements of propositional attitude verbs. The generalized puzzle shows that a range of proposed solutions to the original puzzle fail, or are radically incomplete, and also reveals the connections between Prior’s puzzle and debates over the nature of semantic types and higher-order quantification. I go on to develop a novel, higher-order solution to the generalized form of the puzzle, and I argue that this higher-approach is superior to its first-order alternatives. (shrink)

”It is often assumed that knowledge claims must be justified. But what kind of justification is required for knowledge ? . . . ” (*) -/- presupposition: the kind of epistemic justification depends on the type of the knowledge claim and its respective knowledge claim tradeoff ’vague vs. precise’. -/- procedere: in two - almost purely logical - case studies I account for this tradeoff and question in each case what (if any) were its general outcome wrt justification -/- first (...) for basic measurement statements of the form ′′ϕ(x) = r ∈ IR ± δ′′ (wrt ”measurement accuracy realism” debate) -/- and secondly predication statements of the form ′′x is ( a case of )P′′ (wrt ”epistemic vagueness” debate). (shrink)

This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As it will be argued, once some basic features of our naıve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of validity (...) outlined here, which displays one coherent way to articulate the Stoic intuition, accords with standard formal treatments of deductive validity and encompasses an independently grounded characterization of inductive validity. (shrink)

According to an influential view, when it comes to representing reality, some words are better suited for the job than others. This is elitism. There is reason to believe that the set of the best, or elite, words should not be redundant or arbitrary. However, we are often forced to choose between these two theoretical vices, especially in cases involving theories that seem to be mere notational variants. This is the riddle of redundancy: both redundancy and arbitrariness are vicious, but (...) there are cases in which one must be picked. Logical realists admit that there are some logical constants among the elite words. This leads to awkward questions, such as which among conjunction and disjunction is elite. In this paper, I show how the riddle of redundancy arises for logical realists, and offer a solution. This approach requires us to change how we represent negation. Instead of using some particular symbol, we represent negation by flipping formulae over the horizontal axis. (shrink)

The minimal God exemplifies essential omnipotence, omniscience, and moral perfection, but none of the other properties of the traditional God. I examine the consequences of the minimal God in augmented S5, S4, and Kρσ. The metaphysical consequences for the minimal God in S5 include the impossibility that God—or any other object—might acquire, lose, or exchange an essential property. It is impossible that an essentially divine being might become essentially human, for instance. The epistemological consequences include the impossibility of agnosticism—it is (...) impossible that P(◻︎FG |E) = P(~◻︎FG| E). Indeed, every weaker forms of agnosticism are also impossible—it is impossible that P(◻︎FG |E) = n, n(0 < n < 1). The metaphysical and epistemological consequences for the minimal God in S4 are equally untenable. I show that we can avoid all of these unwelcome epistemological consequences for the minimal God in Kρσ. But Kρσ has some extraordinary metaphysical consequences for the minimal God. All of the problems for the minimal God generalize to the maximal God. (shrink)