I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic is (...) a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

This book is written so as to be ‘accessible to philosophers without a mathematical background’. The reviewer can assure the reader that this aim is achieved, even if only by focusing throughout on just one example of an arithmetical truth, namely ‘7+5=12’. This example’s familiarity will be reassuring; but its loneliness in this regard will not. Quantified propositions — even propositions of Goldbach type — are below the author’s radar.The author offers ‘a new kind of arithmetical epistemology’, one which ‘respects (...) certain important intuitions’ 1 : apriorism, realism, and empiricism. The book contains some clarification of these ‘isms’, and some thoughtful critiques of major positions regarding them, as espoused by such representative figures as Boghossian, Bealer, Peacocke, Field, Bostock, Maddy, Locke, Kant, C.I. Lewis, Ayer, Quine, Fodor, and McDowell. The philosophical reader will find some interest and value in these wider-ranging discussions. Our concern in this review, however, is to examine closely the original positive proposal on offer.Arithmetical truths, the author maintains, are conceptual truths. Knowing truths like 7+5=12 involves no ‘epistemic reliance on any empirical evidence’; but that, she says, is not to claim ‘epistemic independence of the senses altogether’. She wants to show that "experience grounds our concepts … and then mere conceptual examination enables us to learn arithmetical truths ." Concepts that are ‘appropriately sensitive’ to ‘the nature of [an independent] reality’ she calls grounded. Because of the role of grounded concepts, ‘arithmetical truths explain our arithmetical beliefs in the right sort of way for those beliefs to count as knowledge’ .In the context of her concentration on the special nature of arithmetical knowledge, the author offers what could strike some bystanders as an unnecessarily over-ambitious account of knowledge tout court. Knowledge, for the author, is "true belief which … ". (shrink)

In this dissertation, we shall investigate whether Tennant's criterion for paradoxicality(TCP) can be a correct criterion for genuine paradoxes and whether the requirement of a normal derivation(RND) can be a proof-theoretic solution to the paradoxes. Tennant’s criterion has two types of counterexamples. The one is a case which raises the problem of overgeneration that TCP makes a paradoxical derivation non-paradoxical. The other is one which generates the problem of undergeneration that TCP renders a non-paradoxical derivation paradoxical. Chapter 2 (...) deals with the problem of undergeneration and Chapter 3 concerns the problem of overgeneration. Chapter 2 discusses that Tenant’s diagnosis of the counterexample which applies CR−rule and causes the undergeneration problem is not correct and presents a solution to the problem of undergeneration. Chapter 3 argues that Tennant’s diagnosis of the counterexample raising the overgeneration problem is wrong and provides a solution to the problem. Finally, Chapter 4 addresses what should be explicated in order for RND to be a proof-theoretic solution to the paradoxes. (shrink)

Neil Tennant was the first to propose a proof-theoretic criterion for paradoxicality, a framework in which a paradox, formalized through natural deduction, is derived from an unacceptable conclusion that employs a certain form of id est inferences and generates an infinite reduction sequence. Tennant hypothesized that any derivation in natural deduction that formalizes a genuine paradox would meet this criterion, and he argued that while the liar paradox is genuine, Russell's paradox is not. -/- The present paper (...) delves into Tennant's conjecture for genuine paradoxes and suggests that to validate the conjecture, one of two issues must be addressed. The first issue is the need for a philosophical consensus on the identification of a genuine paradox in an informal sense. The second issue is the requirement for a uniform approach to formalize paradoxes in natural deduction. If either of these issues is addressed, the conjecture could be validated, or at the very least, it could hold philosophical importance in delineating the proof-theoretic features of paradoxicality. (shrink)

Many prominent writers on the philosophy of logic, including Michael Dummett, Dag Prawitz, Neil Tennant, have held that the introduction and elimination rules of a logical connective must be ‘in harmony ’ if the connective is to possess a sense. This Harmony Thesis has been used to justify the choice of logic: in particular, supposed violations of it by the classical rules for negation have been the basis for arguments for switching from classical to intuitionistic logic. The Thesis (...) has also had an influence on the philosophy of language: some prominent writers in that area, notably Dummett and Robert Brandom, have taken it to be a special case of a more general requirement that the grounds for asserting a statement must cohere with its consequences. This essay considers various ways of making the Harmony Thesis precise and scrutinizes the most influential arguments for it. The verdict is negative: all the extant arguments for the Thesis are weak, and no version of it is remotely plausible. (shrink)

