We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.

Sometimes it is indeterminate what an agent morally ought do. This generates a Decision Ought Challenge—to give moral guidance to agents in such a scenario. This article is a field guide to the options for a theory of the decision ought for cases of indeterminacy. Three categories of view are evaluated, and the best representative for each is identified.

This study’s objective was to understand Colombian adolescents’ experiences and preferences regarding access to sexual and reproductive health services (SRHS), either alone or accompanied. A mixed-method approach was used, involving a survey of 812 participants aged eleven to twenty-four years old and forty-five semi-structured interviews with participants aged fourteen to twenty-three. Previous research shows that adolescents prefer privacy when accessing SRHS and often do not want their parents involved. Such findings align with the longstanding tendency to frame the ethical principle (...) of autonomy as based on independence in decision-making. However, the present study shows that such a conceptualization and application of autonomy does not adequately explain Colombian adolescent participants’ preferences regarding access to SRHS. Participants shared a variety of preferences to access SRHS, with the majority of participants attaching great importance to having their parents involved, to varying degrees. What emerges is a more complex and non-homogenous conceptualization of autonomy that is not inherently grounded in independence from parental involvement in access to care. We thus argue that when developing policies involving adolescents, policymakers and health professionals should adopt a nuanced “relational autonomy” approach to better respect the myriad of preferences that Colombian (and other) adolescents may have regarding their access to SRHS. (shrink)

A standard line in the contemporary philosophical literature has it that physical theories are equivalent only when they agree on their empirical content, where this empirical content is often understood as being encoded in the equations of motion of those theories. In this article, we question whether it is indeed the case that the empirical content of a theory is exhausted by its equations of motion, showing that (for example) considerations of boundary conditions play a key role in the empirical (...) equivalence (or otherwise) of theories. Having argued for this, we show that philosophical claims made by Weatherall (2016) that electromagnetism in the Faraday tensor formalism is equivalent to electromagnetism in the vector potential formalism, and by Knox (2011) that general relativity is equivalent to teleparallel gravity, can both be called into question. We then show that properly considering the role of boundary conditions in theory structure can potentially restore these claims of equivalence and close with some remarks on the pragmatics of adjudications on theory identity. (shrink)

It is now well-known that Newton–Cartan theory is the correct geometrical setting for modelling the quantum Hall effect. In addition, in recent years edge modes for the Newton–Cartan quantum Hall effect have been derived. However, the existence of these edge modes has, as of yet, been derived using only orthodox methodologies involving the breaking of gauge-invariance; it would be preferable to derive the existence of such edge modes in a gauge-invariant manner. In this article, we employ recent work by Donnelly (...) and Freidel in order to accomplish exactly this task. Our results agree with known physics, but afford greater conceptual insight into the existence of these edge modes: in particular, they connect them to subtle aspects of Newton–Cartan geometry and pave the way for further applications of Newton–Cartan theory in condensed matter physics. (shrink)

In this paper, I argue that although Kant’s account of empirical schemata in the Critique of Pure Reason is primarily used to explain the shared content of intuitions and empirical concepts, it is also informed by methodological problems in natural history. I argue that empirical schemata, which are rules for determining the spatiotemporal form of objects, not only serve to connect individual intuitions with concepts, but also concern the very features of objects on the basis of which they were connected (...) and ordered in taxonomic systems based on similarity of form. I then suggest that Kant likely had scientific illustrations in mind in his discussion of empirical images in the Schematism chapter and that his account of schemata can help explain the epistemic function of these images in early modern science. (shrink)

Many accounts of structural rationality give a special role to logic. This paper reviews the problem case of clear-eyed logical uncertainty. An account of rational norms on belief that does not give a special role to logic is developed: doxastic probabilism.

