Logical necessity

Deductionism assimilates nature to conceptual artifacts (models, equations), and tacitly holds that real physical systems are such artifacts. Some physical concepts represent properties of deductive systems rather than of nature. Properties of mathematical or deductive systems can thereby sometimes falsely be ascribed to natural systems.

This paper explains Wittgenstein’s understanding of the ‘grammar’ of our (or any) language, tracing its origins in the Tractatus’s concept of logical syntax, and then examining the senses in which Wittgenstein, in his later work, viewed grammar as being ‘arbitrary’. Then, armed with this understanding, it moves on to the task of examining how, within the framework of a Wittgensteinian view of language, we should understand the inescapable ‘compellingness’ of logical necessity – what Wittgenstein calls the “hardness of the logical must”. Whereas it is often thought that Wittgenstein’s views on the nature of the ‘grammar’ of our concepts leads him towards a vitiatingly conventionalist or anti‐realist understanding of necessity, in which its logical ‘superhardness’ becomes problematic, this paper will argue that there is actually no such tension in Wittgenstein’s thought. In fact an understanding of the ways in which our conceptual grammar is arbitrary casts a great deal of light on how it is that our concepts can nevertheless support a logically superhard, and normatively commanding, notion of necessity. In support of this view, I distinguish Wittgenstein’s views on necessity from the ‘classical’ conventionalism of the Vienna Circle, and from the radical conventionalism of Michael Dummett, and defend Wittgenstein's view from a powerful recent attack from Quassim Cassam.

This paper is part of a special double issue of symploke on the topic of violence. The paper explores and critiques the idea that violence is necessary through an examination of Machiavelli's idea of well-used violence. I argue that Machiavelli demonstrates that necessity can be created and managed by people, which paradoxically suggests that violence may not be necessary for politics after all.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ must always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis. MSC: 11-XX (Number Theory)

This paper shows that "2+2=4" is not a necessary truth. The result is achieved constructively, by exhibiting a system — as consistent as ordinary arithmetic — in which "2+2=4" is false and "2+2=5" is true. (My more recent paper "Mathematically rigorous systems in which 2+2=5: Analogies with non-Euclidean geometry" discusses this topic further.)

It is widely held that the intelligibility of modal metaphysics has been vindicated.  Quine’s arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.    But even if modal metaphysics is intelligible, it could be misconceived.  It could be that metaphysical necessity is not absolute necessity – the strictest “non-epistemic” (non-deontic) notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every non-epistemic sense.  If there were nothing otherwise “uniquely metaphysically significant” about metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it.  The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime.  In a sense, the latter question has no objective answer.  In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question.  I then discuss the deflationary ramifications of this argument.  I conclude with an alternative conception of the space of possibility.  According to this conception, there is no objective boundary between possibility and impossibility.  Along the way, I sketch an analogy between modal metaphysics and set theory.

This paper shows why the non-trivial zeros of the Riemann zeta function ζ will always be on the critical line Re(s) = 1/2 and not anywhere else on the critical strip bounded by Re(s) = 0 and Re(s) = 1, thus affirming the validity of the Riemann hypothesis. [The paper is published in a journal of number theory.]

There are philosophers who think that it is possible to imagine the metaphysically impossible. On the one hand, there are philosophers that think that only knowledge limits what one can imagine. Prior to knowledge of certain facts the imagination is unbounded. On the other hand, there are philosophers who think that the imagination is unconstrained whatever. I shall argue that (a) it is not actually possible to imagine what is metaphysically impossible, though (b) it appears to be possible. I take this to be a defence of the Kripkean view. I aim to develop an understanding of the imagination that can accommodate this view.

This essay argues for the contingency of necessity, i.e. for the
contingency of reason. This essay is a rebuttal of Quentin Meillassoux’s argument for the necessity of contingency. While Meillassoux is a rationalist who presupposes the validity of the principle of non-contradiction as the condition of Hyper-Chaos, this essay contends that Hyper-Chaos is better explicated as a state both equal and unequal to itself at the same time. The principle of non-contradiction does not hold in Hyper-Chaos. Reason or the law of non-contradiction, therefore, can only be accrued to Hyper-Chaos as a consequent or belated necessity - a contingent necessity.

