I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what I will call the Cut-for-Formulas to Cut-for-Sets Theorem: for a set F and a binary relation |- on Power(F), if |- is finitary, monotonic, and satisfies cut for formulas, then it also satisfies cut for sets. I deduce the CF/CS Theorem from the Ultrafilter Theorem twice; each proof uses a different order-theoretic variant of the Tukey- Teichmüller Lemma. I then discuss relationships between various (...) cut-conditions in the absence of finitariness or of monotonicity. (shrink)

L’article interroge successivement l’éthique intellectuelle centrée sur les vertus et défendue par Roger Pouivet et celle centrée sur les normes rationnelles de la croyance défendue par Pascal Engel. En plus de thèmes propres à chaque éthique, on insistera sur la confrontation métaphysique au naturalisme ainsi que sur le possible caractère tragique de l’éthique intellectuelle. Ces exigences intellectuelles risquent de mener à des formes de mélancolie ou de misanthropie, sauf si l’éthique intellectuelle est solidement associée à une espérance religieuse ou rationnelle (...) qui n’est peut-être pas vraiment compatible avec ces mêmes exigences. (shrink)

This paper considers two reasons that might support Russell’s choice of a ramified-type theory over a simple-type theory. The first reason is the existence of purported paradoxes that can be formulated in any simple-type language, including an argument that Russell considered in 1903. These arguments depend on certain converse-compositional principles. When we take account of Russell’s doctrine that a propositional function is not a constituent of its values, these principles turn out to be too implausible to make these arguments troubling. (...) The second reason is conditional on a substitutional interpretation of quantification over types other than that of individuals. This reason stands up to investigation: a simple-type language will not sustain such an interpretation, but a ramified-type language will. And there is evidence that Russell was tacitly inclined towards such an interpretation. A strong construal of that interpretation opens a way to make sense of Russell’s simultaneous repudiation of propositions and his willingness to quantify over them. But that way runs into trouble with Russell’s commitment to the finitude of human understanding. (shrink)

In this article, I explain how and why different attempts to defend absolute divine simplicity fail. A proponent of absolute divine simplicity has to explain why different attributions do not suppose a metaphysical complexity in God but just one superproperty, why there is no difference between God and His super-property and finally how a absolute simple entity can be the truthmaker of different intrinsic predications. It does not necessarily lead to a rejection of divine simplicity but it shows that we (...) may consider another conception of divine simplicity compatible with some metaphysical complexity in God. (shrink)

Part 1 [Hodes, 2021] “looked under the hood” of the familiar versions of the classical propositional modal logic K and its intuitionistic counterpart. This paper continues that project, addressing some familiar classical strengthenings of K and GL), and their intuitionistic counterparts. Section 9 associates two intuitionistic one-step proof-theoretic systems to each of the just mentioned intuitionistic logics, this by adding for each a new rule to those which generated IK in Part 1. For the systems associated with the intuitionistic counterparts (...) of D and T, these rules are “pure one-step”: their schematic formulations does not use □ or ♢. For the systems associated with the intuitionistic counterparts of K4, etc., these rules meet these conditions: neither □ nor ♢ is iterated; none use both □ and ♢. The join of the two systems associated with each of these familiar logics is the full one-step system for that intuitionistic logic. And further “blended” intuitionistic systems arise from joining these systems in various ways. Adding the 0-version of Excluded Middle to their intuitionistic counterparts yields the one-step systems corresponding to the familiar classical logics. Each proof-theoretic system defines a consequence relation in the obvious way. Section 10 examines inclusions between these consequence relations. Section 11 associates each of the above consequence relations with an appropriate class of models, and proves them sound with respect to their appropriate class. This allows proofs of some failures of inclusion between consequence relations. Section 12 proves that the each consequence relation is complete or weakly complete, that relative to its appropriate class of models. The Appendix presents three further results about some of the intuitionistic consequence relations discussed in the body of the paper. For Keywords, see Part 1. (shrink)