Inscrutability arguments threaten to reduce interpretationist metasemantic theories to absurdity. Can we find some way to block the arguments? A highly influential proposal in this regard is David Lewis’ ‘ eligibility ’ response: some theories are better than others, not because they fit the data better, but because they are framed in terms of more natural properties. The purposes of this paper are to outline the nature of the eligibility proposal, making the case that it is not ad hoc, but (...) instead flows naturally from three independently motivated elements; and to show that severe limitations afflict the proposal. In conclusion, I pick out the element of the eligibility response that is responsible for the limitations: future work in this area should therefore concentrate on amending this aspect of the overall theory. (shrink)

In this paper, I argue that Kant has a far more communitarian theory of aesthetic life than is usually acknowledged. I focus on two aspects of Kant’s theory that might otherwise be taken to support an individualist reading, namely, Kant’s emphasis on aesthetic autonomy and his characterization of judgments of taste as involving demands for agreement. I argue that the full expression of autonomy in fact requires being a member of an aesthetic community and that within such a community, judgments (...) of taste are issued as invitations to others to engage their faculties towards the goal of shared aesthetic appreciation. (shrink)

The harmonious free play of the imagination and understanding is at the heart of Kant’s account of beauty in the Critique of the Power of Judgement, but interpreters have long struggled to determine what Kant means when he claims the faculties are in a state of free play. In this article, I develop an interpretation of the free play of the faculties in terms of the freedom of attention. By appealing to the different way that we attend to objects in (...) aesthetic experience, we can explain how the faculties are free, even when the subject already possesses a concept of the object and is bound to the determinate form of the object in perception. (shrink)

This article investigates the claim that some truths are fundamentally or really true — and that other truths are not. Such a distinction can help us reconcile radically minimal metaphysical views with the verities of common sense. I develop an understanding of the distinction whereby Fundamentality is not itself a metaphysical distinction, but rather a device that must be presupposed to express metaphysical distinctions. Drawing on recent work by Rayo on anti-Quinean theories of ontological commitments, I formulate a rigourous theory (...) of the notion. In the final sections, I show how this package dovetails with ' interpretationist' theories of meaning to give sober content to thought that some things — perhaps sets, or gerrymandered mereological sums — can be 'postulated into existence'. (shrink)

In this paper, I examine the role of attention in Kant’s aesthetic theory in the Critique of the Power of Judgment. While broadly Kantian aestheticians have defended the claim that there is a distinct way that we attend to objects in aesthetic experience, Kant himself is not usually acknowledged as offering an account of aesthetic attention. On the basis of Kant’s more general account of attention in other texts and his remarks on attention in the Critique of the Power of (...) Judgment, I reconstruct Kant’s account of aesthetic attention. On this account, aesthetic attention is simultaneously directed at the form of an object and at the judging subject’s own mental states as she attends to the object. In the experience of beauty, we specifically attend to the harmonious relation between the faculties of imagination and understanding. (shrink)

The question of the cognitive role of fictionality is this: what is the correct cognitive attitude to take to p, when it is fictional that p? We began by considering one answer to this question, implicit in the work of Kendall Walton, that the correct response to a fictional proposition is to imagine that proposition. However, this approach is silent in cases of fictional incompleteness, where neither p nor its negation are fictional. We argue that that Waltonians should embrace a (...) pluralistic account of the cognitive role of fictional incompleteness: in some cases of fictional incompleteness, we are permitted to resolve the incompleteness during our engagement with the target fiction, and in other cases, we are obliged not to resolve the incompleteness. But though pluralism is accommodated by Walton’s wider account of fictionality, it puts tension on his motivating idea that fictionality stands to the imagination as truth stands to belief. And so we develop a rival conception of the cognitive role of fictionality that is built around a different analogy: on this evidentialist approach, (known) fictionality stands to the imagination as evidence stands to credence. (shrink)

