Einstein, like most philosophers, thought that there cannot be mathematical truths which are both necessary and about reality. The article argues against this, starting with prima facie examples such as "It is impossible to tile my bathroom floor with regular pentagonal tiles." Replies are given to objections based on the supposedly purely logical or hypothetical nature of mathematics.

The conditional interpretation of general categorical statements like ‘All men are animals’ as universally quantified material conditionals ‘For all x, if x is F, then x is G’ suggests that the logical structure of law statements is conditional rather than categorical. Disregarding the problem that the universally quantified material conditional is trivially true whenever there are no xs that are F, there are some reasons to be sceptical of Frege’s equivalence between categorical and conditional expressions. -/- Now many philosophers will (...) claim that the material conditional interpretation of laws statements, dispositions ascriptions, or any causal claim is generally accepted as wrong and outdated. Still, there seem to be some basic logical assumptions that are shared by most of the participants in the debate on causal matters which at least stems from the traditional truth functional interpretation of conditionals. This is indicated by the vocabulary in the philosophical debate on causation, where one often speaks of ‘counterfactuals’, ‘possible worlds’ and ‘necessity’ without being explicit on whether or to what extent one accepts the logical-technical definition of these notions. To guarantee a non-Humean and non-extensional approach to causal relations, it is therefore important to be aware of the logical and metaphysical implications of the technical vocabulary. -/- In this paper we want to show why extensional logic cannot deal with causal relations. Via a logical analysis of law-like statements ‘All Fs are Gs’ we hope to throw some new light on interrelated notions like causation, laws, induction, hypotheticality and modality. If successful, our analysis should be of relevance for a deeper understanding of any type of causal relations, whether we understand them to be laws, dispositions, singulars or categoricals. (shrink)

I argue that Plato thinks that a sunaition is a mere tool used by a soul (or by the cosmic nous) to promote an intended outcome. In the first section, I develop the connection between sunaitia and Plato’s teleology. In the second section, I argue that sunaitia belong to Plato’s theory of the soul as a self-mover: specifically, they are those things that are set in motion by the soul in the service of some goal. I also argue against several (...) popular and long-standing interpretations, namely, that sunaitia correspond to Aristotle’s idea of hypothetical necessity, that sunaitia are the ‘how’ in an explanation (whereas the true cause is the ‘why’), and that Plato’s causal views should be read through Aristotle’s fourfold schema. I conclude the article by surveying the history of sunaitia after Plato’s usage. (shrink)

In these pages, we expose the main traits of St. Albert the Great’s doctrine of providence and fate, considered by Palazzo the keystone of his philosophical system. To describe it we examine his systematic works, primarily his Summa of Theology. His discussion follows clearly the guidelines of the Summa of Alexander of Hales, in order to delve into the set of problems faced over the centuries by theological tradition. Albert also restates the reflections of different authors like Boethius or Saint (...) John of Damascus but, in his Summa he incorporates to his reflections also the noteworthy book of Nemesius of Emesa, De natura hominis, which includes some pages on providence. Albert gives his personal solution to the complex questions of providence, destiny and contingency of the world. His conception of providence is developed in the frame of the creative power of the almighty God. God’s knowledge is necessary and inerrant and his providential purposes are infallible, but that does not mean that every event is necessary. He does not communicate His own proprieties to the creatures. In order to understand this problem, Albert recalls the notion of hypothetical necessity coined by Boethius in an Aristotelian framework and the difference between 'necessitas consequentis' and 'necessitas consequentiae' proposed by Alexander of Hales. He also develops his account of providence, closely linked to the topic of fate. However, it would be exaggerated to deem his position deterministic. (shrink)

This argues for a reading of PA I.1, 639b11-640a9 as a continuous argument, which I divide into 3 main sections. Aristotle’s point in the first section is that teleological explanations should precede non-teleological explanations in the order of exposition. His reasoning is that the ends cited in teleological explanations are definitions, and definitions—which are not subject to further explanation—are appropriate starting points, insofar as they prevent explanations from going on ad infinitum. Moreover, I argue that Aristotle proceeds in the following (...) two sections to criticize certain non-teleological accounts offered by his predecessors on the grounds that they are explanatorily defective: I take Aristotle’s complaints to be that those accounts—unlike teleological explanations—neither begin from appropriate starting points nor entail the phenomena that they purport to explain. Along the way, I am defending an alternative way of understanding what "hypothetical necessity" refers to, for Aristotle. Comments are welcome! (shrink)

I argue that Kant acknowledges two models of spontaneous self-determination that rational beings are capable of. The first model involves absolute unconditional necessity and excludes any form of contingency. The second model involves (albeit not as a matter of definition) a form of contingency which entails alternative possibilities for determining oneself. The first model would be exhibited by a divine being; the second model is exhibited by human beings. Human beings do, however, partake in the divine model up to (...) an extent, namely, as far as the legislative spontaneity of their law-giving faculties are concerned. I conclude by suggesting that for Kant, the mechanistic principle that we are exclusively determined by natural causes poses a twofold threat for human agency. In one respect (in relation to the second model), it threatens us with the obliteration of contingency, or with the universality of hypothetical necessity. But in another respect (in relation to the first model), it threatens us (and our putative "laws") with the obliteration of absolute necessity, or with the universality of contingency. (shrink)

