In a recent paper McCain (2012) argues that weak predictivism creates an important challenge for external world scepticism. McCain regards weak predictivism as uncontroversial and assumes the thesis within his argument. There is a sense in which the predictivist literature supports his conviction that weak predictivism is uncontroversial. This absence of controversy, however, is a product of significant plasticity within the thesis, which renders McCain’s argument worryingly vague. For McCain’s argument to work he either (...) needs a stronger version of weak predictivism than has been defended within the literature, or must commit to a more precise formulation of the thesis and argue that weak predictivism, so understood, creates the challenge to scepticism that he hopes to achieve. The difficulty with the former is that weak predictivism is not uncontroversial in the respect that McCain’s argument would require. I consider the prospects of saving McCain’s argument by committing to a particular version of weak predictivism, but find them unpromising for several reasons. (shrink)

According to Hitchcock and Sober’s argument from overfitting for weak predictivism, the fact that a theory accurately predicts a portion of its data is evidence that it has been formulated by balancing simplicity and goodness-of-fit rather than overfitting data. The core argument consists of two likelihood inequalities. In this paper I show that there is a surprising accommodation-friendly implication in their argument, and contend that it is beset by a substantial difficulty, namely, there is no good reason to (...) think that their second likelihood inequality is true. (shrink)

Predictivism, the thesis that all things being equal a hypothesis that predicts a piece of evidence is better supported by that evidence than a hypothesis that only accommodates that evidence, comes in strong and weak forms. Interestingly, weak predictivism, which is widely accepted, can be used to formulate a persuasive argument against some forms of external world scepticism. In this article I formulate this predictivist argument and I explain why it deserves serious consideration despite the fact (...) that it only succeeds as a response to some forms of external world scepticism. (shrink)

Many climate scientists have made claims that may suggest that evidence used in tuning or calibrating a climate model cannot be used to evaluate the model. By contrast, the philosophers Katie Steele and Charlotte Werndl have argued that, at least within the context of Bayesian confirmation theory, tuning is simply an instance of hypothesis testing. In this paper I argue for a weak predictivism and in support of a nuanced reading of climate scientists’ concerns about tuning: there are (...) cases, model-tuning among them, in which predictive successes are more highly confirmatory of a model than accommodation of evidence. (shrink)

Motivated by weaknesses with traditional accounts of logical epistemology, considerable attention has been paid recently to the view, known as anti-exceptionalism about logic, that the subject matter and epistemology of logic may not be so different from that of the recognised sciences. One of the most prevalent claims made by advocates of AEL is that theory choice within logic is significantly similar to that within the sciences. This connection with scientific methodology highlights a considerable challenge for the anti-exceptionalist, as two (...) uncontentious claims about scientific theories are that they attempt to explain a target phenomenon and prove their worth through successful predictions. Thus, if this methodological AEL is to be viable, the anti-exceptionalist will need a reasonable account of what phenomena logics are attempting to explain, how they can explain, and in what sense they can be said to issue predictions. This paper makes sense of the anti-exceptionalist proposal with a new account of logical theory choice, logical predictivism, according to which logics are engaged in both a process of prediction and explanation. (shrink)

Strong predictivism, the idea that novel predictions per se confirm theories more than accommodations, is based on a “no miracle” argument from novel predictions to the truth of theories (NMAT). Eric Barnes rejects both: he reconstructs the NMAT as seeking an explanation for the entailment relation between a theory and its novel consequences, and argues that it involves a fallacious application of Occam’s razor. However, he accepts a no miracle argument for the truth of background beliefs (NMABB): scientists endorsed (...) a successful theory because they were guided by largely true background beliefs. This in turn raises the probability that the theory is true; so Barnes embraces a form of weak predictivism, according to which predictions are only indirectly relevant to confirmation. To Barnes I reply that we should also explain how the successful theory was constructed, not just endorsed; background beliefs are not enough to explain success, scientific method must also be considered; Barnes can account for some measure of confirmation of our theories, but not for the practical certainty conferred to them by some astonishing predictions; true background beliefs and reliability by themselves cannot explain novel success, the truth of theories is also required. Hence, the NMAT is sound, and strong predictivism is right. In fact, Barnes misinterprets the NMAT, which does not involve Occam’s razor, takes as explanandum the building of a theory which turned out to predict surprising facts, and successfully concludes that the theory is true. This accounts for the practically certain confirmation of our most successful theories, in accordance with strong predictivism. (shrink)