Why should we be means-end rational? Why care whether someone’s mental states exhibit certain formal patterns, like the ones formalized in causal decision theory? This paper establishes a dominance argument for these constraints in a finite setting. If you violate the norms of causal decision theory, then your desires will be aptness dominated. That is, there will be some alternative set of desires that you could have had, which would be more apt (closer to the actual values fixed by your (...) sensibility/ what you intrinsically care about) no matter which world is actual. If we care about having apt desires, then, we should never let ourselves violate these norms of means-end rationality. This argument shares a form with now-standard accuracy arguments for probabilism, opening up a new terrain for that discussion. I show that the foundational assumptions about the shape of accuracy and of aptness required to run the arguments for means-end rationality and for probabilism run closely parallel. I show the argument is robust under different theories of subjective actual value, including nonclassical treatments of indeterminacy in actual value; I show the argument may (but need not!) be generalized to objective theories of value. The upshot is that aptness-domination arguments for decision theories should be added to the philosophical playbook. (shrink)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

Decisions are made under uncertainty when there are distinct outcomes of a given action, and one is uncertain to which the act will lead. Decisions are made under indeterminacy when there are distinct outcomes of a given action, and it is indeterminate to which the act will lead. This paper develops a theory of (synchronic and diachronic) decision-making under indeterminacy that portrays the rational response to such situations as inconstant. Rational agents have to capriciously and randomly choose how to resolve (...) the indeterminacy relevant to a given choice-situation, but such capricious choices once made constrain how they will choose in the future. The account is illustrated by the case of self-interested action in situations where it is indeterminate whether you yourself will survive to benefit or suffer the consequences. The conclusion emphasizes some distinctive anti-hedging predictions of the account. (shrink)

In their Why Machines Will Never Rule the World, Landgrebe and Smith (2023) argue that it is impossible for artificial general intelligence (AGI) to succeed, on the grounds that it is impossible to perfectly model or emulate the “complex” “human neurocognitive system”. However, they do not show that it is logically impossible; they only show that it is practically impossible using current mathematical techniques. Nor do they prove that there could not be any other kinds of theories than those in (...) current use. Even if perfect theories were impossible or unlikely, perfection may not be needed and may even be unhelpful. (shrink)

Critical Review of Searle's Minds, Brains and Science.

Might it be that world itself, independently of what we know about it or how we represent it, is metaphysically indeterminate? This article tackles in turn a series of questions: In what sorts of cases might we posit metaphysical indeterminacy? What is it for a given case of indefiniteness to be 'metaphysical'? How does the phenomenon relate to 'ontic vagueness', the existence of 'vague objects', 'de re indeterminacy' and the like? How might the logic work? Are there reasons for postulating (...) this distinctive sort of indefiniteness? Conversely, are there reasons for denying that there is indefiniteness of this sort? (shrink)

This is the introduction to Seeing Wittgenstein Anew, eds. William Day & Victor J. Krebs (Cambridge UP, 2010), a collection of essays on Ludwig Wittgenstein's remarks on aspect-seeing. Section 1: Why Seeing Aspects Now?; Section 2: The Importance of Seeing Aspects; Section 3: The Essays. (The front matter to Seeing Wittgenstein Anew appears above under "Books.").

In the Critique of Judgment, Kant claims that genius is a talent for art, but not for science. Despite his restriction of genius to the domain of fine art, several recent interpreters have suggested that genius has a role to play in Kant’s account of cognition in general and scientific practice in particular. In this paper, I explore Kant’s reasons for excluding genius from science as well as the reasons that one might nevertheless be tempted to think that his account (...) allows room for the scientific genius. I then argue that Kant’s concerns are not only epistemic, but also moral, and together, they give us good reason for resisting the veneration of genius. (shrink)

According to a number of contemporary theorists, aesthetic reasons can invite or entice us but never compel us. In this paper, I develop a Kantian account of the normative force of aesthetic reasons. While Kant would likely agree that aesthetic reasons do not give rise to obligations, his account nevertheless gives us the resources for explaining how aesthetic reasons can still have more force than merely enticing reasons. This account appeals to the distinct normativity of aesthetic judgments on Kant's theory (...) and the way in which this kind of normativity structures aesthetic exchanges with other judging subjects. I argue that, in addition to the moral reasons we have for appreciating and preserving beauty, Kant’s account can accommodate distinctly aesthetic reasons for doing so that stem from our membership in aesthetic communities. (shrink)

Worlds where things divide forever ("gunk" worlds) are apparently conceivable. The conceivability of such scenarios has been used as an argument against "nihilist" or "near-nihilist" answers to the special composition question. I argue that the mereological nihilist has the resources to explain away the illusion that gunk is possible.