Chance and necessity are mainstays of explanation in current biology, dominated by the neo-Darwinian outlook, a blend of the theory of evolution by natural selection with the basic tenets of population genetics. In such a framework the form of living organisms is somehow a side effect of highly contingent, historical accidents. Thus, at a difference of other sciences, biology apparently lacks theoretical principles that in a law-like fashion may explain the emergence and persistence of the characteristic forms of living (...) organisms that paradoxically, given the current importance attributed to chance, can be grouped into organized structural typologies. Nevertheless, the present essay shows that since its origins in Aristotelian natural history, biology aimed at achieving rational, non-accidental, explanations for the wide variety of living forms endowed with characteristic behaviors that constitute the landscape of biological species. (shrink)

Mental actions are things we do with our minds. Consider inferring, deliberating, imagining, remembering, calculating, and so on. I introduce a non-reductive alternative to standard causalist accounts of mental action that understands such action in terms of dispositions for performing mental actions. I call this alternative the powers framework. On the powers framework, habitual and skillful mental actions are themselves infused with practical intelligence by being expressions of the agent’s rational tendencies and capacities, respectively. The intelligence exemplified in the performance (...) of habitual and skillful mental actions stems from the agent’s having shaped the corresponding tendencies and capacities through training and practice. In this way, mental habits and skills are ‘second nature’ to us. I substantiate the powers framework by giving an account of imagining as a type of skillful mental action. In particular, I argue that imagination is a power to construct representations and select their contents as a means to performing learned behaviors like pretending, engaging with fiction, predicting others’ behavior, reasoning about possibility and necessity, reasoning hypothetically or counterfactually about contingent matters of fact, and even imagining for its own sake. I extend the account of imagining to episodic remembering. I argue that such remembering, considered as a mental action, is a kind of imagining by virtue of the agent’s constructing a representation and selecting its content as a means of performing the learned behavior of navigating her personal past. (shrink)

The view that phenomenally conscious robots are on the horizon often rests on a certain philosophical view about consciousness, one we call “nomological behaviorism.” The view entails that, as a matter of nomological necessity, if a robot had exactly the same patterns of dispositions to peripheral behavior as a phenomenally conscious being, then the robot would be phenomenally conscious; indeed it would have all and only the states of phenomenal consciousness that the phenomenally conscious being in question has. We (...) experimentally investigate whether the folk think that certain (hypothetical) robots made of silicon and steel would have the same conscious states as certain familiar biological beings with the same patterns of dispositions to peripheral behavior as the robots. Our findings provide evidence that the folk largely reject the view that silicon-based robots would have the sensations that they, the folk, attribute to the biological beings in question. (shrink)

The passionate and staunch defence of logic of the controversial thinker Ibn Ḥazm, Abū Muḥammad ʿAlī b. Aḥmad b. Saʿīd of Córdoba (384-456/994-1064), had lasting consequences in the Islamic world. Indeed, his book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples (Kitāb al-Taqrīb li-ḥadd al-manṭiq wa-l-mudkhal ilayhi bi-l-alfāẓ al-ʿāmmiyya wa-l-amthila al-fiqhiyya), composed in 1025-1029, was well known and discussed during and after his time; and it paved the way for the studies (...) of his compatriots Ibn Bājjah (d. 1138), Ibn Ṭufayl (1185), and Ibn Rushd (1198), who each gave demonstrative reasoning a privileged place within the methods of attaining knowledge. Unfortunately, as too often in the history of science, Ibn Ḥazm’s innovative perspectives and contributions in logic have been overlooked or considered with an attitude of contempt. On the one hand, his work has been seen, at best, as promulgating the benefits of studying Aristotle’s logic, so that his contribution is assessed as more didactical than conceptual. And on the other hand, those who do examine his innovations often consider them to be mistaken. As indicated by Chejne (1984, p. 2) contempt towards the logical work of Ibn Ḥazm was also present in its reception by the Eastern philosophers who accused him of deviating from Aristotelian logic and of dabbling in things beyond his capability. However, a reassessment of his work on logic has since begun, by delving into the ways the thinker of Córdoba studied the links between deontic and modal qualification of propositions. In this context Lameer’s (2013) paper on the logical sources of Ibn Ḥazm is worth mentioning; the author (p. 417, footnote 1) observes that, although, strictly speaking, it was al-Fārābī who first drew the parallelism between deontic and modal concepts, it was Ibn Ḥazm who developed it and worked it out in a more precise manner. A primary aim of this paper is to help fill some of these gaps by stressing the role of the work of Ibn Ḥazm in developing a notion of deontic necessity deeply rooted in legal normativity, and in explicitly discussing the transference between deontic and modal concepts. According to our view; the basic units of Islamic deontic logic are what we might call, indulging in terminological anachronism, heteronomous imperatives. As it turns out, the heteronomy of imperatives within Islamic legal systems contrasts with those of the purely moral realm, which seem to be closer to an autonomous conception of moral law. There it concurs again with Leibniz’s proposal to define obligatory as “what is necessary for a good person to do”. In the present paper, we will focus on the heteronomous imperatives of legal systems rather than on the imperatives of the purely moral realm. In this context, the work of Ibn Ḥazm extends the parallelism between the necessity of events and that of human actions stressed by his predecessors. According to our understanding, Ibn Ḥazm’s parallelism can be rendered explicit formally by means of a conditional (or hypothetical) structure shared by both deontic and modal propositions. Moreover, this structure makes apparent that this parallelism displays an underlying system of “degrees”. Indeed, while in the domain of events, given some conditions, it makes sense to distinguish between an event that is more likely to happen than another. Ibn Ḥazm speaks of near and distant possibility (such as the higher degree of likelihood of rain, given the condensation of clouds in December, and its lower degree, when the condensation occurs in summer); and, in the domain of actions, the Islamic notion of weighting actions determines degrees of virtue (or of legal and moral value). So whereas the degree of virtue of performing a forbidden act as determined by the distribution of sanction and reward is 0, we obtain the same value by pondering the likelihood of an impossible event to take place. Furthermore, as discussed in section II.3.2, the system of values at work in the parallelism can be seen as opening the way to a more direct correspondence. Thus, while in the realm of nature, likelihood of occurrence of an event is dependent upon the conditions specific to the occurrence of that event; while, in the realm of jurisprudence, likelihood of performing an action is dependent upon the distribution of reward and sanction specific to that action (being that, given the choice to perform or not perform a given action, those that will be rewarded are more likely to be performed than those that are not). According to this perspective, the point of the parallelism is that both deontic and modal qualifications measure the degree of an action or event to become actual; that is – indulging once more in anachronism (but this time from the Leibnizian background) – the degree measures how feasible (facile) an action or event may be. This suggests that Ibn Ḥazm’s perspectives already herald the links to probability and possibility explored by Leibniz six centuries later – see for example Leibniz’s (1671, A VI, I, p. 424-26) use of probability in the context of conditional right. Nevertheless, it also shows a crucial difference to the approach developed in the Elementa Jura Naturalis: whereas Leibniz’s studies seek to define what is to be just or virtuous, the logical system of deontic imperatives within Islamic jurisprudence presupposes that what is to be virtuous has already been settled. Determining what is to be virtuous is not achieved by logical reasoning within the system of legal jurisprudence, but by delving into the higher objectives of the Sharīʿa. While developing our point, we will delve into the logical structure of the heteronomous imperatives. This distinguishes our contribution from the existing literature, such as the papers of Chejne (1984), Lameer (2014), and Guerrero (1997, 2010, 2014), which do not provide a logical analysis of the deontic concepts put into work by Ibn Ḥazm. The true antecedent to the present paper is the work of Farid Zidani (2007, 2015), who, so far as we know, was the first to undertake such a task. Some of our own developments and general epistemological thoughts go beyond Ibn Ḥazm’s framework and motivations; mainly those contained in sections II.3.2 and IV. However, according to our view, these reflections suggest that Ibn Ḥazm’s approach has the substance for a broader and deeper exploration of the logic of norms. The paper is structured as follows:I.Ibn Ḥazm’s Logic of Heteronomous Imperatives. After presenting some extracts of the relevant text, we proceed by providing a formal reconstruction of the five forms of deontic modalities. II. A Landmark in the History of the Logical Analysis of Norms. Duties and Modalities. In this section, we study the transferences from deontic to modal necessity and possibility. We briefly compare the deontic system of Islamic Jurisprudence with that of Leibniz.III. Leibniz and Hypothetical Imperatives in Law.IV. Beyond Ibn Ḥazm: Conclusions and the Work Ahead. We will conclude the paper by discussing briefly some conceptual points that distinguish the logic of heteronomous imperatives from contemporary deontic logic. Our final words will discuss deontic-modal parallelism in the context of Ibn Ḥazm’s rejection of reasoning by conjecture and what we call “the internalization of nature.”. (shrink)