One of the most fundamental questions in the philosophy of mathematics concerns the relation between truth and formal proof. The position according to which the two concepts are the same is called deflationism, and the opposing viewpoint substantialism. In an important result of mathematical logic, Kurt Gödel proved in his first incompleteness theorem that all consistent formal systems containing arithmetic include sentences that can neither be proved nor disproved within that system. However, such undecidable Gödel sentences can be established to (...) be true once we expand the formal system with Alfred Tarski s semantical theory of truth, as shown by Stewart Shapiro and Jeffrey Ketland in their semantical arguments for the substantiality of truth. According to them, in Gödel sentences we have an explicit case of true but unprovable sentences, and hence deflationism is refuted. -/- Against that, Neil Tennant has shown that instead of Tarskian truth we can expand the formal system with a soundness principle, according to which all provable sentences are assertable, and the assertability of Gödel sentences follows. This way, the relevant question is not whether we can establish the truth of Gödel sentences, but whether Tarskian truth is a more plausible expansion than a soundness principle. In this work I will argue that this problem is best approached once we think of mathematics as the full human phenomenon, and not just consisting of formal systems. When pre-formal mathematical thinking is included in our account, we see that Tarskian truth is in fact not an expansion at all. I claim that what proof is to formal mathematics, truth is to pre-formal thinking, and the Tarskian account of semantical truth mirrors this relation accurately. -/- However, the introduction of pre-formal mathematics is vulnerable to the deflationist counterargument that while existing in practice, pre-formal thinking could still be philosophically superfluous if it does not refer to anything objective. Against this, I argue that all truly deflationist philosophical theories lead to arbitrariness of mathematics. In all other philosophical accounts of mathematics there is room for a reference of the pre-formal mathematics, and the expansion of Tarkian truth can be made naturally. Hence, if we reject the arbitrariness of mathematics, I argue in this work, we must accept the substantiality of truth. Related subjects such as neo-Fregeanism will also be covered, and shown not to change the need for Tarskian truth. -/- The only remaining route for the deflationist is to change the underlying logic so that our formal languages can include their own truth predicates, which Tarski showed to be impossible for classical first-order languages. With such logics we would have no need to expand the formal systems, and the above argument would fail. From the alternative approaches, in this work I focus mostly on the Independence Friendly (IF) logic of Jaakko Hintikka and Gabriel Sandu. Hintikka has claimed that an IF language can include its own adequate truth predicate. I argue that while this is indeed the case, we cannot recognize the truth predicate as such within the same IF language, and the need for Tarskian truth remains. In addition to IF logic, also second-order logic and Saul Kripke s approach using Kleenean logic will be shown to fail in a similar fashion. (shrink)

The present paper investigates whether strictly classical inferences contribute to the formalization of (genuine) paradoxes within natural deduction. Tennant's criterion for paradoxicality relies on the generation of an infinite reduction sequence, which distinguishes genuine paradoxes from mere inconsistencies. His methodological conjecture posits that genuine paradoxes are never strictly classical and can be derived without classical inferences such as the Law of Excluded Middle, Dilemma, Classical Reductio, and Double Negation Elimination. -/- It appears that there were two reasons for (...) class='Hi'>Tennant's proposal of the methodological conjecture. The one is that strictly classical inferences hinder the generation of an infinite reduction sequence and the other is that strictly classical inferences have no role in the formalization of genuine paradoxes. -/- This paper raises questions about these two reasons. Focusing on the liar paradox, it will be argued that strictly classical inferences do not interfere with the generation of an infinite reduction sequence and that the liar sentence may implicitly entail strictly classical inferences. Should this analysis hold, it would call into question not only Tennant’s motivation for advancing the methodological conjecture, but also challenge his contention that genuine paradoxes—exemplified by the liar paradox—are never constructed with reliance on strictly classical inferences. (shrink)