The concept of moral wrongness, many think, has a distinctive kind of referential stability, brought out by moral twin earth cases. This article offers a new account of the source of this stability, deriving it from a metaphysics of content: “substantive” radical interpretation, and first-order normative assumptions. This story is distinguished from extant “reference magnetic” explanations of the phenomenon, and objections and replies are considered.

Turner argues that computer programs must have purposes, that implementation is not a kind of semantics, and that computers might need to understand what they do. I respectfully disagree: Computer programs need not have purposes, implementation is a kind of semantic interpretation, and neither human computers nor computing machines need to understand what they do.

This essay considers what it means to understand natural language and whether a computer running an artificial-intelligence program designed to understand natural language does in fact do so. It is argued that a certain kind of semantics is needed to understand natural language, that this kind of semantics is mere symbol manipulation (i.e., syntax), and that, hence, it is available to AI systems. Recent arguments by Searle and Dretske to the effect that computers cannot understand natural language are discussed, and (...) a prototype natural-language-understanding system is presented as an illustration. (shrink)

While Kant was arguably as deeply engaged with the emerging special sciences of his time as he was with Newtonian physics, there is a deep tension in his treatment of these disciplines. On the one hand, Kant endorses a reductionist approach in natural science. On the other hand, Kant is committed to a variety of anti-reductionist positions in empirical psychology, chemistry, and the emerging biological sciences. This chapter examines the precise form that Kant’s anti-reductionism takes in each of these domains (...) and the corresponding set of questions about the extent to which each of these constitutes a genuine science for Kant. (shrink)

Revisionary theories of logic or truth require revisionary theories of mind. This essay outlines nonclassically based theories of rational belief, desire, and decision making, singling out the supervaluational family for special attention. To see these nonclassical theories of mind in action, this essay examines a debate between David Lewis and Derek Parfit over what matters in survival. Lewis argued that indeterminacy in personal identity allows caring about psychological connectedness and caring about personal identity to amount to the same thing. The (...) essay argues that Lewis's treatment of two of Parfit's puzzle cases—degreed survival and fission—presuppose different nonclassical treatments of belief and desire. (shrink)

This chapter defends the account of metaphysical indeterminacy of Barnes and Williams against Eklund's objections.

We develop and apply a multi-dimensional conception of explanatory depth towards a comparative analysis of inflationary and bouncing paradigms in primordial cosmology. Our analysis builds on earlier work due to Azhar and Loeb (2021) that establishes initial condition fine-tuning as a dimension of explanatory depth relevant to debates in contemporary cosmology. We propose dynamical fine-tuning and autonomy as two further dimensions of depth in the context of problems with instability and trans-Planckian modes that afflict bouncing and inflationary approaches respectively. In (...) the context of the latter issue, we argue that the recently formulated trans-Planckian censorship conjecture leads to a trade-off for inflationary models between dynamical fine-tuning and autonomy. We conclude with the suggestion that explanatory preference with regard to the different dimensions of depth is best understood in terms of differing attitudes towards heuristics for future model building. (shrink)

I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker's framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle -- concerning so-called 'reverse Sobel sequences' -- can be resolved by conversation dynamics in a theoryneutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second puzzle, by contrast, (...) relies on the interplay between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called "Gibbard phenomenon" for indicative conditionals. (shrink)

A critical study of John Searle's Minds, Brains and Science (Cambridge, MA: Harvard University Press, 1984).