This essay explores the notion of moral exemplarity, positing that our morality is underpinned by moral exemplars – paradigmatic examples of virtuous individuals or actions. Theoretical precepts of moral exemplarity are explored across historical and contemporary contexts, including the philosophies of Plato, Aristotle, Stoic and Christian ethics, and recent works of Alexandro Ferrara and Linda Zagzebski. This essay debates the necessity of moral exemplars, the intrinsic moral and epistemic exemplarity, and the distinction between categorical and hypothetical exemplarity, as (...) well as referencing the paradoxical Kantian dismissals of moral exemplarity. It critiques current accounts of moral exemplarity and proposes a transcendental explanation, culminating in an examination of the “exemplarist categorical imperative.”. (shrink)

The relationship between mind and necessity is one of the major points of difficulty for the interpretation of Plato’s Timaeus. At times Timaeus seems to say the demiurge is omnipotent in his creation, and at other times seems to say he is limited by pre-existing matter. Most interpretations take one of the two sides, but this paper proposes a novel approach to interpreting this issue which resolves the difficulty. This paper suggests that in his speech Timaeus presents two (...) class='Hi'>hypothetical models of creation, one with an omnipotent demiurge and one where he is limited by matter, so as to investigate their theoretical and empirical validity. Further, he shows that each model is ultimately an inadequate explanation of the first principles of the cosmos. Timaeus’ speech is therefore properly understood to be aporetic: it leaves its listeners aware of the difficulties inherent in the two models of creation, but without a more viable alternative. (shrink)

Fichte’s ambitious project in the Foundations of Natural Right is to provide an a priori deduction of the concept of right independently from morality. So far, interpretations of Fichte’s deduction of the concept of right have persistently fallen into one of two rough categories: either they (re)interpret the normative necessity of right in terms of moral or quasi-moral normativity or they interpret right’s normative necessity in terms of hypothetical imperatives. However, each of these interpretations faces significant exegetical (...) difficulties. By contrast, I argue that we can understand the normative necessity of right in terms of conceptual necessity. On this view, right does not tell us what ought to be done, but instead tells us what we are doing and have done. Not only does this provide for a promising philosophical account of the non-moral normativity of right, but also provides a compelling reading of Fichte’s text in both the deduction of the concept of right in the Foundations of Natural Right as well as his discussion of the application of the concept of right and coercion. (shrink)