L’épistémologie des croyances religieuses qui pose la question de la rationalité des croyances peut être mise en question en introduisant des éléments de sciences sociales des religions et vice-versa. Un modèle épistémologique souligne que les croyances peuvent être garanties sans examen réflexif de la part du croyant. Mais dans un contexte pluraliste où la croyance particulière est mise en débat, l’exigence critique d’examen est une condition nécessaire de rationalité. En cela, l’épistémologie retrouve certains aspects de la sociologie de la critique (...) dans sa compréhension des manières de croire. Cependant, l’épistémologie dépasse l’approche de la sociologie pragma- tique car elle ne renonce pas à l’évaluation de la rationalité des croyances religieuses en évaluant les arguments pro et contra. (shrink)

Logicism is, roughly speaking, the doctrine that mathematics is fancy logic. So getting clear about the nature of logic is a necessary step in an assessment of logicism. Logic is the study of logical concepts, how they are expressed in languages, their semantic values, and the relationships between these things and the rest of our concepts, linguistic expressions, and their semantic values. A logical concept is what can be expressed by a logical constant in a language. So the question “What (...) is logic?” drives us to the question “What is a logical constant?” Though what follows contains some argument, limitations of space constrain me in large part to express my Credo on this topic with the broad brush of bold assertion and some promissory gestures. (shrink)

Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example, the semantic role (...) of number-words is not designation but rather the encoding of cardinality-quantifiers. I also present some reasons for preferring this view. (shrink)

This paper and its sequel “look under the hood” of the usual sorts of proof-theoretic systems for certain well-known intuitionistic and classical propositional modal logics. Section 1 is preliminary. Of most importance: a marked formula will be the result of prefixing a formula in a propositional modal language with a step-marker, for this paper either 0 or 1. Think of 1 as indicating the taking of “one step away from 0.” Deductions will be constructed using marked formulas. Section 2 presents (...) the model-theoretic concepts, based on those in [7], that guide the rest of this paper. Section 3 presents Natural Deduction systems IK and CK, formalizations of intuitionistic and classical one-step versions of K. In these systems, occurrences of step-markers allow deductions to display deductive structure that is covered over in familiar “no step” proof-theoretic systems for such logics. Box and Diamond are governed by Introduction and Elimination rules; the familiar K rule and Necessitation are derived (i.e. admissible) rules. CK will be the result of adding the 0-version of the Rule of Excluded Middle to the rules which generate IK. Note: IK is the result of merely dropping that rule from those generating CK, without addition of further rules or axioms (as was needed in [7]). These proof-theoretic systems yield intuitionistic and classical consequence relations by the obvious definition. Section 4 provides some examples of what can be deduced in IK. Section 5 defines some proof-theoretic concepts that are used in Section 6 to prove the soundness of the consequence relation for IK (relative to the class of models defined in Section 2.) Section 7 proves its completeness (relative to that class). Section 8 extends these results to the consequence relation for CK. (Looking ahead: Part 2 will investigate one-step proof-theoretic systems formalizing intuitionistic and classical one-step versions of some familiar logics stronger than K.). (shrink)

In this paper I argue that Bonjour’s claim that empirical beliefs can only be justified by other empirical beliefs and his use of non-normative “spontaneous empirical beliefs” and the “The Doxastic Preumption” fail to solve the problems of coherence theory. I propose a justification of empirical (and other beliefs) based on the work of B. Lonergan.

L’objectif de cet article est de comprendre l’importance de la métaphysique analytique pour le travail philosophique et pour l’enseignement dans le contexte français. Pour cela, je commencerai par exposer ce qu’il faut entendre par métaphysique analytique, puis j’examinerai plusieurs conditions de possibilité de la métaphysique analytique en France : la relecture de l’histoire de la métaphysique, des découvertes en logique, une réflexion sur l’objectif et un examen rapide des conditions matérielles et sociales d’enseignement et de recherche.

