We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords a purely combinatorial (...) characterisation of polyhedrally complete logics. Using the Nerve Criterion we show, easily, that there are continuum many intermediate logics that are not polyhedrally complete but which have the finite model property. We also provide, at considerable combinatorial labour, a countably infinite class of logics axiomatised by the Jankov–Fine formulas of ‘starlike trees’ all of which are polyhedrally complete. The polyhedral completeness theorem for these ‘starlike logics’ is the second main result of this paper. (shrink)

The theory of embodiment is used in providing an account of the identity of acts and in providing solutions to various puzzles concerning acts.

Throughout the history of mankind, energy security has been always seen as a means of protection from disruptions of essential energy systems. The idea of protection from disorders emerged from the process of securing political and military control over energy resources to set up policies and measures on managing risks that affect all elements of energy systems. The various systems placed in a place to achieve energy security are the driving force towards the energy innovations or emerging trends in the (...) energy sector. Our paper discusses energy security status and innovations in the energy sector in European Union (EU). We analyze the recent up-to-date developments of the energy policy and exploitation of energy sources, as well as scrutinize the channels of energy streaming to the EU countries and the risks associated with this energy import. Moreover, we argue that the shift to the low-carbon production of energy and the massive deployment of renewable energy sources (RES) might become the key issue in ensuring the energy security and independency of the EU from its external energy supplies. Both RES, distributed energy resources (DER) and “green energy” that will be based on the energy efficiency and the shift to the alternative energy supply might change the energy security status quo for the EU. (shrink)

In this chapter, we focus on collective action and intention, and their relation to conventions, status functions, norms, institutions, and shared attitudes more generally. Collective action and shared intention play a foundational role in our understanding of the social. -/- The three central questions in the study of collective intentionality are: -/- (1) What is the ontology of collective intentionality? In particular, are groups per se intentional agents, as opposed to just their individual members? (2) What is the psychology of (...) collective intentionality? Do groups per se have psychological states, in particular propositional attitudes? What is the psychology of the individuals who participate in collective intentional behavior? What is special about their participatory intentions, their we-intentions, as they are called (Tuomela and Miller 1988), as opposed to their I-intentions? (3) How is collective intentionality implicated in the construction of social reality? In particular, how does the content of we-intentions and the intentional activity of individual agents create social institutions, practices and structures? -/- We first discuss collective action and shared intention in informal groups. Next we discuss mechanisms for constructing institutional structures out of the conceptual and psychological resources made available by our understanding of informal joint intentional action. Then we extend the discussion of collective action and intention to institutional groups, such as the Supreme Court, and explain how concepts of such organizations are constructed out of the concepts of a rule, convention, and status function. Finally we discuss collective attitudes beyond intention. (shrink)

We argue that there is a variety of convention, effective coordinating agreement, that has not been adequately identified in the literature. Its distinctive feature is that it is a structure of conditional we-intentions of parties, unlike more familiar varieties of convention, which are structures of expectations and preferences or obligations. We argue that status functions constitutively involve this variety of convention, and that what is special about it explains, and gives precise content to the central feature of status functions, namely, (...) that objects with status functions can perform their functions only insofar as they have been collectively accepted as having them. (shrink)

It is often argued that development aid can and should compensate the restrictions on migration. Such compensation, Shachar has recently argued, should be levied as a tax on citizenship to further the global equality of opportunity. Since citizenship is essentially a ‘birthright lottery’, that is, a way of legalizing privileges obtained by birth, it would be fair to compensate the resulting gap in opportunities available to children born in rich versus poor countries by a ‘birthright privilege levy’. This article sets (...) out a defence of three theses. The first states that equality of opportunity is incompatible with, and cannot be achieved in, segregated territories. The second posits that to believe that material equality compensates the injustice of restrictions on movement is to commit a ‘sedentarist mistake’. The third affirms that any citizenship levy, including the egalitarian and non-sedentarist formula I’m proposing, would be better understood as a penalty rather than a tax. (shrink)