Hume uses the adjectives “civilized” and “barbarous” in a variety of ways, and in a variety of contexts. He employs them to describe individuals, societies, historical eras, and forms of government. These various uses are closely related. Hume thinks that cultural and political development are intimately connected, and are mutually dependent. Civilized government goes together with civilized society. A wise ruler cannot emerge before “refinements have taken place” in the society at large and “science [becomes] known in the world.” At (...) the same time, the policy of a monarch who is “ignorant and uninstructed … for ever prevents all improvements.”. (shrink)

This essay presents an ideal for modern Western romantic love.The basic ideas are the following: people want to form a distinctive sort of plural subject with another, what Nozick has called a "We", they want to be loved for properties of certain kinds, and they want this love to establish and sustain a special sort of commitment to them over time.

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.

The following is a transcript of the interview I (Yasuko Kitano) conducted with Neil Levy (The Centre for Applied Philosophy and Public Ethics, CAPPE) on the 23rd in July 2009, while he was in Tokyo to give a series of lectures on neuroethics at The University of Tokyo Center for Philosophy. I edited his words for publication with his approval.

I defend ethical hedonism, the view that pleasure is the sole good thing, by arguing that it offers the only answer to an argument for moral skepticism. The skeptical problem arises from widespread fundamental moral disagreement, which entails the presence of enough moral error to undermine the reliability of most processes generating moral belief. We know that pleasure is good through the reliable process of phenomenal introspection, which reveals what our experiences are like. If knowing of pleasure’s goodness through phenomenal (...) introspection is the only reliable way to form our initial moral beliefs, we should accept ethical hedonism. (shrink)

Recent work in neuroimaging suggests that some patients diagnosed as being in the persistent vegetative state are actually conscious. In this paper, we critically examine this new evidence. We argue that though it remains open to alternative interpretations, it strongly suggests the presence of consciousness in some patients. However, we argue that its ethical significance is less than many people seem to think. There are several different kinds of consciousness, and though all kinds of consciousness have some ethical significance, different (...) kinds underwrite different kinds of moral value. Demonstrating that patients have phenomenal consciousness — conscious states with some kind of qualitative feel to them — shows that they are moral patients, whose welfare must be taken into consideration. But only if they are subjects of a sophisticated kind of access consciousness — where access consciousness entails global availability of information to cognitive systems — are they persons, in the technical sense of the word employed by philosophers. In this sense, being a person is having the full moral status of ordinary human beings. We call for further research which might settle whether patients who manifest signs of consciousness possess the sophisticated kind of access consciousness required for personhood. (shrink)

This essay makes a number of distinctions between the motives of love and of duty, and argues that ideally they act in concert so as to generate constancy in loving relations. The essay revolves around a case in which a husband or wife is tempted to infidelity. It is argued that resistance to the temptation is optimally grounded in love for the spouse rather than simply in a duty to resist initiated perhaps through promise or vow. This is not, however, (...) to undermine altogether the significance of promises of this sort; it is rather to put a proper emphasis on the sentiment of love as an effective spring to action and to suggest that the sentiment itself ideally brings a past promise or vow of fidelity into present relief in a choice situation. (shrink)

Epistemic akrasia can be rational. I consider a lonely pragmatist who believes that her imaginary friend doesn’t exist, and also believes on pragmatic grounds that she should believe in him. She rationally believes that her imaginary friend doesn’t exist, rationally follows various sources of evidence to the view that she should believe in him to end her loneliness, and rationally holds these attitudes simultaneously. Evidentialism suggests that her ambivalent epistemic state is rational, as considerations grounded in the value of truth (...) justify her beliefs. (shrink)

The rightness and wrongness of actions fits on a continuous scale. This fits the way we evaluate actions chosen among a diverse range of options, even though English speakers don’t use the words “righter” and “wronger”. I outline and defend a version of scalar consequentialism, according to which rightness is a matter of degree, determined by how good the consequences are. Linguistic resources are available to let us truly describe actions simply as right. Some deontological theories face problems in accounting (...) for degrees of rightness, as they don't invoke continuous parameters among the right-making features of action. (shrink)