When this article was first planned, writing was going to be exclusively about two things - the origin of life and human evolution. But it turned out to be out of the question for the author to restrict himself to these biological and anthropological topics. A proper understanding of them required answering questions like “What is the nature of the universe – the home of life – and how did it originate?”, “How can time travel be removed from fantasy and (...) science fiction, to be made scientific and practical?”, and “How can the proposed young age of genus Homo be made to actually be reasonable – when simply stating it would be solid ground for instant rejection and dismissal?” The result is that the article also talks about subjects like Artificial Intelligence, General Relativity, and cosmology. -/- From where did life originate? God? Evolution? Panspermia? If the tendency of humans and scientists to regard undiscovered science as pseudoscience can be overcome, Einstein gave another alternative to consider when he introduced General Relativity. Time isn’t linear – progressing in a straight line from past to present to future. That assumption ignores Relativity which states that space AND TIME are curved. Where did life and the genetic code come from? Can the answer build AI? -/- The first question can be answered by the section of this article titled SETI, Evolution, and Time which says life (possibly multicellular and intelligent) and the genetic code came from humans acquiring knowledge of these things over the centuries, then applying that knowledge – via terraforming, accumulation of raw materials like amino acids and nucleic acids, genetic engineering - to a time in the past when life didn’t exist. From that origin, life evolved through innumerable mutations and adaptations, with humans once again acquiring knowledge of it in cyclic (nonlinear) time. -/- The second question is answered by saying artificial intelligence (AI) as the product of life is only half of the equation. The other half refers to Relativity’s curved space-time and violation of the notion that time always travels from past to future. We have always lived in an artificially intelligent, non-probabilistic universe where everything in time and space is connected into one thing by quantum entanglement – making the brain and genes products of binary-digit activity or artificial intelligence (life is not merely dependent on biology’s “lock and key” mechanisms but also possesses AI). -/- The earliest documented representative of the genus Homo is Homo habilis, which evolved around 2.8 million years ago. Scientists used to believe there was a straight line from H. habilis to us, Homo sapiens. This article will use the “advanced” waves loved by Physics Nobel laureate Richard Feynman, view the history of science through the lens of Conic Sections applied to Relativity’s curved space-time, and incorporate the necessity of so-called imaginary time * – popularized by Prof. Stephen Hawking. While the evolutionary proposals are more in agreement with this early straight line than with modern theories, Albert Einstein’s General Relativity is used to transform the straight line into a curved line, ultimately concluding that Homo habilis (H. habilis) originated only (and unbelievably, as far as today’s science and technology is concerned) ~250,000 years ago. Other branches and dead ends of Homo – e.g. Neanderthals – are the result of mutations and adaptations, with the resultant modifications to anatomy and physiology. The surprisingly young age of H. habilis allows nearly 200,000 years for habilis, or one of its descendants, to reach Australia … if this country’s indigenous Aboriginal population did, as claimed, reach this “island continent” 60,000 years ago. -/- * The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, is a failure of classical physics to predict observed phenomena: it can be shown that a blackbody - a hypothetical perfect absorber and radiator of energy - would release an infinite amount of energy, contradicting the principles of conservation of energy and indicating that a new model for the behaviour of blackbodies was needed. At the start of the 20th century, physicist Max Planck derived the correct solution by making some strange (for the time) assumptions. In particular, Planck assumed that electromagnetic radiation can only be emitted or absorbed in discrete packets, called quanta. Albert Einstein postulated that Planck's quanta were real physical particles (what we now call photons), not just a mathematical fiction. From there, Einstein developed his explanation of the photoelectric effect (when quanta or photons of light shine on certain metals, electrons are released and can form an electric current). So it appears entirely possible that another supposed mathematical trickery (imaginary time and the y-axis of Wick rotation) will find practical application in the future. -/- The article includes mathematical references to cosmology (spoiler alert – you’ll read about things like Vector-Tensor-Scalar Geometry, topology, the “eternal present”, Einstein’s Unified Field, the inverse-square law, and there being no Big Bang and no multiverse - but there will also be no equations). -/- The other subheadings in this essay are – -/- NONLINEAR TIME AND ELECTRICAL ENGINEERING (about a 2009 electrical engineering experiment at America’s Yale University, and cosmic wormholes) -/- BITS AND TOPOLOGY (base-2 maths aka Binary digiTS, Mobius strips, and figure-8 Klein bottles) -/- WICK ROTATION, CAUSALITY, AND UNITING TIME (do past, present and future co-exist in an “eternal present”?) -/- DIGITAL BRAIN, DIGITAL UNIVERSE (if the brain and the universe are ultimately composed of binary digits, we'll someday be able to do the same things with the brain and universe that we now do with computers) -/- PROPOSAL: HUMAN AND ANIMAL INSTINCTS ARE THE RESULT OF THE UNIVERSE BEING UNIFIED BY BINARY DIGITS (AND TOPOLOGY) (If everything in the universe is ultimately composed of electronic BITS, then the universe must possess Artificial Intelligence - some prefer the term Cosmic Consciousness) -/- INFORMATION THEORY CONQUERS A RED GIANT (preserving Earth by keeping the Sun near today’s level of activity forever). 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In this work, I will support a combined notion of harm according to which there are qualitatively different harms. I will support a way in which the severity of harms could be measured. Then, I will provide three principles about the strength of the reasons against harming. The supported thesis will provide some tools to solve some problems of the general part of criminal law. In relation to the analytical stratum of statutory description of an offence, I will show that (...) the defended notion of harm could help to solve cases of hypothetical and alternative causal courses. In relation to the analytical stratum of unlawfulness (or wrongfulness), I will show that the proposed ranking of the severity of harms help us to distinguish between cases of necessity as justification and necessity as excuse. In relation to the analytical stratum of culpability, I will show that the principles regarding the strength of the reasons against harming help us to supply straightforward criteria to measure the punishment to impose for having committed some crime. -/- En este trabajo intentaré defender una noción combinada de daño de acuerdo a la cual existen dos tipos de daños cualitativamente diferentes. Asimismo, defenderé un modo en que la gravedad de los diferentes daños puede ser graduada. Derivado de lo anterior, extraeré tres principios sobre la fuerza de las razones en contra de dañar. La tesis defendida proporcionará herramientas para resolver algunos problemas de la parte general de derecho penal. En relación al tipo penal, mostraré que la noción de daño defendida puede ayudar a resolver casos de cursos causales alternativos e hipotéticos. En referencia a la antijuridicidad, mostraré que la clasificación de la gravedad de los daños propuesta ayuda a distinguir qué casos de estado de necesidad deben considerarse como justificación y cuales como excusa. En referencia a la culpabilidad, mostraré que los principios sobre la diferente fuerza de las razones en contra de dañar ayudan a aportar criterios claros para la individualización de la pena a imponer por la comisión de un delito. (shrink)