In recent years, a growing discussion about how we should design our cities has emerged, particularly for the more controversial modes of design such as “defensive,” “hostile,” or “disciplinary” architecture (i.e., benches on which one cannot sleep, or metal studs on which one cannot skate). Although this debate is relatively mature, many studies have argued that these design notions are undertheorized and are, thus, challenging to study from an empirical and normative perspective. In this paper, I will defne the most (...) common terms used in the literature and show how they are interconnected by utilizing a set of “conditions of adequacy” from philosophy to facilitate a more transparent and well-grounded discussion of them. Terms such as “hostile” and “defensive” design are underlined by several diferent phenomena, not just one as is sometimes commonly assumed. I will also show that these phenomena and their conceptualizations require—and sometimes force us to use—diferent moral reasons when justifying the utilization of diferent designs. (shrink)

This paper establishes a sound and complete semantics for the impure logic of ground. Fine (Review of Symbolic Logic, 5(1), 1–25, 2012a) sets out a system for the pure logic of ground, one in which the formulas between which ground-theoretic claims hold have no internal logical complexity; and it provides a sound and complete semantics for the system. Fine (2012b) [§§6-8] sets out a system for an impure logic of ground, one that extends the rules of the original pure system (...) with rules for the truth-functional connectives, the first-order quantifiers, and λ-abstraction. However, no semantics has yet been provided for this system. The present paper partly fills this lacuna by providing a sound and complete semantics for a system GG containing the truth-functional operators that is closely related to the truth-functional part of the system of Fine (2012b). (shrink)

Epistemic paternalism is the practice of interfering in the process of inquiry of another,without prior consultation and for the sake of her epistemic good. We will examine two main types of epistemic paternalism: eudaimonic and strict. In the case of eudaimonic epistemic paternalism, epistemic improvement is used only as a means to achieve non-epistemic benefits. In the case of strict epistemic paternalism, epistemic improvement is valued as a good in itself. The main objection against each type of epistemic paternalism is (...) that this practice leads to a violation of personal autonomy. We will defend a more moderate form of strict epistemic paternalism which is motivated by both epistemic and non-epistemic benefits. At the same time, this moderate form leads to the development of specific epistemic virtues, which results in an increase rather than a violation of personal autonomy. We will show that the question of the justification of epistemic paternalism is especially relevant in crises, such as the current pandemic caused by the covid-19 virus. (shrink)

I attempt to meet some criticisms that Williamson makes of my attempt to carry out Prior's project of reducing possibility discourse to actualist discourse.

An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of (...) entailment, showing that it is compact and decidable. We then investigate the effect of various restrictions on the semantics. We also formulate a sequent-style proof system for exact entailment and give soundness and completeness results. (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)

A significant strand of the ethical psychology, aesthetics and politics of Plato's Republic revolves around the concept of poikilia, ‘fascinating variety’. Plato uses the concept to caution against harmful appetitive pleasures purveyed by democracy and such artistic or cultural practices as mimetic poetry. His aim, this article shows, is to contest a prominent conceptual connection between poikilia and beauty (kallos, to kalon). Exploiting tensions in the archaic and classical Greek concept, Plato associates poikilia with dangerous pleasures to redirect admiration toward (...) a distinctly philosophical pursuit of the nature of beauty. This is to displace a prominent and problematic cultural sensibility—the aesthetics of poikilia—not to deny that fascinating variety, even in mimetic poetry, may be beautiful. Rather, Plato's cultural critique lays bare an epistemological problem in the ethical psychology of beauty: since they cannot be distinguished from what seems beautiful, how should one respond to fascinating yet dangerous attractions? (shrink)

A crux of Plato’s Symposium is how beauty relates to the good. Diotima distinguishes beauty from the good, I show, to explain how erotic pursuits are characteristically ambivalent and opaque. Human beings pursue beauty without knowing why or thinking it good; yet they are rational, if aiming at happiness. Central to this reconstruction is a passage widely taken to show that beauty either coincides with the good or demands disinterested admiration. It shows rather that what one loves as beautiful does (...) not appear good, a proposal with ramifications for ethical psychology. (shrink)

This volume in the Oxford Readings in Philosophy looks at central areas in Plato's philosophy: ethics, politics, religion, and the soul. It includes essays on virtue, knowledge, and happiness; justice and happiness; pleasure; Platonic love; feminism; the ideally just state, democracy and totalitarianism; and the nature of the soul and moral motivation.