Ford’s Helen Keller Was Never in a Chinese Room claims that my argument in How Helen Keller Used Syntactic Semantics to Escape from a Chinese Room fails because Searle and I use the terms ‘syntax’ and ‘semantics’ differently, hence are at cross purposes. Ford has misunderstood me; this reply clarifies my theory.

Jeff Paris proves a generalized Dutch Book theorem. If a belief state is not a generalized probability then one faces ‘sure loss’ books of bets. In Williams I showed that Joyce’s accuracy-domination theorem applies to the same set of generalized probabilities. What is the relationship between these two results? This note shows that both results are easy corollaries of the core result that Paris appeals to in proving his dutch book theorem. We see that every point of accuracy-domination defines (...) a dutch book, but we only have a partial converse. (shrink)

In this paper, I propose a novel interpretation of the role of the understanding in generating the unity of space and time. On the account I propose, we must distinguish between the unity that belongs to determinate spaces and times – which is a result of category-guided synthesis and which is Kant’s primary focus in §26 of the B-Deduction, including the famous B160–1n – and the unity that belongs to space and time themselves as all-encompassing structures. Non-conceptualist readers of Kant (...) have argued that this latter unity cannot be the product of categorial synthesis. While they are correct that this unity is not the product of any particular act of category-guided synthesis, I argue that conceptualists are right to nevertheless attribute this unity to the understanding. I argue that it is a result of what we can think of as the ‘original’ synthesis of understanding and sensibility themselves – it is a synthesis, moreover, in which the whole is logically prior to the parts. (shrink)

John Searle once said: "The Chinese room shows what we knew all along: syntax by itself is not sufficient for semantics. (Does anyone actually deny this point, I mean straight out? Is anyone actually willing to say, straight out, that they think that syntax, in the sense of formal symbols, is really the same as semantic content, in the sense of meanings, thought contents, understanding, etc.?)." I say: "Yes". Stuart C. Shapiro has said: "Does that make any sense? Yes: Everything (...) makes sense. The question is: What sense does it make?" This essay explores what sense it makes to say that syntax by itself is sufficient for semantics. (shrink)

Some argue that theories of universals should incorporate structural universals, in order to allow for the metaphysical possibility of worlds of 'infinite descending complexity' ('onion worlds'). I argue that the possibility of such worlds does not establish the need for structural universals. So long as we admit the metaphysical possibility of emergent universals, there is an attractive alternative description of such cases.

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic thatnorms beliefas classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterizedegrees of determinacy. It applies the methodology above to focus ondegree logic. (...) This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allowdegreesof consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail. (shrink)

While epistemic democrats have claimed that majority rule recruits the wisdom of the crowd to identify correct answers to political problems, the conjecture remains abstract. This article illustrates how majority rule leverages the epistemic capacity of the electorate to practically enhance the instrumental value of elections. To do so, we identify a set of sufficient conditions that effect such a majority rule mechanism, even when the decision in question is multidimensional. We then look to the case of sociotropic economic voting (...) in US presidential elections to provide empirical tractability for these conditions. We find that absent such an epistemic capacity a number of presidential elections might well have been decided differently. By generating clear conditions for the plausibility of claims made by epistemic democrats, and demonstrating their correspondence to empirical data, this article strengthens the broader instrumental grounds recommending democracy. (shrink)

Lewis (1973) gave a short argument against conditional excluded middle, based on his treatment of ‘might’ counterfactuals. Bennett (2003), with much of the recent literature, gives an alternative take on ‘might’ counterfactuals. But Bennett claims the might-argument against CEM still goes through. This turns on a specific claim I call Bennett’s Hypothesis. I argue that independently of issues to do with the proper analysis of might-counterfactuals, Bennett’s Hypothesis is inconsistent with CEM. But Bennett’s Hypothesis is independently objectionable, so we should (...) resolve this tension by dropping the Hypothesis, not by dropping CEM. (shrink)

The authors argue that their target is orthogonal to the realism and instrumentalist debate. I argue that it is born directly from it. While the distinction is helpful in illuminating how some ontological commitments demand a theory of implementation, it's less clear whether different views cleanly map onto the epistemic and metaphysical uses defined in the paper.