Scientific theories are developed in response to a certain set of phenomena and subsequently evaluated, at least partially, in terms of the quality of fit between those same theories and appropriately distinctive phenomena. To differentiate between these two stages it is popular to describe the former as involving the accommodation of data and the latter as involving the prediction of data. Predictivism is the view that, ceteris paribus, correctly predicting data confers greater confirmation than successfully accommodating data. In this (...) paper, I take issue with a variety of predictivist theses, argue that their role for issues of confirmation is extremely limited, and attempt to account for the appeal that predictivism has enjoyed. Introduction Temporal Predictivism Heuristic Predictivism Weak Predictivism 4.1 Inference to better theories 4.2 Inference to better methods Arguments for Strong Heuristic Predictivism 5.1 Best explanations argument 5.2 Conditional support 5.3 Unique explanations Increased Explanatory Unification 6.1 Explaining what other theories can't 6.2 Contrived hypotheses 6.2 Strength and simplicity Conclusions CiteULike Connotea Del.icio.us What's this? (shrink)

The history of the diffusion and confirmation of Mendeleev’s periodic table of elements has proven to be a challenging testbed for contemporary philosophical debates on the role of predictions in science. More than ten years of fruitful literature came after Scerri and Worrall :407–452, 2001) versus Maher and Lipton ; nevertheless, such a long-lasting debate left quite a few open questions. The aim of this contribution is to go through the various cases that emerged during the debate, in an effort (...) to explain them coherently in a weak predictivist perspective. Maher’s early account—according to which the astounding success of the major predictions alone was enough to explain the confirmation of the periodic table—can now be replaced by a more balanced and thorough picture, where both predictions and accommodations do weight. (shrink)

El realismo científico enfrenta el problema de la subdeterminación de la teoría por los datos generada por la equivalencia empírica entre teorías rivales. Podría superarlo si fuera verdadero el predictivismo –el débil, ya que el fuerte tropieza con una dificultad que parece insuperable–. En tal caso, contribuiría además a refutar el escepticismo con respecto al mundo externo, pero no, como se ha sostenido, porque la experiencia dé más apoyo al realismo “ingenuo” del sentido común que a dicho escepticismo sino porque (...) el realismo científico implica el realismo metafísico. (shrink)

El realismo científico enfrenta el problema de la subdeterminación de la teoría por los datos generada por la equivalencia empírica entre teorías rivales. Podría superarlo si fuera verdadero el predictivismo –el débil, ya que el fuerte tropieza con una dificultad que parece insuperable–. En tal caso, contribuiría además a refutar el escepticismo con respecto al mundo externo, pero no, como se ha sostenido, porque la experiencia dé más apoyo al realismo “ingenuo” del sentido común que a dicho escepticismo sino porque (...) el realismo científico implica el realismo metafísico. (shrink)

There is considerable disagreement about the epistemic value of novel predictive success, i.e. when a scientist predicts an unexpected phenomenon, experiments are conducted, and the prediction proves to be accurate. We survey the field on this question, noting both fully articulated views such as weak and strong predictivism, and more nascent views, such as pluralist reasons for the instrumental value of prediction. By examining the various reasons offered for the value of prediction across a range of inferential contexts (...) , we can see that neither weak nor strong predictivism captures all of the reasons for valuing prediction available. A third path is presented, Pluralist Instrumental Predictivism; PIP for short. (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)