[Condensed abstract] Socrates' ironic use of 'makaria' (blessedness) in the Republic exhorts Glaucon to think more critically. Certain features of the supposedly ideal city, motivated by Glaucon's character, may be protreptic for Glaucon to practice philosophical courage and intellectual moderation.

This chapter presents several of the dominant ideas and intellectual debates about human beauty from archaic Greece to early Christianity. At issue are ideals of character, ethical ideals of who one should be and how one should live. What constitutes beauty and why beauty matters change alongside conceptions of body and soul, virtue and happiness, and the relationship between human beings and the divine.

This paper pursues the philosophical significance of a relatively unexplored point of Platonic aesthetics: the social dimension of beauty. The social dimension of beauty resides in its conceptual connection to shame and honour. This dimension of beauty is fundamental to the aesthetic education of the Republic, as becoming virtuous for Plato presupposes a desire to appear and to be admired as beautiful. The ethical significance of beauty, shame, and honour redound to an ethically rich notion of appearing before others which (...) corresponds to a public conception of virtue. I suggest how this dimension of beauty in Plato – particularly the emphasis on beautification – proves fruitful for reconsidering the scope and the nature of aesthetic experience. (shrink)

This series aims to bring together important recent writing in major areas of philosophical inquiry, selected from a variety of sources. The editor of each volume contributes an introductory essay on the items chosen and on the questions with which they deal. A selective bibliography is appended as a guide to further reading.

Review of the first comprehensive companion to the growing scholarship on ancient Greek and Roman aesthetics.

The Simulation Hypothesis proposes that all of reality, including the earth and the universe, is in fact an artificial simulation, analogous to a computer simulation, and as such our reality is an illusion. In this essay I describe a method for programming mass, length, time and charge (MLTA) as geometrical objects derived from the formula for a virtual electron; $f_e = 4\pi^2r^3$ ($r = 2^6 3 \pi^2 \alpha \Omega^5$) where the fine structure constant $\alpha$ = 137.03599... and $\Omega$ = (...) 2.00713494... are mathematical constants and the MLTA geometries are; M = (1), T = ($2\pi$), L = ($2\pi^2\Omega^2$), A = ($4\pi \Omega)^3/\alpha$. As objects they are independent of any set of units and also of any numbering system, terrestrial or alien. As the geometries are interrelated according to $f_e$, we can replace designations such as ($kg, m, s, A$) with a rule set; mass = $u^{15}$, length = $u^{-13}$, time = $u^{-30}$, ampere = $u^{3}$. The formula $f_e$ is unit-less ($u^0$) and combines these geometries in the following ratio M$^9$T$^{11}$/L$^{15}$ and (AL)$^3$/T, as such these ratio are unit-less. To translate MLTA to their respective SI Planck units requires an additional 2 unit-dependent scalars. We may thereby derive the CODATA 2014 physical constants via the 2 (fixed) mathematical constants ($\alpha, \Omega$), 2 dimensioned scalars and the rule set $u$. As all constants can be defined geometrically, the least precise constants ($G, h, e, m_e, k_B$...) can also be solved via the most precise ($c, \mu_0, R_\infty, \alpha$), numerical precision then limited by the precision of the fine structure constant $\alpha$. (shrink)

There is a curious bifurcation in the literature on ground and its logic. On the one hand, there has been a great deal of work that presumes that logical complexity invariably yields grounding. So, for instance, it is widely presumed that any fact stated by a true conjunction is grounded in those stated by its conjuncts, that any fact stated by a true disjunction is grounded in that stated by any of its true disjuncts, and that any fact stated by (...) a true double negation is grounded in that stated by the doubly-negated formula. This commitment is encapsulated in the system GG axiomatized and semantically characterized by [deRosset and Fine, 2023] (following [Fine, 2012]). On the other hand, there has been a great deal of important formal work on “flatter” theories of ground, yielding logics very different from GG [Correia, 2010] [Fine, 2016, 2017b]. For instance, these theories identify the fact stated by a self-conjunction $$(\phi \wedge \phi )$$ with that stated by its conjunct $$\phi $$. Since, in these systems, no fact grounds itself, the “flatter” theories are inconsistent with the principles of GG. This bifurcation raises the question of whether there is a single notion of ground suited to fulfill the philosophical ambitions of grounding enthusiasts. There is, at present, no unified semantic framework employing a single conception of ground for simultaneously characterizing both GG and the “flatter” approaches. This paper fills this gap by specifying such a framework and demonstrating its adequacy. (shrink)