There are many branches of philosophy called “the philosophy of X,” where X = disciplines ranging from history to physics. The philosophy of artificial intelligence has a long history, and there are many courses and texts with that title. Surprisingly, the philosophy of computer science is not nearly as well-developed. This article proposes topics that might constitute the philosophy of computer science and describes a course covering those topics, along with suggested readings and assignments.

A brief introduction to Meinong, his theory of objects, and modern interpretations of it. Sections include: The Theory of Objects, Castañeda's Theory of Guises, Parsons,'s Theory of Nonexistent Objects, Rapaport's Theory of Meinongian Objects, Routley's Theory of Items.

This paper examines two puzzles of indeterminacy. The first puzzle concerns the hypothesis that there is a unified phenomenon of indeterminacy. How are we to reconcile this with the apparent diversity of reactions that indeterminacy prompts? The second puzzle focuses narrowly on borderline cases of vague predicates. How are we to account for the lack of theoretical consensus about what the proper reaction to borderline cases is? I suggest (building on work by Maudlin) that the characteristic feature of indeterminacy is (...) alethic normative silence, and use this to explain both plurality and lack of consensus. (shrink)

Seeing Wittgenstein Anew is the first collection to examine Ludwig Wittgenstein’s remarks on the concept of aspect-seeing. These essays show that aspect-seeing was not simply one more topic of investigation in Wittgenstein’s later writings, but, rather, that it was a pervasive and guiding concept in his efforts to turn philosophy’s attention to the actual conditions of our common life in language. Arranged in sections that highlight the pertinence of the aspect-seeing remarks to aesthetic and moral perception, self-knowledge, mind and consciousness, (...) linguistic agreement, philosophical therapy, and “seeing connections,” the sixteen essays, which were specially commissioned for this volume, demonstrate the unity of not only Philosophical Investigations but also Wittgenstein’s later thought as a whole. They open up novel paths across familiar fields of thought: the objectivity of interpretation, the fixity of the past, the acquisition of language, and the nature of human consciousness. Significantly, they exemplify how continuing consideration of the interrelated phenomena and concepts surrounding aspect-seeing might produce a fruitful way of doing philosophy. The volume includes a concordance for the unnumbered remarks in the various editions of Philosophical Investigations, including the latest (4th) edition. (The front matter is posted here. The introduction - "Seeing Aspects in Wittgenstein" - appears below under "Published articles."). (shrink)

The term “medium independence” has different meanings. One sense maps onto “abstract-as-abstracta” descriptions while the other maps onto “abstract-as-omission” descriptions. Both senses have been deployed when it comes to understanding the nature of physical computation. However, because medium independence is a polysemic term, the sense being used should be clearly stated. If the sense is not clearly stated, then those who wish to engage in debates regarding medium independence and physical computation run the risk of conflating different but related issues (...) which can have consequences when it comes to thinking about physical computation across contexts. (shrink)

Joyce (1998) gives an argument for probabilism: the doctrine that rational credences should conform to the axioms of probability. In doing so, he provides a distinctive take on how the normative force of probabilism relates to the injunction to believe what is true. But Joyce presupposes that the truth values of the propositions over which credences are defined are classical. I generalize the core of Joyce’s argument to remove this presupposition. On the same assumptions as Joyce uses, the credences of (...) a rational agent should always be weighted averages of truth value assignments. In the special case where the truth values are classical, the weighted averages of truth value assignments are exactly the probability functions. But in the more general case, probabilistic axioms formulated in terms of classical logic are violated—but we will show that generalized versions of the axioms formulated in terms of non-classical logics are satisfied. (shrink)