Philosophers from Hart to Lewis, Johnston and Bennett have expressed various degrees of reservation concerning the doctrine of double effect. A common concern is that, with regard to many activities that double effect is traditionally thought to prohibit, what might at first look to be a directly intended bad effect is really, on closer examination, a directly intended neutral effect that is closely connected to a foreseen bad effect. This essay examines the extent to which the commonsense concept of intention (...) supports a reasonably consistent and coherent application of double effect. Two important conclusions are these: (1) a number of traditionally proscribed activities involve a kind of “targeting” of innocents that can be taken to exhibit a direct intention to harm them; (2) a direct intention to harm need not involve a desire to harm in any ordinary sense of the latter expression. (shrink)

A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...) to necessitate the addition of subsets to V. We argue that despite the prima facie incoherence of such talk for the Universist, she nonetheless has reason to try and provide interpretation of this discourse. We analyse extant interpretations of such talk, and analyse various tradeoffs in naturality that might be made. We conclude that the Universist has promising options for interpreting different forcing constructions. (shrink)

It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...) the continuum is a proper class. We examine several principles based on maximality considerations in this framework, and show how some (namely Ordinal Inner Model Hypotheses) enable us to incorporate standard set theories (including ZFC with large cardinals added). We conclude that the systems considered raise questions concerning the foundational purposes of set theory. (shrink)

This essay defends a strong version of the Humean theory of motivation on which desire is necessary both for motivation and for reasoning that changes our desires. Those who hold that moral judgments are beliefs with intrinsic motivational force need to oppose this view, and many of them have proposed counterexamples to it. Using a novel account of desire, this essay handles the proposed counterexamples in a way that shows the superiority of the Humean theory. The essay addresses the classic (...) objection that the Humean theory cannot explain the feeling of obligation, Stephen Darwall's example of motivationally potent reasoning that is not based on preexisting desires, Thomas Scanlon's criticism that the Humean theory fails to account for the structure and phenomenology of deliberation, and the phenomenon of akrasia as discussed by John Searle. In each case a Humean account explains the data at least as thoroughly as opposing views can, while fitting within a simpler total account of how we deliberate and act. (shrink)

We can infer moral conclusions from nonmoral evidence using a three-step procedure. First, we distinguish the processes generating belief so that their reliability in generating true belief is statistically predictable. Second, we assess the processes’ reliability, perhaps by observing how frequently they generate true nonmoral belief or logically inconsistent beliefs. Third, we adjust our credence in moral propositions in light of the truth ratios of the processes generating beliefs in them. This inferential route involves empirically discovering truths of the form (...) “Process P, which generates belief in moral proposition M, has truth ratio T", and using them to discover probabilities for moral propositions. The inferential route is noncircular, and progress along it is driven fundamentally by induction. (shrink)

Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.

Multiverse Views in set theory advocate the claim that there are many universes of sets, no-one of which is canonical, and have risen to prominence over the last few years. One motivating factor is that such positions are often argued to account very elegantly for technical practice. While there is much discussion of the technical aspects of these views, in this paper I analyse a radical form of Multiversism on largely philosophical grounds. Of particular importance will be an account of (...) reference on the Multiversist conception, and the relativism that it implies. I argue that analysis of this central issue in the Philosophy of Mathematics indicates that Radical Multiversism must be algebraic, and cannot be viewed as an attempt to provide an account of reference without a softening of the position. (shrink)

In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...) sufficiently precise. Instead, we suggest that the process of justification in set theory should not be thought of as neatly divisible in this way, but should rather be understood as a conceptually indivisible notion linked to the goal of explanation. (shrink)

What is posthumanism and why does it matter? This book offers an introduction to the ways in which humanism's belief in the natural supremacy of the Family of Man has been called into question at different moments and from different theoretical positions. What is the relationship between posthumanism and technology? Can posthumanism have a politics—postcolonial or feminist? Are postmodernism and poststructuralism posthumanist? What happens when critical theory meets Hollywood cinema? What links posthumanism to science fiction. Posthumanism addresses these and other (...) questions in an attempt to come to terms with one of the most pressing issues facing contemporary society. (shrink)

This paper presents the Universality Argument that pleasure is goodness. The first premise defines goodness as what should please all. The second premise reduces 'should' to perceptual accuracy. The third premise invokes a universal standard of accuracy: qualitative identity. Since the pleasure of all is accurate solely about pleasure, pleasure is goodness, or universal moral value. The argument proceeds from a moral sense theory that analyzes moral concepts as concerned with what all should hope for, feel guilty about, and admire. (...) This requires rejecting practical anti-empiricism, the view that moral judgment concerns empirically inaccessible norms governing action. (shrink)

