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 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)

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)

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)

Weak emergence has been offered as an explication of the ubiquitous notion of emergence used in complexity science (Bedau 1997). After outlining the problem of emergence and comparing weak emergence with the two other main objectivist approaches to emergence, this paper explains a version of weak emergence and illustrates it with cellular automata. Then it explains the sort of downward causation and explanatory autonomy involved in weak emergence.

Discussions of risk have assumed that risk must be modeled the same in all cases. This is a mistake. Normally, if people know that those affected by an agent’s choice have conflicting interests, th...

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 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)

In this paper we propose an extension of Defeasible Logic to represent and compute different concepts of defeasible permission. In particular, we discuss some types of explicit permissive norms that work as exceptions to opposite obligations or encode permissive rights. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with a (...) new operator representing ordered sequences of strong permissions. The logical system is studied from a computational standpoint and is shown to have linear computational complexity. (shrink)

In contrast to the robust mutual interpretability phenomenon in set theory, Ali Enayat proved that bi-interpretation is absent: distinct theories extending ZF are never bi-interpretable and models of ZF are bi-interpretable only when they are isomorphic. Nevertheless, for natural weaker set theories, we prove, including Zermelo–Fraenkel set theory $\mathrm {ZFC}^{-}$ without power set and Zermelo set theory Z, there are nontrivial instances of bi-interpretation. Specifically, there are well-founded models of $\mathrm {ZFC}^{-}$ that are bi-interpretable, but not isomorphic—even $\langle H_{\omega _1},\in (...) \rangle $ and $ \langle H_{\omega _2},\in \rangle $ can be bi-interpretable—and there are distinct bi-interpretable theories extending $\mathrm {ZFC}^{-}$. Similarly, using a construction of Mathias, we prove that every model of ZF is bi-interpretable with a model of Zermelo set theory in which the replacement axiom fails. (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 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)

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)

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)

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.

This paper presents a sound and complete five-sided sequent calculus for first-order weak Kleene valuations which permits not only elegant representations of four logics definable on first-order weak Kleene valuations, but also admissibility of five cut rules by proof analysis.

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)

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)

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)

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)

Sentences attributing beliefs, doubts, wants, and the like have posed a major problem for semantics. Recently the pragmatic description of language has become more systematic. I shall discuss the formalization of pragmatics, and propose an analysis of belief attribution that avoids some main problems apparently inherent in the semantic approach.

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)

In this paper we study local induction w.r.t. Σ1‐formulas over the weak arithmetic. The local induction scheme, which was introduced in, says roughly this: for any virtual class that is progressive, i.e., is closed under zero and successor, and for any non‐empty virtual class that is definable by a Σ1‐formula without parameters, the intersection of and is non‐empty. In other words, we have, for all Σ1‐sentences S, that S implies, whenever is progressive. Since, in the weak context, we (...) have (at least) two definitions of Σ1, we obtain two minimal theories of local induction w.r.t. Σ1‐formulas, which we call Peano Corto and Peano Basso.In the paper we give careful definitions of Peano Corto and Peano Basso. We establish their naturalness both by giving a model theoretic characterization and by providing an equivalent formulation in terms of a sentential reflection scheme.The theories Peano Corto and Peano Basso occupy a salient place among the sequential theories on the boundary between weak and strong theories. They bring together a powerful collection of principles that is locally interpretable in. Moreover, they have an important role as examples of various phenomena in the metamathematics of arithmetical (and, more generally, sequential) theories. We illustrate this by studying their behavior w.r.t. interpretability, model interpretability and local interpretability. In many ways the theories are more like Peano arithmetic or Zermelo Fraenkel set theory, than like finitely axiomatized theories as Elementary Arithmetic, and. On the one hand, Peano Corto and Peano Basso are very weak: they are locally cut‐interpretable in. On the other hand, they behave as if they were strong: they are not contained in any consistent finitely axiomatized arithmetical theory, however strong. Moreover, they extend, the theory of parameter‐free Π1‐induction. (shrink)

This article investigates Kripke-style semantics for two sorts of logics: pseudo-Boolean and weak-Boolean logics. As examples of the first, we introduce G3 and S53pB.G3 is the three-valued Dummett–Gödel logic; S53pB is the modal logic S5 but with its orthonegation replaced by a pB negation. Examples of wB logic are G3wB and S53wB.G3wB is G3 with a wB negation in place of its pB negation; S53wB is S5 with a wB negation replacing its orthonegation. For each system, we provide a (...) three-valued Kripke-style semantics with and without star operation . We prove soundness and completeness theorems in each case. Note that wB logics may be equivalent to logics with Baaz’s projection Δ. We finally introduce the G3 and the S53pB both with Δ and show that they are equivalent to G3wB and S53wB, respectively. (shrink)

Strong adaptationists explore complex organic design as taskspecific adaptations to ancestral environments. This strategy seems best when there is evidence of homology. Weak adaptationists don't assume that complex organic (including cognitive and linguistic) functioning necessarily or primarily represents taskspecific adaptation. This approach to cognition resembles physicists' attempts to deductively explain the most facts with fewest hypotheses. For certain domainspecific competencies (folkbiology) strong adaptationism is useful but not necessary to research. With grouplevel belief systems (religion) strong adaptationism degenerates into spurious (...) notions of social function and cultural selection. In other cases (language, especially universal grammar) weak adaptationism's 'minimalist' approach seems productive. (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 2020, Daniele Molinini published a paper outlining two types of mathematical objectivity. One could say that with this paper Molinini not only separated two mathematical concepts in terms of terminology and content, but also contrasted two mathematical-philosophical contexts, the traditional-idealistic and the modern-practical. Since the first context was the theoretical basis for a large number of analyses that we find in the framework of the philosophy of mathematics, the space was now offered to re-examine such analyses in the second (...) context. More specifically, with respect to the second context, we will analyse the strength of one of the few explicit Platonic arguments that seeks to justify the ontological status of mathematical objects and the central claim of mathematical Platonism about the existence of mathematical objects. (shrink)

The nature of health is one of the central topics in the philosophy of medicine. The concept of health is complex because it comprises multiple features and there is no consensus on which feature is most basic or even whether some particular feature has any importance at all. This paper focuses on how several basic elements play a role in the formation of the concept of health. My central claim is that the theory of emergence offers a way to construct (...) a theory of health that is sympathetic to both analytic and holistic perspectives. In one way, this emergent theory of health looks very much like a holistic theory in that it considers not only biological factors as fundamental to understanding health, but also psychological, and social factors. In another way, this theory looks very much like an analytic theory because it sees health as a phenomenon that emerges from more basic elements: biology, psychology, and sociology. This may seem ambiguous, but this kind of ambiguity might just be the biggest virtue of the theory. (shrink)