We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present a Fitch-style natural deduction system for the logic that contains only the introduction and elimination rules for the logical constants. From this starting point, if one adds the rule that Fitch called Reiteration, one obtains a proof system for intuitionistic logic in the given signature; (...) if instead of adding Reiteration, one adds the rule of Reductio ad Absurdum, one obtains a proof system for orthologic; by adding both Reiteration and Reductio, one obtains a proof system for classical logic. Arguably neither Reiteration nor Reductio is as intimately related to the meaning of the connectives as the introduction and elimination rules are, so the base logic we identify serves as a more fundamental starting point and common ground between proponents of intuitionistic logic, orthologic, and classical logic. The algebraic semantics for the logic we motivate proof-theoretically is based on bounded lattices equipped with what has been called a weak pseudocomplementation. We show that such lattice expansions are representable using a set together with a reflexive binary relation satisfying a simple first-order condition, which yields an elegant relational semantics for the logic. This builds on our previous study of representations of lattices with negations, which we extend and specialize for several types of negation in addition to weak pseudocomplementation; in an appendix, we further extend this representation to lattices with implications. Finally, we discuss adding to our logic a conditional obeying only introduction and elimination rules, interpreted as a modality using a family of accessibility relations. (shrink)

This work is part of a wider investigation into lattice-structured algebras and associated dual representations obtained via the methodology of canonical extensions. To this end, here we study lattices, not necessarily distributive, with negation operations. We consider equational classes of lattices equipped with a negation operation ¬ which is dually self-adjoint (the pair (¬,¬) is a Galois connection) and other axioms are added so as to give classes of lattices in which the negation is De Morgan, orthonegation, antilogism, pseudocomplementation (...) or weak pseudocomplementation. These classes are shown to be canonical and dual relational structures are given in a generalized Kripke-style. The fact that the negation is dually self-adjoint plays an important role here, as it implies that it sends arbitrary joins to meets and that will allow us to define the dual structures in a uniform way. (shrink)

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal logics via algebraic representation theorems. We begin with complete lattices L equipped with an antitone operation ¬ sending 1 to 0, a completely multiplicative operation ◻, and a completely additive operation ◊. Such lattice expansions can be represented by means of a set X together with binary relations (...) ⊲, R, and Q, satisfying some first-order conditions, used to represent (L,¬), ◻, and ◊, respectively. Indeed, any lattice L equipped with such a ¬, a multiplicative ◻, and an additive ◊ embeds into the lattice of propositions of a frame (X,⊲,R,Q). Building on our recent study of "fundamental logic", we focus on the case where ¬ is dually self-adjoint (a≤¬b implies b≤¬a) and ◊¬a≤¬◻a. In this case, the representations can be constrained so that R=Q, i.e., we need only add a single relation to (X,⊲) to represent both ◻ and ◊. Using these results, we prove that a system of fundamental modal logic is sound and complete with respect to an elementary class of bi-relational structures (X,⊲,R). (shrink)

A pO -algebra $${(L; f, \, ^{\star})}$$ is an algebra in which ( L ; f ) is an Ockham algebra, $${(L; \, ^{\star})}$$ is a p -algebra, and the unary operations f and $${^{\star}}$$ commute. Here we consider the endomorphism monoid of such an algebra. If $${(L; f, \, ^{\star})}$$ is a subdirectly irreducible pK 1,1 - algebra then every endomorphism $${\vartheta}$$ is a monomorphism or $${\vartheta^3 = \vartheta}$$ . When L is finite the endomorphism monoid of L is (...) regular, and we determine precisely when it is a Clifford monoid. (shrink)

In this paper, we introduce a variety bdO of Ockham algebras with balanced double pseudocomplementation, consisting of those algebras of type where is an Ockham algebra, is a double p -algebra, and the operations and are linked by the identities [ f ( x )]* = [ f ( x )] + = f 2 ( x ), f ( x *) = x ** and f ( x + ) = x ++ . We give a description of (...) the congruences on the algebras, and show that there are precisely nine non-isomorphic subdirectly irreducible members in the class of the algebras via the Priestley duality. We also describe all axioms in the variety bdO , and provide a characterization of all subvarieties of bdO determined by 12 none-equivalent axioms, identifying therein the biggest subvariety in which every principal congruence is complemented. (shrink)