This paper is a concise survey of recent expressivist theories of discourse, focusing on the ethical case. For each topic discussed recent trends are summarised and suggestions for further reading provided. Issues covered include: the nature of the moral attitude; ‘hybrid’ views according to which moral judgements express both beliefs and attitudes; the quasi-realist programmes of Simon Blackburn and Allan Gibbard; the problem of creeping minimalism; the nature of the ‘expression’ relation; the Frege-Geach problem; the problem of wishful thinking; the (...) role of moral intuitions; expressivism in aesthetics. (shrink)

The Continuum Hypothesis featured top of Hilbert's list of 23 problems in 1900. Today, we still consider the question, with various programmes pulling in different directions. This conceptual diversity raises a puzzle: In what sense do we disagree when we talk about it? A standard assumption takes it that the content of our thought about classes and the Continuum Hypothesis has not changed. Assuming a moderate view of how content is determined, I reject this assumption but also argue that whilst (...) the Continuum Hypothesis can have different content for different agents, it can also be determinate for certain programmes. In particular, I suggest that there is a fault line between those who think there are uncountable sets and recent countabilist programmes. (shrink)

This paper elaborates and defends an expressivist account of the claims of mind-independence embedded in ordinary moral thought. In response to objections from Zangwill and Jenkins it is argued that the expressivist 'internal reading' of such claims is compatible with their conceptual status and that the only 'external reading' available doesn't commit expressivisists to any sort of subjectivism. In the process a 'commitment-theoretic' account of the semantics of conditionals and negations is defended.

Causal exclusion arguments are taken to threaten the autonomy of the special sciences, and the causal efficacy of mental properties. A recent line of response to these arguments has appealed to “independently plausible” and “well grounded” theories of causation to rebut key premises. In this paper I consider two papers which proceed in this vein and show that they share a common feature: they both require causes to be proportional to their effects. I argue that this feature is a bug, (...) and one that generalises: any attempt to rescue the autonomy of the special sciences, or the efficacy of the mental, from exclusion worries had better not look to proportionality for help. (shrink)

I argue that one intends that ϕ if one has a desire that ϕ and an appropriately related means-end belief. Opponents, including Setiya and Bratman, charge that this view can't explain three things. First, intentional action is accompanied by knowledge of what we are doing. Second, we can choose our reasons for action. Third, forming an intention settles a deliberative question about what to do, disposing us to cease deliberating about it. I show how the desire- belief view can explain (...) why these phenomena occur when they occur, and why they don't when they don't. (shrink)

Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...) work in numerical cognition and ontogenetic studies. (shrink)

Propositionalism is the view that the contents of intentional attitudes have a propositional structure. Objectualism opposes propositionalism in allowing the contents of these attitudes to be ordinary objects or properties. Philosophers including Talbot Brewer, Paul Thagard, Michelle Montague, and Alex Grzankowski attack propositionalism about such attitudes as desire, liking, and fearing. This article defends propositionalism, mainly on grounds that it better supports psychological explanations.

Awarding rights to rivers, forests, and other environmental entities (EEs) is a new and increasingly popular approach to environmental protection. The distinctive feature of such rights of nature (RoN) legislation is that direct duties are owed to the EEs. This paper presents a novel rebuttal of the strongest argument against RoN: the no interest argument. The crux of this argument is that because EEs are not sentient, they cannot possess the kinds of interests necessary to ground direct duties. Therefore, they (...) cannot be legitimate rights-bearers. After considering and rejecting standard responses to this argument, the paper challenges its fundamental assumption: that rights-correlative duties must be grounded in the interests of the rights-bearer. The paper then presents the RoN critic with a dilemma. The critic must either accept that EEs are legitimate rights-bearers, or delegitimise many well-established rights-bearers along with EEs. Either way, the no interest argument loses its force. (shrink)

A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...) the status of reflection principles as axioms is left open for the Zermelian. (shrink)