Hume shed a great doubt on the cosmological argument and made the work of many philosophers in proving religion a frustrating task. While the arguments against the need for a first cause defuses a priori reasoning in general, such reasoning is shown to be offensive to the pious as well. When wielded by the hand of Hume, this hypothetical argument a priori renders the existence of God not only improbable, but quite contradictory given the ostensible necessity of the (...) existence of the universe. (shrink)

The categorical imperative inherent in Kant’s ethics has had indubitable historical influence on societies worldwide whether in the form of laws, democracy or public deliberation. The Toronto Van Attack of 2018 and its subsequent legal trial is a case example that shows how the categorical imperative can be applied to assist in understanding the reasoning for the case’s guilty verdict. This paper will convey the applicability of the categorical imperative for examining criminal case studies by closing the gap between ethical (...) theory and practice. Such closure will be shown to assist in understanding why a perpetrator of a crime can be found guilty of following a hypothetical imperative to base their actions. The rationale for the verdict in this case will be shown to be based on the perpetrator’s responsibility in the form of maintaining autonomy despite having an autism diagnosis. The perpetrator will be shown to have acted on an irrational will and yet was treated in the legal sense as a rational individual. Such rationality was maintained despite complications with their autonomy in the form of relativism and ethical solipsism. (shrink)

In this article, I present a schema for generating counterexamples to the argument form known as Hypothetical Syllogism with indicative conditionals. If my schema for generating counterexamples to HS works as I think it does, then HS is invalid for indicative conditionals.

ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in (...) different authors. For instance, we find ‘If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C’. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is ‘is’, where it occurs, predicative, existential, or veridical? That is, should ‘A esti’ be translated as ‘it is an A’, ‘A exists’, ‘As exist’ or ‘It is true/the case that A’? If A, B, C are term letters, and ‘is’ is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. (shrink)

Hypothetical contracts have been said to be not worth the paper they are not written on. This paper defends hypothetical consent theories of justice, such as Rawls's, against the view that they lack justificatory power. I argue that while hypothetical consent cannot generate political obligation, it can generate political legitimacy.

A basic conviction in moral non-cognitivism is: only hypothetical norms may be justified. Hartmut Kliemt argues for a moderate variant: there are only hypothetical justifications of norms whether the norms are hypothetical or categorical in kind. In this paper the con- cept of ‘hypothetical justification’ is analyzed. It is argued that hypothetical justifications are not of the kind that we should look for in normative ethics.

In this paper, I consider an argument of Harvey Siegel's according to which there can be no hypothetical normativity anywhere unless there is categorical normativity in epistemology. The argument fails because it falsely assumes people must be bound by epistemic norms in order to have justified beliefs.

According to the standard view, Kant held that hypothetical imperatives are universally binding edicts with disjunctive objects: take-the-means-or-don't-have-the-end. But Kant thought otherwise. He held that they are edicts binding only on some - those who have an end.

Upward monotonic semantics for necessity modals give rise to Ross’s Puzzle: they predict that □φ entails □(φ ∨ ψ), but common intuitions about arguments of this form suggest they are invalid. It is widely assumed that the intuitive judgments involved in Ross’s Puzzle can be explained in terms of the licensing of ‘Diversity’ inferences: from □(φ ∨ ψ), interpreters infer that the truth of each disjunct (φ, ψ) is compatible with the relevant set of worlds. I introduce two pieces (...) of data that this analysis fails to explain. Analyzing this data, I argue, suggests that necessity modals with embedded disjunctions license ‘Independence’ inferences: from the truth of □(φ ∨ ψ), interpreters infer that φ-without-ψ and ψ-without-φ are each compatible with the relevant set of worlds. I outline a bilateral inquisitive semantics for necessity modals that predicts the validity of the Independence inferences. I then argue that the resulting theory should be understood as one on which disjunctions denote pluralities of propositions, and necessity modals behave like collective predicates applied to these pluralities. (shrink)

The debate over Hypothetical Syllogism is locked in stalemate. Although putative natural language counterexamples to Hypothetical Syllogism abound, many philosophers defend Hypothetical Syllogism, arguing that the alleged counterexamples involve an illicit shift in context. The proper lesson to draw from the putative counterexamples, they argue, is that natural language conditionals are context-sensitive conditionals which obey Hypothetical Syllogism. In order to make progress on the issue, I consider and improve upon Morreau’s proof of the invalidity of (...) class='Hi'>Hypothetical Syllogism. The improved proof relies upon the semantic claim that conditionals with antecedents irrelevant to the obtaining of an already true consequent are themselves true. Moreover, this semantic insight allows us to provide compelling counterexamples to Hypothetical Syllogism that are resistant to the usual contextualist response. (shrink)