In this paper, I argue that the interpretation of the necessity modal prepi in Greek and the individuation of the modalities (epistemic vs. deontic reading) depends on causation rather than the argument structure (raising vs. control) of the modal verb. The necessity verb behaves like volitional and directive verbs, and triggers the force individuation criterion as defined in Copley et al. (2015), distinguishing between CAUSE and ENABLE causal frames. The individuation between epistemic necessity and deontic necessity depends on the conceptualization of agency and the different configurations of force. I show, first, that the phenomenon is not just syntactical among many others): the variation in the interpretation (epistemic vs. deontic) is the result of differences in the argument structure (raising vs. control) of the modal auxiliary verbs. The key, I argue is causation, which triggers a shift from pure necessity, to intention as force (in the sense of Copley et al. (2015), i.e., as a field generating force. In Greek, the epistemic and deontic reading of the necessity modal comes about in a conceptual causal frame, where the two clauses are connected with the subjunctive particle na 'to/that'— a pattern that we find also in other languages, including English, at least with some performative verbs such as agree, insist where the different modal reading are visible through complement choice. The current analysis implies a meaning of modality richer than mere argument structure (raising vs. control); and, by capitalizing on the causal frame and the presence of force in modal structures, the analysis enables a principled explanation of the shift to intention-necessity without positing ambiguity for the necessity verb prepi.

I consider the dispute, not with a view to reaching a final verdict, but for the light it sheds on the notion of philosophical nonsense.  How does it look to a sceptic about philosophical nonsense?  It is generally agreed that the Tractatus is an unsatisfactory work, if the traditional reading of, for example, G. E. M. Anscombe or Peter Hacker is correct.  But is it any better on the ‘resolute’ reading of Cora Diamond or James Conant?  I maintain that it is more difficulty to handle the concept of nonsense than nonsensicalists of any stripe realise.  If the ‘ineffable truths’ and ‘important nonsense’ of traditional readings raise problems, so too do the contrast between meaningful frame and nonsensical core, Diamond’s idea that one can imaginatively identify with the nonsense-talker and the mysterious new entity, ‘transitional’ nonsense.  Meaning and communication, I suggest, keep reappearing precisely where they should not.

International workshop
“The Free Will Question at the Turn of 18th Century”
26 and 27 September 2019
Université de Neuchâtel
Paper: «From Collins to Hume and Priestley: determinism faces the challenges of skepticism and theism»

Anthony Collins’ determinism was an essential part of his philosophy. A strong determinism that could be better defined as a “logical necessitarianism”; in the Inquiry on Human Liberty Collins states that the necessity of events is equal to the necessity of arithmetics: 2 + 2 gives as result 4 with the same necessity that Senate was the place where Caesar died. The “chain of causes” started from the first, first cause that Collins deprives of moral attributes. His necessitarian and materialistic systems seem devoted to unlock the door of a philosophical “dogmatical” atheism. Priestley was, by his own confession, converted to determinism by Collins. The two also share a materialistic background. But how, and in what extent, can Priestley – a honest believer in the faith of Christ –, accept at the same time Collins’ necessitarianism and challenge Bayle’s argument on “evil”? Finally, what shares Hume the skeptic with Collins the dogmatic? How can Hume’s skeptic critique on the relation of cause and effect be reconciled with his reflexions on Liberty of Necessity? Does he restate a new, a contemporary flavoured, concept of determinism? Or he’s simply incoherent with himself? And what about Hume and the problem of Evil stated in section of Liberty and Necessity of his Enquiry?

Hale has argued that logical necessities are absolute in the sense that there is no competing kind of modality under which they may be false. In this paper, I argue that there are competing kinds of modality, which I call “essentialist modalities,” under which logical necessities may be false. Since it is counter-intuitive to say that logical necessities are not absolute, my argument, if correct, shows that Hale’s characterization of absolute necessity does not adequately capture the intuitive notion of absolute necessity. Then, a qualified version of Hale’s characterization of absolute necessity is proposed. On the qualified version, the absoluteness of logical necessities is no longer defeated by essentialist possibilities.

In this article we propose to study how the modeling options for the knowledge of the semantic value of intensions led to a tension that challenges the idea of model itself. We suggest that this tension mimics the philosophical soil that led to the ancient Kantian thesis that we cannot have intuitive knowledge of intellectual determinations. Models for intensional representation are inaccessible in intuitive representations, which means there is an inevitable pressure towards discursive generality in modeling the “possible”. Hyperintensional models are modern discussions about how much one can break that inertia towards the general and abstract. It is the discussion about the reach and limit of our fine-grained knowledge of dissidence about the possible. We will explore some options of philosophical interpretation for that phenomenon and the tensions it brings to the status of necessary knowledge in restricted or empirical soil. The tension is between the knowledge of that fine-grained differences that can be modeled only ideally and those that become explicit in the semantic codification of language when it has already become synchronic to the scientific needs of representation of truth in that language.