It is common in recent epistemology to distinguish different senses, or conceptions, of epistemic justification. The proposed oppositions include the objective/subjective, internalist/externalist, regulative/nonregulative, resource-relative/resource-independent, personal/verific, and deontological/evaluative conceptions of justification. In some of these cases, writers regard both members of the contrasting pair as legitimate; in other cases only one member. In this paper I want to propose another contrasting pair of conceptions of justification, and hold that both are defensible and legitimate. The contrast will then be used to construct (...) a modified version of reliabilism, one which handles certain problem cases more naturally than my previous versions of reliabilism. (shrink)

In trying to explain the possibility of akrasia , it seems plausible to deny that there is a conceptual connection between motivation and evaluation ; akrasia occurs when the agent is motivated to do something that she does not judge to be good . However, it is hard to see how such accounts could respect our intuition that the akratic agent acts freely, or that there is a difference between akrasia and compulsion. It is also hard to see how such (...) accounts could be extended to the realm of theoretical reason, but this is generally not taken Ito be a problem, because it is generally assumed that there is no similar phenomenon in the realm of theoretical reason. This paper argues that there is such a thing as theoretical akrasia, and that we can find a characterization of this phenomenon in Descartes’s Meditations. Drawing on certain passages in the Meditations, we can construct an account of theoretical akrasia; this account can then be adapted to resolve the original problem of akrasia in the realm of practical reason. The account asserts that there is a conceptual connection between motivation and evaluation in free action; it also enables us to show how the akratic agent is still acting freely when he does something that he does not judge to be the best all things considered. (shrink)

According to the knowledge norm of belief, one should believe p only if one knows p. However, it can easily seem that the ordinary notion of belief is much weaker than the knowledge norm would have it. It is possible to rationally believe things one knows to be unknown The aim of belief, Oxford University Press, Oxford, 2013). One response to this observation is to develop a technical notion of ‘outright’ belief. A challenge for this line of response is to (...) find a way of getting a grip on the targeted notion of belief. In order to meet this challenge, I characterize ‘outright’ belief in this paper as the strongest belief state implied by knowledge. I show that outright belief so construed allows this notion to play important theoretical roles in connection with knowledge, assertion and action. (shrink)

In light of many recent critiques of Western modernity and its conceptual foundations, the problem of adequately justifying our most basic moral and political values looms large. Without recourse to traditional ontological or metaphysical foundations, how can one affirm — or sustain — a commitment to fundamentals? The answer, according to Stephen White, lies in a turn to “weak” ontology, an approach that allows for ultimate commitments but at the same time acknowledges their historical, contestable character. This turn, White (...) suggests, is already underway. His book traces its emergence in a variety of quarters in political thought today and offers a clear and compelling account of what this might mean for our late modern self-understanding. (shrink)

This paper offers a new and very simple alternative to Bochvar's well known nonsense -- or meaninglessness -- interpretation of Weak Kleene logic. To help orient discussion I begin by reviewing the familiar Strong Kleene logic and its standard interpretation; I then review Weak Kleene logic and the standard interpretation. While I note a common worry about the Bochvar interpretation my aim is only to give an alternative -- and I think very elegant -- interpretation, not necessarily a (...) replacement. (shrink)

In this paper we focus on some new normativist positions and compare them with traditional ones. In so doing, we claim that if normative judgments are involved in determining whether a condition is a disease only in the sense identified by new normativisms, then disease is normative only in a weak sense, which must be distinguished from the strong sense advocated by traditional normativisms. Specifically, we argue that weak and strong normativity are different to the point that one (...) ‘normativist’ label ceases to be appropriate for the whole range of positions. If values and norms are not explicit components of the concept of disease, but only intervene in other explanatory roles, then the concept of disease is no more value-laden than many other scientific concepts, or even any other scientific concept. We call the newly identified position “value-conscious naturalism” about disease, and point to some of its theoretical and practical advantages. (shrink)

The thesis of existentialism holds that if a proposition p exists and predicates something of an object a, then in any world where a does not exist, p does not exist either. If “possibly, p” entails “in some possible world, the proposition that p exists and is true,” then existentialism is prima facie incompatible with the truth of claims like “possibly, the Eiffel Tower does not exist.” In order to avoid this claim, a distinction between two kinds of world-indexed truth (...) –and two associated kinds of modality –is needed. This paper embodies an attempt to develop a full account of just such a distinction. (shrink)

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the (...) class='Hi'>weak relevant logics and , respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance. (shrink)