In all three of his major works on moral philosophy, Kant conceives of moral obligation, moral permissibility, and moral impermissibility in decidedly modal terms, namely in terms of moral necessity, moral possibility, and moral impossibility respectively. This terminology is not Kant’s own, however, but has a rather long history stretching back to a group of Spanish Jesuit theologians in the early seventeenth century, and it was used in two contexts: first, in the context of divine and human action to (...) explain how volition can be both metaphysically and physically free and yet morally necessary, and second in a deontic context to refer to moral obligation, permissibility, and impermissibility. In this paper, my first and primary aim is to sketch the way in which four of Kant’s most important German predecessors, namely Leibniz, Christian Wolff, Alexander Gottlieb Baumgarten, and Christian August Crusius, used the language of moral necessity, possibility, and impossibility in both the context of action and obligation. My second, more limited aim is to suggest that Kant’s use of these terms can be clarified by taking this background into consideration. (shrink)

Finean essentialists take metaphysical necessity to be metaphysically explained by essence. But whence the explanatory power of essence? A recent wave of criticism against the Finean account has put pressure on essentialists to answer this question. Wallner and Vaidya (2020) have responded by offering an axiomatic account of the explanatory power of essence. This paper discusses their account in light of some recent criticism by Bovey (2022). Building on work by Glazier (2017), Bovey succeeds in showing that Wallner and (...) Vaidya’s account is in need of modification and clarification. In this paper, I take up Bovey’s challenge and argue that Wallner and Vaidya have the resources available to incorporate the necessary modifications. I discuss the details of this modification, specifically, the question of what kind of metaphysical explanation is at work in the explanation of the necessity of essence itself. To get clear on this, I will introduce the distinction between generative and non-generative metaphysical explanation. In this way the paper contributes to both, the debate about whether essences can explain necessity and to the ongoing debate about metaphysical explanation. (shrink)

There is an important and fairly straightforward link between necessity and apriority which can shed light on our knowledge of the former, but initially plausible attempts to spell out what it is fall victim to counterexamples. Casullo discusses one such proposal, argues—following Anderson :1–20, )—that it fails, and suggests an alternative. In this paper, I argue that Casullo’s alternative also fails, before making a suggestion for which I can find no counterexamples and which, notably, handles some recent examples due (...) to Kipper and Strohminger and Yli-Vakkuri. (shrink)

Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.

The last few decades have given rise to the study of practical reason as a legitimate subfield of philosophy in its own right, concerned with the nature of practical rationality, its relationship to theoretical rationality, and the explanatory relationship between reasons, rationality, and agency in general. Among the most central of the topics whose blossoming study has shaped this field, is the nature and structure of instrumental rationality, the topic to which Kant has to date made perhaps the largest contribution, (...) under the heading of his treatment of hypothetical imperatives. (shrink)

Moti Mizrahi (2013) presents some novel counterexamples to Hypothetical Syllogism (HS) for indicative conditionals. I show that they are not compelling as they neglect the complicated ways in which conditionals and modals interact. I then briefly outline why HS should nevertheless be rejected.

The aim of this chapter is to explore to some extent the relationship between identity and necessity in logic and metaphysics. First, I provide a historically-based summary of proofs of the necessity of identity, highlighting the importance of the role that self-identity plays. Second, I introduce two examples of metaphysical topics where the necessity of identity has played a pivotal role: the necessary a posteriori, and the coincidence of material objects. I argue that important aspects of these (...) debates rest on how we represent identity. Third, I consider some recent work on generalized identity. This opens up new prospects for explaining why identity is necessary. (shrink)

Grounding necessitarianism (GN) is the view that full grounds necessitate what they ground. Although GN has been rather popular among philosophers, it faces important counterexamples: For instance, A=[Socrates died] fully grounds C=[Xanthippe became a widow]. However, A fails to necessitate C: A could have obtained together with B=[Socrates and Xanthippe were never married], without C obtaining. In many cases, the debate essentially reduces to whether A indeed fully grounds C – as the contingentist claims – or if instead C is (...) fully grounded in A+, namely A plus some supplementary fact S (e.g. [Xanthippe was married to Socrates]) – as the necessitarian claims. Both sides typically agree that A+ necessitates C, while A does not; they disagree on whether A or A+ fully grounds C. This paper offers a novel defence of the claim that, in these typical cases, unlike A+, A fails to fully ground C – thereby bringing further support to GN. First and foremost, unlike A+, A fails to fully ground C because it fails to contain just what is relevant to do so, in two distinct senses – explanatory and generative relevance. Second, going for A, rather than A+, as a full ground undermines not just grounding necessitarianism, but modally weaker views which even contingentists may want to preserve. (shrink)

Many philosophers have suggested that claims of need play a special normative role in ethical thought and talk. But what do such claims mean? What does this special role amount to? Progress on these questions can be made by attending to a puzzle concerning some linguistic differences between two types of 'need' sentence: one where 'need' occurs as a verb, and where it occurs as a noun. I argue that the resources developed to solve the puzzle advance our understanding of (...) the metaphysics of need, the meaning of 'need' sentences, and the function of claims of need in ethical discourse. (shrink)

ABSTRACTThe Necessity of Origins is the thesis that, necessarily, if a material object wholly originates from some particular material, then it could not have wholly originated from any significantly non-overlapping material. Several philosophers have argued for this thesis using as a premise a principle that we call ‘Single Origin Necessity’. However, we argue that Single Origin Necessity is false. So any arguments for The Necessity of Origins that rely on Single Origin Necessity are unsound. We (...) also argue that the Necessity of Origins itself is false. Our arguments rely on a thesis in the ontology of art that we find plausible: Multi-Work Materialism. It is the thesis that works of art that have multiple concrete manifestations are co-located with those manifestations. (shrink)