What is money? Paraphrasing Goodman, I say that’s the wrong question to ask. The right question is, When is money? And to get the answer, Searle’s general formula for social objects (X couns as Y in context C) is fine, as long as you give it a different reading.

In this paper I will present three arguments (based on the notions of constitution, metaphysical reality, and truth, respectively) with the aim of shedding some new light on the structure of Fine’s (2005, 2006) ‘McTaggartian’ arguments against the reality of tense. Along the way, I will also (i) draw a novel map of the main realist positions about tense, (ii) unearth a previously unnoticed but potentially interesting form of external relativism (which I will label ‘hyper-presentism’) and (iii) sketch a novel (...) interpretation of Fine’s fragmentalism (which I contrast with Lipman’s 2015, 2016b, forthcoming). (shrink)

Fine (2005, 2006) has presented a ‘trilemma’ concerning the tense-realist idea that reality is constituted by tensed facts. According to Fine, there are only three ways out of the trilemma, consisting in what he takes to be the three main families of tense-realism: ‘presentism’, ‘(external) relativism’, and ‘fragmentalism’. Importantly, although Fine characterises tense-realism as the thesis that reality is constituted (at least in part) by tensed facts, he explicitly claims that tense realists are not committed to their fundamental existence. Recently, (...) Correia and Rosenkranz (2011, 2012) have claimed that Fine’s tripartite map of tense realism is incomplete as it misses a fourth position they call ‘dynamic absolutism’. In this paper, I will argue that dynamic absolutists are committed to the irreducible existence of tensed facts and that, for this reason, they face a similar trilemma concerning the notion of fact-content. I will thus conclude that a generalised version of Fine’s trilemma, concerning both fact-constitution and fact-content, is indeed inescapable. (shrink)

According to the Fine-Tuning Argument, the existence of life in our universe confirms the Multiverse Hypothesis. A standard objection to FTA is that it violates the Requirement of Total Evidence. I argue that RTE should be rejected in favor of the Predesignation Requirement, according to which, in assessing the outcome of a probabilistic process, we should only use evidence characterizable in a manner available before observing the outcome. This produces the right verdicts in some simple cases in which RTE leads (...) us astray, and, when applied to FTA, it shows that our evidence does confirm HM. (shrink)

I offer an interpretation and a partial defense of Kit Fine's ‘Argument from Passage’, which is situated within his reconstruction of McTaggart's paradox. Fine argues that existing A-theoretic approaches to passage are no more dynamic, i.e. capture passage no better, than the B-theory. I argue that this comparative claim is correct. Our intuitive picture of passage, which inclines us towards A-theories, suggests more than coherent A-theories can deliver. In Finean terms, the picture requires not only Realism about tensed facts, but (...) also Neutrality, i.e. the tensed facts not being ‘oriented towards’ one privileged time. However unlike Fine, and unlike others who advance McTaggartian arguments, I take McTaggart's paradox to indicate neither the need for a more dynamic theory of passage nor that time does not pass. A more dynamic theory is not to be had: Fine's ‘non-standard realism’ amounts to no more than a conceptual gesture. But instead of concluding that time does not pass, we should conclude that theories of passage cannot deliver the dynamicity of our intuitive picture. For this reason, a B-theoretic account of passage that simply identifies passage with the succession of times is a serious contender. (shrink)