This paper extends Fitting's epistemic interpretation of some Kleene logics, to also account for Paraconsistent Weak Kleene logic. To achieve this goal, a dualization of Fitting's "cut-down" operator is discussed, rendering a "track-down" operator later used to represent the idea that no consistent opinion can arise from a set including an inconsistent opinion. It is shown that, if some reasonable assumptions are made, the truth-functions of Paraconsistent Weak Kleene coincide with certain operations defined in this track-down fashion. Finally, (...) further reflections on conjunction and disjunction in the weak Kleene logics accompany this paper, particularly concerning their relation with containment logics. These considerations motivate a special approach to defining sound and complete Gentzen-style sequent calculi for some of their four-valued generalizations. (shrink)

In this paper, I argue that arguments from expert opinion, i.e., inferences from “Expert E says that p” to “p,” where the truth value of p is unknown, are weak arguments. A weak argument is an argument in which the premises, even if true, provide weak support—or no support at all—for the conclusion. Such arguments from expert opinion are weak arguments unless the fact that an expert says that p makes p significantly more likely to be (...) true. However, research on expertise shows that expert opinions are only slightly more accurate than chance and much less accurate than decision procedures. If this is correct, then it follows that arguments from expert opinion are weak arguments. (shrink)

Mainstream epistemologists have recently made a few isolated attempts to demonstrate the particular ways, in which specific types of knowledge are partly social. Two promising cases in point are Lackey’s dualism in the epistemology of testimony and Goldberg’s process reliabilist treatment of testimonial and coverage-support justification. What seems to be missing from the literature, however, is a general approach to knowledge that could reveal the partly social nature of the latter anytime this may be the case. Indicatively, even though Lackey (...) :345–361, 2007) has recently launched an attack against the Credit Account of Knowledge on the basis of testimony, she has not classified her view of testimonial knowledge into any of the alternative, general approaches to knowledge. Similarly, even if Goldberg’s attempt to provide a process reliabilist explanation of the social nature of testimonial knowledge is deemed satisfactory, his attempt to do the same in the case of coverage-support justification does not deliver the requisite result. This paper demonstrates that CAK can in fact provide, pace Lackey’s renunciation of the view, a promising account of the social nature of both testimonial and coverage-supported knowledge. Additionally, however, it can display further explanatory power by also revealing the social nature of knowledge produced on the basis of epistemic artifacts. Despite their disparities, all these types of knowledge count as partly social in nature, because in all these cases, according to CAK, the epistemic credit for the individual agent’s true belief must spread between the individual agent and certain parts of her epistemic community. Accordingly, CAK is a promising candidate for providing a unified approach to several and, perhaps all possible, instances of what we may call ‘weak epistemic anti-individualism’ within mainstream epistemology: i.e., the claim that the nature of knowledge can occasionally be both social and individual at the same time. (shrink)

Cognitivists about intention hold that intending to do something entails believing you will do it. Non-cognitivists hold that intentions are conative states with no cognitive component. I argue that both of these claims are true. Intending entails the presence of a belief, even though the intention is not even partly the belief. The result is a form of what Sarah Paul calls Non-Inferential Weak Cognitivism, a view that, as she notes, has no prominent defenders.

Working within weak subsystems of second-order arithmetic Z2 we consider two versions of the Baire Category theorem which are not equivalent over the base system RCA0. We show that one version (B.C.T.I) is provable in RCA0 while the second version (B.C.T.II) requires a stronger system. We introduce two new subsystems of Z2, which we call RCA+ 0 and WKL+ 0, and show that RCA+ 0 suffices to prove B.C.T.II. Some model theory of WKL+ 0 and its importance in view (...) of Hilbert's program is discussed, as well as applications of our results to functional analysis. (shrink)

In the following paper we propose a model-theoretical way of comparing the “strength” of various truth theories which are conservative over $$PA$$. Let $${\mathfrak {Th}}$$ denote the class of models of $$PA$$ which admit an expansion to a model of theory $${ Th}$$. We show (combining some well known results and original ideas) that $$\begin{aligned} {{\mathfrak {PA}}}\supset {\mathfrak {TB}}\supset {{\mathfrak {RS}}}\supset {\mathfrak {UTB}}\supseteq \mathfrak {CT^-}, \end{aligned}$$ where $${\mathfrak {PA}}$$ denotes simply the class of all models of (...) $$PA$$ and $${\mathfrak {RS}}$$ denotes the class of recursively saturated models of $$PA$$. Our main original result is that every model of $$PA$$ which admits an expansion to a model of $$CT ^-$$, admits also an expansion to a model of $$UTB$$. Moreover, as a corollary to one of the results (brought to us by Carlo Nicolai) we conclude that $$UTB$$ is not relatively interpretable in $$TB$$, thus answering the question from Fujimoto (Bull Symb Log 16:305–344, 2010). (shrink)