David Chalmers argues that consciousness -- authentic, first-person, conscious consciousness -- cannot be reduced to brain events or to any physical event, and that efforts to find a workable mind-body identity theory are, therefore, doomed in principle. But for Chalmers and non-reductionist in general consciousness consists exclusively, or at least paradigmatically, of phenomenal or qualia-consciousness. This results in a seriously inadequate understanding both of consciousness and of the “hard problem.” I describe other, higher-order cognitional events which must be conscious if (...) the “hard problem” is to be solved -- in any sense of ‘solve’ which would make us any the wiser about it -- but whose consciousness is quite different from the qualia and phenomena usually inventoried. Events of this kind are both part of the hard problem and the means by which we will solve it, if we ever do. (shrink)

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic predicates.

Pour penser philosophiquement les attitudes religieuses, le concept de croyance est parfois considéré comme inadéquat. Un des reproches souvent développés est qu’une croyance propositionnelle, croire que p, est une attitude trop théorique qui ne peut rendre compte de la foi et de la vie religieuse en général. Il est possible de répondre à ces objections mais cet article évalue la pertinence d’un concept apparemment plus fructueux : l’acceptation. Ce concept permet de rendre compte de certaines attitudes et pratiques religieuses mais (...) aussi d’une partie de la méthode des sciences sociales et de la philosophie des religions. (shrink)

A model-theoretic approach to the semantics of set-theoretic discourse.

Dans cette contribution, j'examinerai l'argument qui renvoie dos à dos le théisme et l'athéisme et qui structure la présentation de l'alternative que constitue le Dieu à venir. N'étant ni adhérant, ni sympathisant du réalisme spéculatif, je ne proposerai pourtant pas de critique externe de la philosophie de la religion proposée par Meillassoux. De manière heuristique, je vais tenir pour acquis Après la finitude et je montrerai ce qui me semble être les faiblesses de l'argument, critiques rendant finalement peu crédible l'affirmation (...) que peut encore venir un Dieu qui ne serait ni le Dieu métaphysique, ni le Dieu du sentiment religieux. Pour cela, je vais reprendre le dilemme spectral (Meillassoux) et discuter la cohérence du concept de Dieu à venir ainsi que sa pertinence pour résoudre le dilemme. Il apparaitra alors que si l'on admet la contingence absolue, on ne peut croire raisonnablement en un Dieu, même à venir. D'où le désespoir absolu. (shrink)

Figure majeure de la philosophie morale, Derek Parfit (1942-2017) reste encore peuconnu en France. Cette introduction vise à montrer l'ampleur des thématiques abordées de Parfit en les rattachant au projet d'une éthique rationnelle, tandis que le numéro dansson ensemble, sans prétendre être exhaustif, propose des présentations et discussions de différents éléments clefs de sa philosophie.

Some theists have adopted materialism for human persons. They associate this metaphysics with their belief in resurrection and focus on problems arising from personal identity, temporal gaps or material constitution, but, in this paper, I argue that being a materialist for human persons leads to an epistemological problem regarding our knowledge of God’s life. The only way to avoid this problem is to choose a particular materialist metaphysics for human persons, that is, a constitution theory that emphasizes the irreducibility of (...) the first-person perspective. (shrink)

On peut inscrire les travaux de Engel dans le sillage rationaliste des Pères de la philosophie analytique, mais après le tournant naturaliste opéré par Quine. Ce sont les diverses bonnes raisons, exposées de manière non systématique par Engel, d’associer naturalisme et rationalisme que je souhaite présenter tout en cherchant à identifier la difficulté constitutive de ce programme qui ne reçoit pas de solution complète: la normativité épistémique ne semble ni éliminable, ni correctement intégrée à ce programme.

David Lewis n’a pas développé de philosophie complète de la religion à proprement parler mais il s’est penché précisément sur différents thèmes religieux comme le rapport entre Dieu et le possible, l’argument ontologique ou la théodicée. Bien que dénuées de toute systématicité, les publications de Lewis sur le religieux défendent un athéisme très argumenté. L'article vise à montrer comment son athéisme s'articule à l'existence d'une pluralité de dieux.