Predictivism holds that, where evidence E confirms theory T, E confirms T more strongly when E is predicted on the basis of T and subsequently confirmed than when E is known in advance of T's formulation and used, in some sense, in the formulation of T. Predictivism has lately enjoyed some strong supporting arguments from Maher (1988, 1990, 1993) and Kahn, Landsberg, and Stockman (1992). Despite the many virtues of the analyses these authors provide it is my view (...) that they (along with all other authors on this subject) have failed to understand a fundamental truth about predictivism: the existence of a scientist who predicted T prior to the establishment that E is true has epistemic import for T (once E is established) only in connection with information regarding the social milieu in which the T-predictor is located and information regarding how the T-predictor was located. The aim of this paper is to show that predictivism is ultimately a social phenomenon that requires a social level of analysis, a thesis I deem social predictivism. (shrink)

There has been a lively debate in the philosophy of science over _predictivism_: the thesis that successfully predicting a given body of data provides stronger evidence for a theory than merely accommodating the same body of data. I argue for a very strong version of the thesis using statistical results on the so-called “model selection” problem. This is the problem of finding the optimal model (family of hypotheses) given a body of data. The key idea that I will borrow from (...) the statistical literature is that the level of support a hypothesis, _H,_ receives from a body of data, _D,_ is inversely related to the number of adjustable parameters of the model from which _H_ was constructed. I will argue that when _D_ is not essential to the design of _H_ (i.e., when it is predicted), the model to which _H_ belongs has fewer adjustable parameters than when _D_ is essential to the design of _H_ (when it is accommodated)_._ This, I argue, provides us with an argument for a very strong version of predictivism. (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)

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.

Predictivism asserts that novel confirmations carry special probative weight. Epistemic pluralism asserts that the judgments of agents (about, e.g., the probabilities of theories) carry epistemic import. In this paper, I propose a new theory of predictivism that is tailored to pluralistic evaluators of theories. I replace the orthodox notion of use-novelty with a notion of endorsement-novelty, and argue that the intuition that predictivism is true has two roots. I provide a detailed Bayesian rendering of this theory and (...) argue that pluralistic theory evaluation pervades scientific practice. I compare my account of predictivism with those of Maher and Worrall. Introduction Why construction is a red herring for pluralist evaluators The unvirtuous accommodator Virtuous endorsers and the two roots of predictivism The two roots in Bayesian terms: the priors and background beliefs of endorsers Who are the pluralist evaluators? Two contemporary theories of predictivism 7.1 Maher: Reliable methods of theory construction 7.2 Worrall: The confirmation of core ideas Conclusion. (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)

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)

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)

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)

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)

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.

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...

We show that several logics of common belief and common knowledge are not only complete, but also strongly complete, hence compact. These logics involve a weakened monotonicity axiom, and no other restriction on individual belief. The semantics is of the ordinary fixed-point type.

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)

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)

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.

This is a comment on the paper by Barnes and the responses from Scerri and Worrall, debating the thesis that a fact successfully predicted by a theory is stronger evidence than a similar fact known before the prediction was made. Since Barnes and Scerri both use evidence presented in my paper on Mendeleev’s periodic law to support their views, I reiterate my own position on predictivism. I do not argue for or against predictivism in the normative sense that (...) philosophers of science employ, rather I describe how scientists themselves use facts and predictions to support their theories. I find wide variations, and no support for the assumption that scientists use a single ‘Scientific Method’ in deciding whether to accept a proposed new theory.Keywords: Predictivism; Novel predictions; Accommodation; Periodic law; Periodic table; Dmitri Mendeleev. (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)

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 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)

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)

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)

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; and (...) (iii) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules. (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)

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)

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)

Italian critical theorist Giorgio Agamben is well known for his rigorous attempts to redefine political, aesthetic, and theological concepts through messianic categories. For Agamben, the messianic is not concerned with perpetual waiting for a savior to come and redeem the world. Rather, it concerns the radically open potentiality for action within the contemporary moment. While the temporality of the messianic moment has been emphasized both by Agamben and by the vast secondary literature that has provided ample reflections on his body (...) of work, the important concept of messianic space has not been given equal treatment. Space and time must be thought together if we are to appreciate the unique qualities of .. (shrink)