Some proponents of the Integrated Information Theory of consciousness profess strong views on the Neural Correlates of Consciousness, namely that large swathes of the neocortex, the cerebellum, at least some sensory cortices, and the so-called limbic system are all not essential for any form of conscious experiences. We argue that this connection is not incidental. Conflation between strong and weak versions of the theory has led these researchers to adopt definitions of NCC that are inconsistent with their own previous (...) definitions, inadvertently betraying the promises of an otherwise fruitful empirical endeavour. (shrink)

This paper introduces an interesting class of predicates that come in pairs, so-called total and partial predicates. It will be shown that such predicates contribute to an explanation for the weak and strong interpretations of donkey sentences. This paper proposes that the phenomenon of weak and strong interpretations is real, and that whether a sentence receives the weak or the strong interpretation depends on the predicate in the nuclear scope of the sentence. It also proposes that sum (...) individuals are calculated at some level before the nuclear scope of the sentence is processed. Once the sum individuals are calculated, it will be decided whether the nuclear scope is true of at least one element of the sum individual (weak interpretation) or true of all elements of the sum individual (strong interpretation). (shrink)

Following a previous elaboration of the concept of weak individuality and some examples of its instances in ecology and biology, the article focuses on general features of the concept, arguing that in any ontological field individuals are understood on the basis of our knowledge of interactions, through the application of these general formulas for extracting individuals from interactions. Then, the specificities of the individuality in the sense of this weak concept are examined in ecology; I conclude by addressing (...) the differences between ecosystems and organisms as they appear in the viewpoint of such concept. (shrink)

Hare proposes a view he calls prospectism for making choices in situations in which preferences have a common, but problematic structure. I show that prospectism permits the decision-maker to make a series of choices she knows in advance will lead to a sure loss. I also argue that a theory that permits the decision-maker to make choices she knows in advance will lead to a sure loss should be rejected.

In this paper, I reply to Seidel’s objections against my argument from expert performance to the effect that arguments from expert opinion are weak arguments. I clarify what Seidel takes to be unclear points in my argument and show that it withstands Seidel’s objections.

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice. It turns out that parallelization is a closure operator for this semi-lattice and that the parallelized Weihrauch degrees even form a lattice into which the Medvedev lattice and the Turing degrees can be embedded. The (...) importance of Weihrauch degrees is based on the fact that multi-valued functions on represented spaces can be considered as realizers of mathematical theorems in a very natural way and studying the Weihrauch reductions between theorems in this sense means to ask which theorems can be transformed continuously or computably into each other. As crucial corner points of this classification scheme the limited principle of omniscience LPO, the lesser limited principle of omniscience LLPO and their parallelizations are studied. It is proved that parallelized LLPO is equivalent to Weak Kőnig's Lemma and hence to the Hahn—Banach Theorem in this new and very strong sense. We call a multi-valued function weakly computable if it is reducible to the Weihrauch degree of parallelized LLPO and we present a new proof, based on a computational version of Kleene's ternary logic, that the class of weakly computable operations is closed under composition. Moreover, weakly computable operations on computable metric spaces are characterized as operations that admit upper semi-computable compact-valued selectors and it is proved that any single-valued weakly computable operation is already computable in the ordinary sense. (shrink)

In the literature, regress arguments often take one of two different forms: either they conclude that a given solution fails to solve any problem of a certain kind (the strong conclusion), or they conclude that a given solution fails to solve all problems of a certain kind (the weaker conclusion). This gives rise to a logical problem: do regresses entail the strong or the weaker conclusion, or none? In this paper I demonstrate that regress arguments can in fact take both (...) forms, and clearly set out the logical difference between them. Throughout the paper, I confine myself to metaphysical examples from the early Russell. Only now that we know they are valid can we start to discuss whether they are sound. (shrink)

Einar Bohn has argued that principles of composition must be contingent if gunky objects and junky worlds are both metaphysically possible. This paper critically examines such a case for contingentism about composition. I argue that weak mereological universalism, the principle that any two objects compose something, is consistent with the metaphysical possibility of both gunky objects and junky worlds. I further argue that, contra A. J. Cotnoir, the weak mereological universalist can accept a plausible mereological remainder axiom. The (...) proponent of contingent composition will have to look elsewhere for an argument in favor of his position. (shrink)

This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This (...) paper provides much background, but is not self-contained. Some results from [9] are called on, and are not reproved here. [9] Melvin C. Fitting. “A Family of Strict/Tolerant Logics”. In: Journal of Philosophical Logic. Online. Print publication forthcoming. (shrink)