Depuis plus d’une dizaine d’années, Albert Piette travaille à renouveler les méthodes et les concepts de l’anthropologie. Cette refondation s’appuie sur ses propres travaux empiriques, notamment sur le religieux, sur l’usage de méthodes plus pointillistes comme la photographie ou la description des détails, ainsi que sur des hypothèses relatives à la différence entre Sapiens et Néandertal. Les nouvelles propositions de travail qu’il avance empruntent souvent à la philosophie comme moyen d’une réflexion épistémologique, mais aussi parfois à la métaphysique. C’est pourquoi (...) je me propose de discuter en philosophe son ouvrage Contre le relationnisme. Lettre aux anthropologues. Il ne s’agit pas de réactiver la pratique philosophique de la science ultime couronnant les autres disciplines grâce à une réflexivité plus radicale, mais de suivre la démarche de Piette dans ses motivations profondes qui, comme il l’admet lui-même, l’oblige à passer par la philosophie. (shrink)

On conçoit assez souvent l’espace public des discussions comme devant être neutre et par conséquent sans mention des croyances religieuses comme raisons justifiant une décision. La neutralité vise à garantir l’acceptabilité par tous d’une décision pouvant être contraignante. On montrera que l’on peut articuler raisons neutres et raisons religieuses à condition que les raisons neutres restent les raisons ultimes. Cela implique que les raisons religieuses correctement liées à des raisons neutres sont parfaitement légitimes pour justifier une décision politique ou publique.

Discussion de la phénoménologie de la religion, et notamment certaines propositions de Heidegger ou Falque.

Where $\underline{a}$ is a Turing degree and ξ is an ordinal $ , the result of performing ξ jumps on $\underline{a},\underline{a}^{(\xi)}$ , is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through $(\aleph_1)^{L^\underline{a}}$ of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation.

Proof uses forcing on perfect trees for 2-quantifier sentences in the language of arithmetic. The result extends to exact pairs for the hyperarithmetic degrees.

Bernard Lonergan has argued for a theory of cognition that is transcendentally secure, that is, one such that any plausible attempt to refute it must presuppose its correctness, and one that also grounds a correct metaphysics and ontology. His proposal combines an identity theory of knowledge with an intentional relation between knower and known. It depends in a crucial way upon an appropriation of one’s own cognitional motives and acts, that is, upon “knowing one’s own knowing.” I argue that because (...) of conflicts between the identity and intentionality components of the theory, rational self-appropriation cannot, as Lonergan claims, be an iteration of just the same acts by which we acquire other sorts of knowledge. I propose an amended theory in which the relation between intending-subject and intended-object of first-level cognition becomes, in RSA, a numerical identity of knower and known and of the epistemic and the ontological. (shrink)

This note calls attention to the fact that efficient causes – the sort of cause that changes something or makes something happen – can play no constitutive role in the immediate, cognitively conscious relation between cognitive subject and a cognit-ive object. It notes that: (1) it is a necessary condition for an efficient causal relation that it alter its relata; and (2) it is a necessary condition for a conscious cognitive relat-ion that it does not alter its relata. This has (...) important implication for the theories of knowledge and consciousness, the “Hard Problem,” and related puzzles. (shrink)

Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds on I (...) never has a minimal member; if ∪ I = L α [ A] ∩ ω ω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces. (shrink)

Where AR is the set of arithmetic Turing degrees, 0 (ω ) is the least member of { $\mathbf{\alpha}^{(2)}|\mathbf{a}$ is an upper bound on AR}. This situation is quite different if we examine HYP, the set of hyperarithmetic degrees. We shall prove (Corollary 1) that there is an a, an upper bound on HYP, whose hyperjump is the degree of Kleene's O. This paper generalizes this example, using an iteration of the jump operation into the transfinite which is based on (...) results of Jensen and is detailed in [3] and [4]. In $\S1$ we review the basic definitions from [3] which are needed to state the general results. (shrink)

In this paper I call attention to the fact that Lonergan gives two radically opposed accounts of how sense perception relates us to the external world and of how we know that this relation exists. I argue that the position that Lonergan characteristically adopts is not the one implied by what is most fundamental in his theory of cognition. I describe the initial epistemic position with regard to the problem of skepticism about the external material world that is in fact (...) implied by his theory of cognition, and I sort out some confusion about various forms of direct and representative perceptual realism. The paper concludes with a critique of Lonergan’s theory of description and explanation in empirical science that makes evident the difficulties into which he is led by lack of clarity in his theory of perception. (shrink)

Réponses à Juliette Grange sur ses remises en cause peu argumentées d'une partie de la philosophie en France.