In his more recent version(s) of his argument against naturalism, Alvin Plantinga distinguishes indicative representations (indicators) from depictive representations (depictors). Only the latter qualify as beliefs, since by depicting the world as being a certain way, depictors have propositional content and so can be true or false. Plantinga, echoing Leibniz, argues that it is a category mistake to think that material objects or processes can have content. They may be able to indicate, but they cannot depict. Moreover, natural selection could only see indicators. Even if we identify a given indicator with a depictor, evolution would only select it for its indicative properties, and this just presents us with the Plantinga/Leibniz claim again. With these two points, given naturalism, we have a reason to be sceptical about whether our beliefs are generally true or reliably formed. However, the story is more complicated than this: there are ways in which indicators and depictors associate with each other. According to teleosemantics we can build up a true depictor from an accurate indicator. Moreover, a depictor also indicates something, and so can be seen as a type of indicator. We will explore whether these connections serve to either rescue naturalism or strengthen Plantinga’s argument. Finally, we will put the entire issue in the context of Daniel Dennett’s discussion of “skyhooks” and “cranes,” and whether his condemnation of the former is successful.

L’événement philosophique le plus radical de la période précritique kantienne
consiste peut-être dans la réfutation du caractère analytique ou logique
de l’existence grâce à la redéfinition de l’existence sur le mode de la « position
absolue d’une chose »1, en dialogue entre autres avec Descartes, Leibniz, Crusius,
Baumgarten et Wolff. La théorie précritique de l’existence, vraisemblablement
la plus critique (dans la formulation, non pas dans les implications) de
toutes les théories précritiques de Kant, peut être considérée comme le point
d’intersection de plusieurs lignes de force, notamment la logique et l’ontologie
des modalités, la théodicée, invariablement fondée sur la preuve ontologique
de l’existence de Dieu, et enfin la doctrine du vrai (entre adéquation et cohé-
rence) et son rapport à l’activité de l’esprit. C’est ainsi que, de L’unique fondement
aux Rêves d’un visionnaire, on signale un recentrage de la positio
quaestionis sur la notion d’esprit. En effet, la théodicée ainsi que l’ontologie
modale présupposent et répondent, parfois d’une façon absolument non thématisée,
à une théorie de l’esprit. La compréhension de la philosophie précritique
exige donc d’explorer ces articulations et d’expliciter son impensé fondamental
ou, plutôt, sa pensée confuse et inchoative fondamentale : la structure et la dynamique
du lieu de la vérité qu’est l’esprit, émergeant graduellement sous le
signe de la force d’agir et de pâtir. Le possible – et plus précisément le possible
en tant que nécessité en soi et fondement nécessaire du réel – constitue la
pierre angulaire de la logique modale précritique.

It is commonly claimed that the conclusion of a valid deductive argument is contained in its premises and says nothing new. In 'Deduction and Novelty,' in The Reasoner 5 (4), pp. 56-57, I refuted that claim. In The Reasoner, 8 (3), pp. 24-25, David McBride criticised my refutation. I show that McBride’s arguments are unsound.

In his more recent version(s) of his argument against naturalism, Alvin Plantinga distinguishes indicative representations (indicators) from depictive representations (depictors). Only the latter qualify as beliefs, since by depicting the world as being a certain way, depictors have propositional content and so can be true or false. Plantinga, echoing Leibniz, argues that it is a category mistake to think that material objects or processes can have content. They may be able to indicate, but they cannot depict. Moreover, natural selection could only see indicators. Even if we identify a given indicator with a depictor, evolution would only select it for its indicative properties, and this just presents us with the Plantinga/Leibniz claim again. With these two points, given naturalism, we have a reason to be sceptical about whether our beliefs are generally true or reliably formed. However, the story is more complicated than this: there are ways in which indicators and depictors associate with each other. According to teleosemantics we can build up a true depictor from an accurate indicator. Moreover, a depictor also indicates something, and so can be seen as a type of indicator. We will explore whether these connections serve to either rescue naturalism or strengthen Plantinga’s argument. Finally, we will put the entire issue in the context of Daniel Dennett’s discussion of “skyhooks” and “cranes,” and whether his condemnation of the former is successful.