Could God have created a better universe? Well, the fundamental scientific laws and parameters of the universe have to be within a certain miniscule range, for a life-sustaining universe to develop: the universe must be ‘Fine Tuned’. Therefore the ‘embryonic universe’ that came into existence with the ‘big bang’ had to be either exactly as it was or within a certain tiny range, for there to develop a life-sustaining universe. If it is better that there exist a life-sustaining universe than (...) not, then it was better that the embryonic universe was one of this small set of very similar embryonic universes than that it was not. Furthermore, there are no firm grounds for claiming that of this small set of very similar embryonic universes, there is one which would have developed into a universe better than ours. Therefore there are no firm grounds for claiming that God could have created a better universe than ours. (shrink)

In this paper, I propose that, in addition to the multiverse hypothesis, which is commonly taken to be an alternative explanation for fine-tuning, other than the design hypothesis, the simulation hypothesis is another explanation for fine-tuning. I then argue that the simulation hypothesis undercuts the alleged evidential connection between ‘designer’ and ‘supernatural designer of immense power and knowledge’ in much the same way that the multiverse hypothesis undercuts the alleged evidential connection between ‘fine-tuning’ and ‘fine-tuner’ (or ‘designer’). If this is (...) correct, then the fine-tuning argument is a weak argument for the existence of God. (shrink)

Do philosophers use intuitions? Should philosophers use intuitions? Can philosophical methods (where intuitions are concerned) be improved upon? In order to answer these questions we need to have some idea of how we should go about answering them. I defend a way of going about methodology of intuitions: a metamethodology. I claim the following: (i) we should approach methodological questions about intuitions with a thin conception of intuitions in mind; (ii) we should carve intuitions finely; and, (iii) we should carve (...) to a grain to which we are sensitive in our everyday philosophising. The reason is that, unless we do so, we don’t get what we want from philosophical methodology. I argue that what we want is information that will aid us in formulating practical advice concerning how to do philosophy responsibly/well/better. (shrink)

Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new category of entity, (...) are we theoreticians epistemically justified in holding that there are such entities? This would hardly seem sufficient. To be epistemically justified, the ontology to which we theoreticians are committed must pass strict standards: the entities must be of the sort required by our best comprehensive theory of the world. The thesis of this paper is that fine-grained type-free intensional entities are like this. If the thesis is right, these entities have a special objective status perhaps not possessed by some of the other ontological categories associated with special syntactic constructions in natural language. In fact, it is plausible to hold that fine-grained type-free intensional entities provide the proper minimal framework for constructing logical and linguistic theories. In this paper my strategy will be to survey the competing conceptions of fine-grained type-free intensionality and to present arguments in support of one of them. Following this narrowing down process, I will go on to the indicated epistemological considerations. (shrink)

Perry Hendricks’ original impairment argument for the immorality of abortion is based on the impairment principle (TIP): if impairing an organism to some degree is immoral, then ceteris paribus, impairing it to a higher degree is also immoral. Since abortion impairs a fetus to a higher degree than fetal alcohol syndrome (FAS) and giving a fetus FAS is immoral, it follows that abortion is immoral. Critics have argued that the ceteris paribus is not met for FAS and abortion, and so (...) we proposed the Modified Impairment Principle (MIP) to avoid these difficulties. Dustin Crummett has responded, arguing that MIP is open to various counterexamples which show it to be false. He also shows that MIP can generate moral dilemmas. Here, we propose a modification to MIP that resolves the issues Crummett raises. Additionally, Alex Gillham has criticized our appropriation of Don Marquis’ ‘future like ours’ reasoning about the wrongness of impairment. We show that his objections have minimal implications for our argument. (shrink)

The fundamental constants that are involved in the laws of physics which describe our universe are finely-tuned for life, in the sense that if some of the constants had slightly different values life could not exist. Some people hold that this provides evidence for the existence of God. I will present a probabilistic version of this fine-tuning argument which is stronger than all other versions in the literature. Nevertheless, I will show that one can have reasonable opinions such that the (...) fine-tuning argument doesn’t lead to an increase in one’s probability for the existence of God. (shrink)

Can pornographic depictions have artistic value? Much pornography closely resembles art, at least in many superficial respects. Films, photographs, paintings—all of these can have artistic value. Of course, films, photographs and paintings can also be pornographic. If some photographs have artistic value, and some photographs are pornographic, can pornographic photographs have artistic value too? I argue that pornography may only possess artistic value despite, not by virtue of, its pornographic content.