Consider two deeply appealing thoughts: first, that we experience external particulars, and second, that what it’s like to have an experience – the phenomenal character of an experience – is somehow independent of external particulars. The first thought is readily captured by phenomenal particularism, the view that external particulars are sometimes part of the phenomenal character of experience. The second thought is readily captured by phenomenal generalism, the view that external particulars are never part of phenomenal character. -/- Here I (...) show that a novel version of phenomenal generalism can capture both thoughts in a satisfying fashion. Along the way, I reveal severe problems facing phenomenal particularism and also shed light on the mental kinds under which experiences fall. (shrink)

This paper explores connections between theories of morality and theories of properties. It argues that (1) moral realism is in tension with predicate, class and mereological nominalism; (2) moral non-naturalism is incompatible with standard versions of resemblance nominalism, immanent realism and trope theory; and (3) the standard semantic arguments for property realism do not support moral realism. I also raise doubts about trope-theoretic explanations of moral supervenience and argue against one version of the principle that we should accept theories that (...) maintain neutrality. (shrink)

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...) and meta-theoretic properties when comparing first-order and second-order logic. (shrink)

Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...) perturbations in modal space to bear on the debate, we will suggest that a promising option for representing current set-theoretic thought is given by formulating set theory using quasi-weak second-order logic. These observations indicate that the usual division of structures into \particular (e.g. the natural number structure) and general (e.g. the group structure) is perhaps too coarse grained; we should also make a distinction between intentionally and unintentionally general structures. (shrink)

This chapter considers the nature of imagination and belief, exploring how deeply these two states of mind differ. It first addresses a range of cognitive and motivational differences between imagination and belief which suggest that they're fundamentally different states of mind. Then it addresses imaginative immersion, delusions, and the different norms we apply to the two mental states, which some theorists regard as providing support for a more unified picture of imagination and belief.

Heidegger's ontological theories, his observations about liberalism and fascism, and his evaluation of Being are three premises of an argument for fascism. The ontological premise is that integrated wholes and instruments or objects of will are ontologically superior, as Being and Time suggests in discussing Being‐a‐whole and using tools. The social premise is that fascist societies are wholes integrated by dictatorial will, while liberal societies are looser aggregates of free individuals, as Heidegger describes in his 1930s seminars. The evaluative premise, (...) shared with the medieval tradition and expressed in his notebook remarks about war, is that ontological superiority makes things better. The conclusion that fascism is better than liberalism should be rejected along with the evaluative premise. (shrink)

Some philosophers (including Urmson, Humberstone, Shah, and Velleman) hold that believing that p distinctively involves applying a norm according to which the truth of p is a criterion for the success or correctness of the attitude. On this view, imagining and assuming differ from believing in that no such norm is applied. I argue against this view with counterexamples showing that applying the norm of truth is neither necessary nor sufficient for distinguishing believing from imagining and assuming. Then I argue (...) that the different functional properties of these mental states are enough to distinguish them, and that norm-application doesn't help us draw the functional distinctions. (shrink)

This paper argues that a counterpart-theoretic treatment of events, combined with a counterfactual theory of causation, can help resolve three puzzles from the causation literature. First, CCT traces the apparent contextual shifts in our causal attributions to shifts in the counterpart relation which obtains in those contexts. Second, being sensitive to shifts in the counterpart relation can help diagnose what goes wrong in certain prominent examples where the transitivity of causation appears to fail. Third, CCT can help us resurrect the (...) much-maligned fragility response to the problems of late pre-emption by understanding fragility in counterpart-theoretic terms. Some reasons to prefer this CCT approach to rivals are discussed. (shrink)

In the past decade, three philosophers in particular have recently explored the relation between desert and intrinsic value. Fred Feldman argues that consequentialism need not give much weight – or indeed any weight at all – to the happiness of persons who undeservedly experience pleasure. He defends the claim that the intrinsic value of a state of affairs is determined by the “fit” between the amount of well-being that a person receives and the amount of well-being that the person deserves. (...) Shelly Kagan uses a similar claim to motivate the view that equality is not intrinsically valuable. Thomas Hurka argues that desert is a third-order value, which is a function of the relation between the second-order value of having a virtuous or vicious character and the first-order value of experiencing pleasure or pain. In this paper, we sketch a theory of desert as fittingness and defend a general account of the relation between desert, well-being, and intrinsic value. We then discuss various applications of our “geometry of desert,” including a solution to the problem of the Repugnant Conclusion. In so doing, we explain, revise, and extend many of these authors’ central ideas. (shrink)