This article concentrates on the Jacobs and Daly criticisms (Environmental Values, Spring 1994) of my earlier article in the same journal (Autumn 1994) criticising the concept of 'sustainable development'. Daly and Jacobs agreed with my criticisms of 'weak' sustainability, but defended 'strong' sustainability on the grounds that natural and manmade capital were 'complements' in the productive process and that economists are wrong, therefore, in assuming that they are infinitely substitutable. This article maintains that they are confusing different concepts of (...) 'complementarity' and 'substitutability'. It is also argued that, in fact, they do both sell crucial passes in their defence of strong sustainability without providing any clear criteria for their abandonment of it in certain cases. It is also denied that the fact that environmental services may provide different satisfactions from those obtained from other goods and services elevates it to the status of some over-riding moral value, or that discounting future costs and benefits is 'unfair' to future generations. (shrink)

We show that Weak Vopěnka’s Principle, which is the statement that the opposite category of ordinals cannot be fully embedded into the category of graphs, is equivalent to the large cardinal principle Ord is Woodin, which says that for every class [Formula: see text] there is a [Formula: see text]-strong cardinal. Weak Vopěnka’s Principle was already known to imply the existence of a proper class of measurable cardinals. We improve this lower bound to the optimal one by defining (...) structures whose nontrivial homomorphisms can be used as extenders, thereby producing elementary embeddings witnessing [Formula: see text]-strongness of some cardinal. (shrink)

The development of some COVID-19 vaccines by private companies like Moderna and Sanofi-GSK has been substantially funded by various governments. While the Sanofi CEO has previously suggested that countries that fund this development ought to be given some priority, this suggestion has not been taken seriously in the literature. Considerations of nationalism, sustainability, need, and equitability have been more extensively discussed with respect to whether and how much a country is entitled to advance purchase orders of the vaccine under conditions (...) of absolute scarcity. Yet, little attention has been paid to whether prior investment into developing a vaccine entitles a country to some priority with respect to these orders. Moreover, while not a majority view, some survey results show that a significant minority of the populace does endorse some view like this. This article argues that the minority have a point: recognizing funder countries some priority is justified by the weak Lockean claim (WLC). According to the WLC, the fact that someone has contributed to the development of something gives them some entitlement to the resultant product. This article will defend the WLC, and address objections to the argument, including those pertaining to questions of historical injustice and medical need. This argument does not imply an unconstrained entitlement. Rather, contribution to development is one morally relevant factor that must be tempered by and weighed against potentially more substantial claims to priority based on need, equity, and other considerations. (shrink)

Reverse inference is a crucial inferential strategy used in cognitive neuroscience to derive conclusions about the engagement of cognitive processes from patterns of brain activation. While widely employed in experimental studies, it is now viewed with increasing scepticism within the neuroscience community. One problem with reverse inference is that it is logically invalid, being an instance of abduction in Peirce’s sense. In this paper, we offer the first systematic analysis of reverse inference as a form of abductive reasoning and highlight (...) some relevant implications for the current debate. We start by formalising an important distinction that has been entirely neglected in the literature, namely the distinction between weak and strong reverse inference. Then, we rely on case studies from recent neuroscientific research to systematically discuss the role and limits of both strong and weak reverse inference; in particular, we offer the first exploration of weak reverse inference as a discovery strategy within cognitive neuroscience. (shrink)

Uniformism about the epistemology of modality is the view that there is only one basic route to modal knowledge; non-uniformism is the view that there are several. Non-uniformism is becoming an increasingly popular stance, but how can it be defended? I prise apart two ways of understanding the uniformism/non-uniformism conflict that are mixed up in the literature. I argue that once separated, it is evident that they lead up to two different non-uniformist theses that need to be argued for in (...) very different ways. In particular, one construal allows only for a weak thesis about the actual lay of the current theoretical land in modal epistemology, while the other allows for a strong thesis that can be defended without reliance on claims about the alleged goodness or badness of individual accounts of modal justification. I argue that philosophers inclined towards non-uniformism ought to go for the strong, rather than the weak, thesis. (shrink)

In this paper it is shown how plausible reasoning of the kind illustrated in the ancient Greek example of the weak and strong man can be analyzed and evaluated using a procedure in which the pro evidence is weighed against the con evidence using formal, computational argumentation tools. It is shown by means of this famous example how plausible reasoning is based on an audience’s recognition of situations of a type they are familiar with as normal and comprehensible in (...) their shared common knowledge. The paper extends previous work on this example by using three new multiagent argumentation schemes closely related to the scheme for argument from negative consequences. (shrink)