I observe that the “concept-generator” theory of Percus and Sauerland (2003), Anand (2006), and Charlow and Sharvit (2014) does not predict an intuitive true interpretation of the sentence “Plato did not believe that Hesperus was Phosphorus”. In response, I present a simple theory of attitude reports which employs a fine-grained semantics for names, according to which names which intuitively name the same thing may have distinct compositional semantic values. This simple theory solves the problem with the concept-generator theory, but, as (...) I go on to show, it has problems of its own. I present three examples which the concept-generator theory can accommodate, but the simple fine-grained theory cannot. These examples motivate the full theory of the paper, which combines the basic ideas behind the concept-generator theory with a fine-grained semantics for names. The examples themselves are of interest independently of my theory: two of them constrain the original concept-generator theory more tightly than previously discussed examples had. (shrink)

A central objection to McDowell’s conceptualism about empirical content concerns the fine-grained phenomenology of experience, which supposedly entails that the actual content of experience cannot be matched in its particularity by our concepts. While McDowell himself has answered this objection in recourse to the possibility of demonstrative concepts, his reply has engendered a plethora of further objections and is widely considered inadequate. I believe that McDowell’s critics underestimate the true force of his reply because they tend to read unrecognized empiricist (...) presuppositions into his account of experience. To show this, I introduce a new hylomorphic reading of McDowell’s account of experience and argue that the objections to his reply all rest on a specific empiricist assumption, which is untenable because it conflates the form of experience with its content. Consequently, conceptualism so understood can resist all of these objections, as I attempt to show by systematizing and answering them. (shrink)

Kit Fine, the leading proponent of the metaphysical project of grounding theory, has offered a number of potentially devastating objections to truthmaker theory, the branch of metaphysics dedicated to exploring the ontological grounds for truths. In this paper I show what presuppositions about truthmaker theory Fine’s objections are based upon, and why they are false. I discuss four objections that Fine raises, and demonstrate how truthmaker theorists may respond to them. I then showcase the positive contribution that truthmaker theory can (...) make to metaphysics, including its ability to speak to a core metaphysical topic (the ontological grounds for truths) that Fine’s approach to grounding must ultimately remain silent on. I conclude by exploring what I take to be the best option when it comes to understanding how truthmaking and grounding fit together. (shrink)

The Monster Objection has often been considered one of the main reasons to explore non-standard mereological views, such as hylomorphism. Still, it has been rarely discussed and then only in a cursory fashion. This paper fills this gap by offering the first thorough assessment of the objection. It argues that different metaphysical stances, such as presentism and three- and four-dimensionalism, provide different ways of undermining the objection.

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas (...) and results, and outline further research perspectives. (shrink)

In his paper ‘The possibility of vagueness’ (Fine in Synthese 194(10):3699–3725, 2017), Kit Fine proposes a new logic of vagueness, CL, that promises to provide both a solution to the sorites paradox and a way to avoid the impossibility result from Fine (Philos Perspect 22(1):111–136, 2008). The present paper presents a challenge to his new theory of vagueness. I argue that the possibility theorem stated in Fine (Synthese 194(10):3699–3725, 2017), as well as his solution to the sorites paradox, fail in (...) certain reasonable extensions of the language of CL. More specifically, I show that if we extend the language with any negation operator that obeys reductio ad absurdum, we can prove a new impossibility result that makes the kind of indeterminacy that Fine takes to be a hallmark of vagueness impossible. I show that such negation operators can be conservatively added to CL and examine some of the philosophical consequences of this result. Moreover, I demonstrate that we can define a particular negation operator that behaves exactly like intuitionistic negation in a natural and unobjectionable propositionally quantified extension of CL. Since intuitionistic negation obeys reductio, the new impossibility result holds in this propositionally quantified extension of CL. In addition, the sorites paradox resurfaces for the new negation. (shrink)