En la polémica entre actualistas y realistas modales, se ha recurrido a las nociones de necesidad y posibilidad lógicas, para responder a la pregunta por la existencia de los mundos posibles, defendiendo a partir de ellas sus contrapartidas metafísicas. Sin embargo, ¿pueden definirse unas puramente en términos de las otras? ¿O acaso es necesario algo más? En este trabajo se muestra que la relación entre estas nociones asume compromisos metafísicos previos recayendo en una justificación circular, por lo que no puede ser una opción viable para responder a tal pregunta.

In the controversy between actualists and modal realist, the notions of logical necessity and possibility have been used to answer the question for the existence of possible worlds, defending from them their metaphysical counterparts. However, can ome be defined purely in terms of the others? Or maybe something else is needed? In this paper it is shown that the relation between these notions assumes previous metaphysical commitments falling into a circular justification, so it can not be a viable option to answer such a question.

http://www.cintademoebio.uchile.cl/index.php/CDM/article/view/47809

This paper discusses the free will scepticism claim and discerns whether the compatibilism-incompatibilism debate presupposes a rationalistic/necessitarism stance about if a subject S acts freely. The last ten years makes it possible to establish a relevant distinction between an action being free, without discarding causal antecedents of that action. Specifically, this does not lead to a compromise with the so-called Principle of Alternative Possibilities or with the Consequence Argument. It will be discussed how the experiment developed by Libet comprises whether a free action is equivalent to a conscious action, considering the relevance of freedom of veto and the role of the control criterion of an action. A relevant edge in this analysis will be the epiphenomenalist stance. Finally, it will be evaluated the impossibilist modal alternative and its role in a sceptical position regarding free will. Resumen El presente escrito tiene por objetivo discutir los alcances de la postura denominada escepticismo sobre el libre albedrío (Free Will Scepticism) y evaluar si el debate compatibilismo – incompatibilismo supone una postura racionalista y/o necesitarista respecto a si un sujeto S actúa libremente. La discusión de los últimos diez años sobre este tópico permite establecer una distinción relevante entre que una acción sea libre, sin que ello descarte antecedentes causales de esa acción. En particular, sin que ello conduzca a un compromiso con el denominado principio de posibilidades alternativas (principle of alternate possibilities) ni con el denominado argumento consecuencial (consequence argument). Se discutirá cómo el experimento desarrollado por Libet comprende el si una acción libre es equivalente a una acción consciente, considerando la relevancia de la libertad de veto y el rol del criterio de control de una acción. Una arista relevante en este análisis será la postura epifenomenalista. Finalmente, se evaluará la alternativa modal denominada imposibilismo y su rol en una postura escéptica respecto al libre albedrío. 1. Introducción ¿Es libre el ser humano? ¿Es responsable? ¿Son las consecuencias de sus acciones atribuibles a sus decisiones? ¿Son sus decisiones libres? ¿Qué quiere decir ser libre? Durante los últimos diez años, un punto central en discusión respecto a este tópico es si un sujeto S puede decidir entre A o B de modo indeterminado (underdetermine), es decir: Que S tenga efectivamente la posibilidad de elegir entre A o B,

According to an interpretation of Stoic logic advocated by some of its most recent scholars, Stoic logic already contains a distinction that became important in contemporary modern logic, namely, one between propositions tautologically necessary, i.e. necessary in virtue of being true under any possible interpretation of its variables (e.g. If A, A) and propositions that are not tautologous but still necessary in virtue of their meaning (e.g. If Peter is a bachelor, Peter is not married). The present paper does not question the presence of this distinction in Stoic logic. Its aim is just to show that the textual evidence normally aduced in its favour is questionable and we need to appeal to other sources to find clear evidence for it.

Does the "transcendental" kind of argument exist? If so, what does it consist in and what are its historical beginnings? At the start of the third millennium, Frederick Peter Strawson caused quite a stir and an enduring controversy on the margins of what he labelled the "transcendental argument". This presentation will provide an introduction to this topic and expose some of its backgrounds. The thesis is that these backgrounds are shaded by the fact that, although the starting point of Strawson's apparently simplifying "descriptive metaphysics" was Kant's transcendental philosophy, he missed its gist and purpose, while permeating its subsequent reception.

RESEARCH ARTICLES
Alex Blum, Can It Be that Tully=Cicero?
Michael Campbell, Companions in Guilt Arguments and Moore's Paradox
Arnold Cusmariu, The Prometheus Challenge Redux
Hili Razinsky, Ambivalence, Emotional Perceptions, and the Concern with Objectivity
DISCUSSION NOTES/DEBATE
Rocco J. Gennaro, In Defense of H.O.T. Theory: A Second Reply to Adams and Shreve
Terence Rajivan Edward, Artefacts as Mere Illustrations of a Worldview