The low representation (< 30%) of women in philosophy in English-speaking countries has generated much discussion, both in academic circles and the public sphere. It is sometimes suggested (Haslanger 2009) that unconscious biases, acting at every level in the field, may be grounded in gendered schemas of philosophers and in the discipline more widely, and that actions to make philosophy a more welcoming place for women should address such schemas. However, existing data are too limited to fully warrant such an (...) explanation, which therefore will not satisfy those in favor of the status quo or those who argue against the need to address gender imbalance. In this paper, we propose measures to improve the profession that ought to be implemented without referring explicitly to this underrepresentation or to the climate for women and other underrepresented groups. Such recommendations are based on empirical research already carried out in other disciplines and do not rest on whether it is possible to identify the cause of this low representation. We argue that we need not wait for new or better data to ensure that fairer practices are enacted for women, other underrepresented groups, and everybody else, if only out of precaution. (shrink)

This paper presents a conception of corruption informed by epistemic democratic theory. I first explain the view of corruption as a disease of the political body. Following this view, we have to consider the type of actions that debase a political entity of its constitutive principal in order to assess corruption. Accordingly, we need to consider what the constitutive principle of democracy is. This is the task I undertake in the second section where I explicate democratic legitimacy. I present democracy (...) as a procedure of social inquiry about what ought to be done that includes epistemic and practical considerations. In the third section, I argue that the problem of corruption for a procedural conception of democracy is that the epistemic value of the procedure is diminished by corrupted agents’ lack of concern for truth. Corruption, according to this view, consists in two deformities of truth: lying and bullshit. These deformities corrupt since they conceal private interests under the guise of a concern for truth. In the fourth section, I discuss the difficulties a procedural account may face in formulating solutions to the problem of corruption. (shrink)

Two slogans define structuralism: contemporary mathematics studies structures; mathematical objects are places in those structures. Shapiro’s version of structuralism posits abstract objects of three sorts. A system is “a collection of objects with certain relations” between these objects. “An extended family is a system of people with blood and marital relationships.” A baseball defense, e.g., the Yankee’s defense in the first game of the 1999 World Series, is a also a system, “a collection of people with on-field spatial and ‘defensive-role’ (...) relations”. “A structure is the abstract form of a system” ; it consists of “a collection of places [sometimes called positions or offices] and a finite collection of functions and relations on these places”. (shrink)

Some philosophical considerations over Yann LeCun’s position paper “A Path Towards Autonomous Machine Intelligence”.

The aim of this essay is to show that Yann Martel’s Life of Pi can be read as illustrating what philosophers usually name as pragmatic arguments for religious belief. Ultimately, this seems to be the reason why, in the short prologue that accompanies the novel, Martel claims Life of Pi to be “a story to make you believe in God”. To put it briefly, these arguments claim that even conceding that the question of whether to believe that God exists (...) or that He does not exist cannot be decided upon the evidence we have, we are still justified to decide to believe in God because of the practical beneficial consequences this belief will bring to us. In Martel’s Life of Pi it is this kind of pragmatic reasoning that originates and what makes the “story with animals” preferable over the “story without animals.” I also point out that these arguments appear more convincing if they are not understood as referring to belief in the ordinary and common usage of the term, as the acceptance as being true the factual claim that the world is such that God does actually exist, but as referring to a subjective, non-truth-dependent way of understanding the world and of relating to it. I show that this is precisely the kind of conception of religious faith that is illustrated by the character of Pi through the novel. (shrink)