Kant’s most prominent formulation of the Categorical Imperative, known as the Formula of Universal Law (FUL), is generally thought to demand that one act only on maxims that one can will as universal laws without this generating a contradiction. Kant's view is standardly summarized as requiring the 'universalizability' of one's maxims and described in terms of the distinction between 'contradictions in conception' and 'contradictions in the will'. Focusing on the underappreciated significance of the simultaneity condition included in the FUL, (...) I argue, by contrast, that the principle is better read as requiring that one be able to will two things simultaneously without self-contradiction, namely, that a maxim be one's own and that it be a universal law. This amounts to a new interpretation of the FUL with significant interpretive and philosophical advantages. (shrink)

I present a novel objection to fine-tuning arguments for God's existence. On any values of the physical constants, the psychophysical laws could be set to permit intelligent and happy beings, so the specific values of the physical constants in our world provide little evidence for God's existence. For example, even if the physical constants didn't allow carbon or any atoms larger than hydrogen, the psychophysical laws could be set so that charge is sufficient to realize romantic desire. Then every hydrogen (...) atom would be a proton and electron in love. (shrink)

The fine-structure constant, which determines the strength of the electromagnetic interaction, is briefly reviewed beginning with its introduction by Arnold Sommerfeld and also includes the interest of Wolfgang Pauli, Paul Dirac, Richard Feynman and others. Sommerfeld was very much a Pythagorean and sometimes compared to Johannes Kepler. The archetypal Pythagorean triangle has long been known as a hiding place for the golden ratio. More recently, the quartic polynomial has also been found as a hiding place for the golden ratio. The (...) Kepler triangle, with its golden ratio proportions, is also a Pythagorean triangle. Combining classical harmonic proportions derived from Kepler’s triangle with quartic equations determine an approximate value for the fine-structure constant that is the same as that found in our previous work with the golden ratio geometry of the hydrogen atom. These results make further progress toward an understanding of the golden ratio as the basis for the fine-structure constant. (shrink)

After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with the golden (...) ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients. (shrink)

This paper defends a novel sceptical response to the fine-tuning argument for the existence of God (FTA). According to this response, even if FTA can establish, what I call, the confirmation proposition: ‘fine-tuning confirms the God hypothesis’, there is no reason to think that a strengthening of FTA can establish the evidence-favouring proposition: ‘fine-tuning favours the God hypothesis over its competitors’. My argument is that, any criteria for the explanation of fine-tuning that permit us to take the God hypothesis seriously (...) ought to make us sceptical that fine-tuning favours the God hypothesis over its competitors. As taking the God hypothesis seriously requires us to give a fair hearing to all sorts of non-theistic explanations, including the so-called weird sorts of atheism. (shrink)

After briefly outlining the fine-tuning argument (FTA), I explain how it relies crucially on the claim that it is not improbable that God would design a fine-tuned universe. Against this premise stands the divine psychology objection: the contention that the probability that God would design a fine-tuned universe is inscrutable. I explore three strategies for meeting this objection: (i) denying that the FTA requires any claims about divine psychology in the first place, (ii) defining the motivation and intention to design (...) a fine-tuned universe into the theistic hypothesis, and (iii) providing arguments that the relevant probability is not terribly low. While I reject the first two, I conclude, in line with the third, that considerations about life's objective value establish that it is not absurdly improbable that God would design a fine-tuned universe, whether one regards the FTA as an inference merely to a cosmic designer, or to theism proper. Accordingly, the divine psychology objection fails. (shrink)

In this article, we provide three generators of propositional formulae for arbitrary languages, which uniformly sample three different formulae spaces. They take the same three parameters as input, namely, a desired depth, a set of atomics and a set of logical constants (with specified arities). The first generator returns formulae of exactly the given depth, using all or some of the propositional letters. The second does the same but samples up-to the given depth. The third generator outputs formulae with exactly (...) the desired depth and all the atomics in the set. To make the generators uniform (i.e. to make them return every formula in their space with the same probability), we will prove various cardinality results about those spaces. (shrink)

Formula thinking is a kind of thinking strictly by route in which the thinker never deviates from a set course. Craft thinking involves a rough approximation to a set course but allows for deviation. The arts involve craft thinking. Repairing a machine involves formula thinking. America has become almost completely dominated by formula thinking.