In this paper the logic of broad necessity is explored. Definitions of what it means for one modality to be broader than another are formulated, and it is proven, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. It is shown, moreover, that it is possible to give a reductive analysis of this necessity in extensional language. This relates more generally to a conjecture that it (...) is not possible to define intensional connectives from extensional notions. This conjecture is formulated precisely in higher-order logic, and concrete cases in which it fails are examined. The paper ends with a discussion of the logic of broad necessity. It is shown that the logic of broad necessity is a normal modal logic between S4 and Triv, and that it is consistent with a natural axiomatic system of higher-order logic that it is exactly S4. Some philosophical reasons to think that the logic of broad necessity does not include the S5 principle are given. (shrink)

Hájek (Erkenntnis 70(2):211–235, 2009) argues that probabilities cannot be the limits of relative frequencies in counterfactual infinite sequences. I argue for a different understanding of these limits, drawing on Norton’s (Philos Sci 79(2):207–232, 2012) distinction between approximations (inexact descriptions of a target) and idealizations (separate models that bear analogies to the target). Then, I adapt Hájek’s arguments to this new context. These arguments provide excellent reasons not to use hypothetical frequencies as idealizations, but no reason not to use them (...) as approximations. (shrink)

Prior to Kripke’s seminal work on the semantics of modal logic, McKinsey offered an alternative interpretation of the necessity operator, inspired by the Bolzano–Tarski notion of logical truth. According to this interpretation, ‘it is necessary that A’ is true just in case every sentence with the same logical form as A is true. In our paper, we investigate this interpretation of the modal operator, resolving some technical questions, and relating it to the logical interpretation of modality and some views (...) in modal metaphysics. In particular, we present an hitherto unpublished solution to problems 41 and 42 from Friedman’s 102 problems, which uses a different method of proof from the solution presented in the paper of Tadeusz Prucnal. (shrink)

Non-modalists about essence reject the idea that metaphysical modality is prior to essence, e.g., in the sense that the latter can be reduced to or defined in terms of the former. On the contrary, according to these theorists, the explanation, if anything, proceeds in the opposite direction: metaphysical modality does not explain, but is instead explained in terms of, essence. Thus, for non-modalists like Aristotle, Kit Fine and E. J. Lowe, one of the primary theoretical roles of essence is to (...) provide an explanatory basis for metaphysical necessity and possibility. This chapter explores a range of different types of explanatory connections which raise the question of how the non-modalist’s program of explaining metaphysical modality in terms of essence is best carried out. The considerations advanced in this chapter suggest that non-modalists must proceed by way of a non-logical case-by-case engagement with specific cases, since no logical “one-size-fits- all” strategy appears to be available. (shrink)

The principle of non-combatant immunity protects non-combatants against intentional attacks in war. It is the most widely endorsed and deeply held moral constraint on the conduct of war. And yet it is difficult to justify. Recent developments in just war theory have undermined the canonical argument in its favour – Michael Walzer's, in Just and Unjust Wars. Some now deny that non-combatant immunity has principled foundations, arguing instead that it is entirely explained by a different principle: that of necessity. (...) In war, as in ordinary life, harms to others can be justified only if they are necessary. Attacking non-combatants, the argument goes, is never necessary, so never justified. Although often repeated, this argument has never been explored in depth. In this article, I evaluate the necessity-based argument for non-combatant immunity, drawing together theoretical analysis and empirical research on anti-civilian tactics in interstate warfare, counterinsurgency, and terrorism. (shrink)

Necessity is a touchstone issue in the thought of Charles Peirce, not least because his pragmatist account of meaning relies upon modal terms. We here offer an overview of Peirce’s highly original and multi-faceted take on the matter. We begin by considering how a self-avowed pragmatist and fallibilist can even talk about necessary truth. We then outline the source of Peirce’s theory of representation in his three categories of Firstness, Secondness and Thirdness, (monadic, dyadic and triadic relations). These have (...) modal purport insofar as the first category corresponds to possibility, the second to mechanical necessity and the third to a kind of semantic or intentional necessity. We then turn to Peirce’s explicit modal epistemology and show how it began as information-relative, with different modalities (e.g. logical, physical, practical) distinguished in terms of respective ‘designated states of information’, and shifted later in his life towards a more robust realism founded in direct perception of ideas in their relations. We then turn to Peirce’s formal logic, focusing on his diagrammatic system of Existential Graphs where he did his most serious logical research. Finally we discuss Peirce’s modal metaphysics and its implications for determinism and realism about universals. (shrink)

In this paper I offer an alternative to the standard, mechanistic/fatalistic account of causal necessity, one compatible with the existence of laws of nature but not deterministic in the way this is usually understood.