It is commonly assumed that causation is transitive and in this paper I aim to reconcile this widely-held assumption with apparent evidence to the contrary. I will discuss a familiar approach to certain well-known counterexamples, before introducing a more resistant sort of case of my own. I will then offer a novel solution, based on Yablo’s proportionality principle, that succeeds in even these more resistant cases. There is a catch, however. Either proportionality is a constraint on which causal claims are (...) true, and the solution works, or it is not and causation is not transitive after all. I will argue that the first horn has unacceptable consequences and should be rejected, but that the second horn is less costly than it might initially appear. (shrink)

This paper applies the theory of teleosemantics to the issue of moral content. Two versions of teleosemantics are distinguished: input-based and output-based. It is argued that applying either to the case of moral judgements generates the conclusion that such judgements have both descriptive (belief-like) and directive (desire-like) content, intimately entwined. This conclusion directly validates neither descriptivism nor expressivism, but the application of teleosemantics to moral content does leave the descriptivist with explanatory challenges which the expressivist does not face. Since teleosemantics (...) ties content to function, the paper also offers an account of the evolutionary function of moral judgements. (shrink)

Trust not only disposes us to feel betrayed, trust can be betrayed. Understanding what a betrayal of trust is requires understanding how trust can ground an obligation on the part of the trusted person to act specifically as trusted. This essay argues that, since trust cannot ground an appropriate obligation where there is no prior obligation, a betrayal of trust should instead be conceived as the violation of a trust-based obligation to respect an already existing obligation. Two forms of trust (...) are evaluated for their potential to ground such a second-order obligation. One form counts as a gift to the trusted person only because it does not involve an expectation of trustworthiness; the other form cannot count as a gift but confers an honor because it does include an expectation of trustworthiness. Only trust that confers an honor generates a second-order obligation whose violation would be a betrayal of trust. -/- . (shrink)

The moral belief problem is that of reconciling expressivism in ethics with both minimalism in the philosophy of language and the syntactic discipline of moral sentences. It is argued that the problem can be solved by distinguishing minimal and robust senses of belief, where a minimal belief is any state of mind expressed by sincere assertoric use of a syntactically disciplined sentence and a robust belief is a minimal belief with some additional property R. Two attempts to specify R are (...) discussed, both based on the thought that beliefs are states that aim at truth. According to the first, robust beliefs are criticisable to the extent that their content fails to match the state of the world. This sense fails to distinguish robust beliefs from minimal beliefs. According to the second, robust beliefs function to have their content match the state of the world. This sense succeeds in distinguishing robust beliefs from minimal beliefs. The conclusion is that the debate concerning the cognitive status of moral convictions needs to address the issue of the function of moral convictions. Evolutionary theorising may be relevant, but will not be decisive, in answering this question. (shrink)

In this paper I draw apart two different contexts of Freirean pedagogical practice that I label interactional and institutional. The interactional refers to the immediate learning environment with relation to the interaction between the students and the teacher. In contrast, the institutional refers to how the institutions of education are managed, constructed, and organised and how they relate to the individuals those institutions are composed of. I begin by presenting a brief overview of Freire’s argument in favour of a revolutionary (...) pedagogy. I then highlight how this project is represented at both interactional and institutional levels with a particular focus upon the practice of the revolutionary leaders and their role in the development of the humanisation of the oppressed. In presenting the interactional and institutional elements of Freire’s pedagogy separately the tension between the individual and the state is made plain and the limitations of his politico-educational project are drawn out. I argue that due to an inconsistent application of the relationship between means and ends in Freire’s politico-educational project an incoherence between the interactional and institutional levels of education is highlighted. In responding to this limitation of Freire’s politico-educational project with a thoroughly interconnected relationship of means and ends I show that there remains a necessary conflict between the interests of the individual and the state. As a result of this a door is opened for the development of an argument in favour of the disestablishment of education and state from a Freirean perspective. (shrink)