The necessity of origin suggests that a person’s identity is determined by the particular pair of gametes from which the person originated. An implication is that speculative scenarios concerning how we might otherwise have been had our gametic origins been different are dismissed as being metaphysically impossible. Given, however, that many of these speculations are intelligible and commonplace in the discourses of competent speakers, it is overhasty to dismiss them as mistakes. This paper offers a way of understanding these (...) speculations that does not commit them to incoherence but aims to make the best sense of what they are expressing. Using the philosophical framework of two‐dimensional semantics, it proposes that the speculative scenarios are best analysed as epistemic possibilities, rather than as metaphysical possibilities. It then explores some implications of this analysis for the ethical challenges associated with the non‐identity problem. (shrink)

It is generally agreed that using lethal or otherwise serious force in self-defense is justified only when three conditions are satisfied: first, there are some grounds for the defender to give priority to his own interests over those of the attacker (whether because the attacker has lost the protection of his right to life, for example, or because of the defender’s prerogative to prefer himself to others); second, the harm used is proportionate to the threat thereby averted; third, the harm (...) is necessary to avert that threat. The first and second conditions have been exhaustively discussed, but the third has been oddly neglected. Meanwhile a prominent school of thought has arisen, in the ethics of war, which seeks to ground the justification of killing in war in principles of individual self-defense. They too have failed to offer any substantive analysis of necessity, while at the same time appealing to it when it suits them to do so. In this paper, I attempt a detailed analysis of the necessity constraint on defensive force, and explore the implications of that analysis for the attempt to transpose principles of individual self-defense into the context of warfare. (shrink)

My main purpose in this article is to present an argument for the idea that necessity qua truth in all possible worlds, without other qualifications, leads us to contradiction. If we do not want to accept the contradiction, we will face a dilemma: or accepting that everything we take as contingent is in fact necessary, or accepting that we cannot translate some sentences – at least the indexed to worlds sentences – to the possible worlds vocabulary. We have an (...) intuition – and we develop an argument for it – that if “P”, evaluated in w*, is a contingent truth, so it cannot be the case that “P in w*” is a necessary truth. Generally, the argument tries to show that “P”, evaluated in w*, and “P in w*” are made true by the same contingent fact. If we suppose that “P in w*” is necessary, we would have to suppose that the fact that makes it true is also necessary, which would be contradictory with the fact that makes “P” true in w*, if we accept that what makes “P” in w* and “P in w*” true is the same fact. I attain such an aim by presenting an argument that is divided in two parts, one to imply the contradiction and the other to show that there is no relevant difference between the indicated sentences, by showing how the dilemma arises, and by answering some possible objections. This is an important objective because the possible worlds vocabulary is the default vocabulary to treat the modalities of necessity and possibility. And if it is flawed, it is important that we identify the flaw and fix it – which is exactly what we intend to do at the end of this article, by suggesting some qualification at the necessity notion, that the necessity is the native truth in all possible worlds. And this would save the possible worlds vocabulary from the presented objection. (shrink)

What level of government subsidy of higher education is justified, in what form, and for what reasons? We answer these questions by applying the hypothetical insurance approach, originally developed by Ronald Dworkin in his work on distributive justice. On this approach, when asking how to fund and deliver public services in a particular domain, we should seek to model what would be the outcome of a hypothetical insurance market: we stipulate that participants lack knowledge about their specific resources (...) and risks, and ask what insurance contracts they would take out to secure different types of benefit and protection in the domain in question. The great benefit of the hypothetical insurance approach is that it allows us to take apparently intractable questions about interpersonal distribution and transform them into questions about intrapersonal distributions: that is, questions about how an individual would choose to distribute risks and resources across the various lives that they might end up living, in light of their individual ambitions and preferences. Applying this approach to higher education, we argue that the UK model of higher education funding in which the costs of an individual's higher education are shared between general taxation and the individual herself, with the latter element to be paid retrospectively through an income-contingent state-backed loan, is vindicated as just. In particular, we argue that it is more just than alternatives such as a graduate tax, full funding through general taxation, and full privatisation. (shrink)

There is a long tradition of logic, from Aristotle to Gödel, of understanding a proof from the concepts of necessity and causality. Gödel's attempts to define provability in terms of necessity led him to the distinction of formal and absolute (abstract) provability. Turing's definition of mechanical procedure by means of a Turing machine (TM) and Gödel's definition of a formal system as a mechanical procedure for producing formulas prompt us to understand formal provability as a mechanical causality. We (...) propose a formalism which makes explicit the mechanical causal nature of a TM's work. We claim that Gödel's axiomatised ontotheology and his ontological proof give a clue for the understanding of the concept of absolute provability and the pattern of the corresponding absolute completeness proof, respectively. (shrink)

In many diagrams one seems to perceive necessity – one sees not only that something is so, but that it must be so. That conflicts with a certain empiricism largely taken for granted in contemporary philosophy, which believes perception is not capable of such feats. The reason for this belief is often thought well-summarized in Hume's maxim: ‘there are no necessary connections between distinct existences’. It is also thought that even if there were such necessities, perception is too passive (...) or localized a faculty to register them. We defend the perception of necessity against such Humeanism, drawing on examples from mathematics. (shrink)

Data involving epistemic modals suggest that some classically valid argument forms, such as _reductio_, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a _de re–de dicto_ collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern the (...) use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic. (shrink)

In "Essence and Modality", Kit Fine proposes that for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of all objects whatsoever. Call this view Fine's Thesis. This paper is a study of Fine's Thesis in the context of Fine's logic of essence (LE). Fine himself has offered his most elaborate defense of the thesis in the context of LE. His defense rests on the widely shared assumption that metaphysical necessity obeys (...) the laws of the modal logic S5. In order to get S5 for metaphysical necessity, he assumes a controversial principle about the nature of all objects. I will show that the addition of this principle to his original system E5 leads to inconsistency with an independently plausible principle about essence. In response, I develop a theory that avoids this inconsistency while allowing us to maintain S5 for metaphysical necessity. However, I conclude that our investigation of Fine's Thesis in the context of LE motivates the revisionary conclusion that metaphysical necessity obeys the principles of the modal logic S4, but not those of S5. I argue that this constitutes a distinctively essentialist challenge to the received view that the logic of metaphysical necessity is S5. (shrink)