There is a basic distinction, in the realm of spatial boundaries, between bona fide boundaries on the one hand, and fiat boundaries on the other. The former are just the physical boundaries of old. The latter are exemplified especially by boundaries induced through human demarcation, for example in the geographic domain. The classical problems connected with the notions of adjacency, contact, separation and division can be resolved in an intuitive way by recognizing this two-sorted ontology of boundaries. Bona fide boundaries (...) yield a notion of contact that is effectively modeled by classical topology; the analogue of contact involving fiat boundaries calls, however, for a different account, based on the intuition that fiat boundaries do not support the open/closed distinction on which classical topology is based. In the presence of this two-sorted ontology it then transpires that mereotopology—topology erected on a mereological basis—is more than a trivial formal variant of classical point-set topology. (shrink)

Techniques from behavioral economics—nudges—may help physicians increase pediatric vaccine compliance, but critics have objected that nudges can undermine autonomy. Since autonomy is a centrally important value in healthcare decision-making contexts, it counts against pediatric vaccination nudges if they undermine parental autonomy. Advocates for healthcare nudges have resisted the charge that nudges undermine autonomy, and the recent bioethics literature illustrates the current intractability of this debate. This article rejects a principle to which parties on both sides of this debate sometimes seem (...) committed: that nudges are morally permissible only if they are consistent with autonomy. Instead, I argue that, at least in the case of pediatric vaccination, some autonomy-undermining nudges may be morally justified. This is because parental autonomy in pediatric decision-making is not as morally valuable as the autonomy of adult patients, and because the interests of both the vaccinated child and other members of the community can sometimes be weighty enough to justify autonomy-infringing pediatric vaccination nudges. This article concludes with a set of worries about the effect of pediatric vaccination nudges on parent-physician relationships, and it calls on the American Academy of Pediatrics to draw on scientific and bioethics research to develop guidelines for the use of nudges in pediatric practice and, in particular, for the use of pediatric vaccination nudges. (shrink)

The New Evil Demon Problem is supposed to show that straightforward versions of reliabilism are false: reliability is not necessary for justification after all. I argue that it does no such thing. The reliabilist can count a number of beliefs as justified even in demon worlds, others as unjustified but having positive epistemic status nonetheless. The remaining beliefs---primarily perceptual beliefs---are not, on further reflection, intuitively justified after all. The reliabilist is right to count these beliefs as unjustified in demon worlds, (...) and it is a challenge for the internalist to be able to do so as well. (shrink)

Majority cycling and related social choice paradoxes are often thought to threaten the meaningfulness of democracy. But deliberation can prevent majority cycles – not by inducing unanimity, which is unrealistic, but by bringing preferences closer to single-peakedness. We present the first empirical test of this hypothesis, using data from Deliberative Polls. Comparing preferences before and after deliberation, we find increases in proximity to single-peakedness. The increases are greater for lower versus higher salience issues and for individuals who seem to have (...) deliberated more versus less effectively. They are not merely a byproduct of increased substantive agreement. Our results both refine and support the idea that deliberation, by increasing proximity to single-peakedness, provides an escape from the problem of majority cycling. (shrink)

Neutral monism is a position in metaphysics defended by Mach, James, and Russell in the early twentieth century. It holds that minds and physical objects are essentially two different orderings of the same underlying neutral elements of nature. This paper sets out some of the central concepts, theses and the historical background of ideas that inform this doctrine of elements. The discussion begins with the classic neutral monism of Mach, James, and Russell in the first part of the paper, then (...) considers recent neo-Russellian versions in the second half. The chances for a revival of neutral monism are probably slight; its key ideas and starting points lie far from those in contemporary philosophy of mind. A better route might be through the philosophy of science and a deeper understanding of causation. (shrink)

Certain advocates of the so-called “neo-logicist” movement in the philosophy of mathematics identify themselves as “neo-Fregeans” (e.g., Hale and Wright), presenting an updated and revised version of Frege’s form of logicism. Russell’s form of logicism is scarcely discussed in this literature and, when it is, often dismissed as not really logicism at all (in light of its assumption of axioms of infinity, reducibility and so on). In this paper I have three aims: firstly, to identify more clearly the primary meta-ontological (...) and methodological differences between Russell’s logicism and the more recent forms; secondly, to argue that Russell’s form of logicism offers more elegant and satisfactory solutions to a variety of problems that continue to plague the neo-logicist movement (the bad company objection, the embarrassment of richness objection, worries about a bloated ontology, etc.); thirdly, to argue that neo-Russellian forms of logicism remain viable positions for current philosophers of mathematics. (shrink)

Many believe that the rational evaluation of actions depends on the rational evaluation of even basic desires. Hume, though, viewed desires as "original existences" which cannot be contrary to either truth or reason. Contemporary critics of Hume, including Norman, Brandt and Parfit, have sought a basis for the rational evaluation of desires that would deny some basic desires reason-giving force. I side with Hume against these modern critics. Hume's concept of rational evaluation is admittedly too narrow; even basic desires are, (...) despite their nonrepresentational nature, subject to rational evaluation. But this evaluation is not relevant to their tendency to generate reasons for action, and does not undermine the spirit of the Humean view of rational action. (shrink)

One of the attractions of the Humean instrumentalist theory of practical rationality is that it appears to offer a special connection between an agent's reasons and her motivation. The assumption that Humeanism is able to assert a strong connection between reason and motivation has been challenged, most notably by Christine Korsgaard. She argues that Humeanism is not special in the connection it allows to motivation. On the contrary, Humean theories of practical rationality do connect reasons and motivation in a unique (...) and attractive way, though the nature of this connection has sometimes been misunderstood by both defenders and detractors of the theory. (shrink)

Neo-Humean instrumentalist theories of reasons for acting have been presented with a dilemma: either they are normatively trivial and, hence, inadequate as a normative theory or they covertly commit themselves to a noninstrumentalist normative principle. The claimed result is that no purely instrumentalist theory of reasons for acting can be normatively adequate. This dilemma dissolves when we understand what question neo-Humean instrumentalists are addressing. The dilemma presupposes that neo-Humeans are attempting to address the question of how to act, 'simpliciter'. Instead, (...) they are evaluating actions from the agent's normative perspective. (shrink)

That parthood is a transitive relation is among the most basic principles of classical mereology. Alas, it is also very controversial. In a recent paper, Ingvar Johansson has put forward a novel diagnosis of the problem, along with a corresponding solution. The diagnosis is on the right track, I argue, but the solution is misleading. And once the pieces are properly put together, we end up with a reinforcement of the standard defense of transitivity on behalf of classical mereology.

Skipper and Millstein analyze natural selection and mechanism, concluding that natural selection is not a mechanism in the sense of the new mechanistic philosophy. Barros disagrees and provides his own account of natural selection as a mechanism. This discussion identifies a missing piece of Barros's account, attempts to fill in that piece, and reconsiders the revised account. Two principal objections are developed: one, the account does not characterize natural selection; two, the account is not mechanistic. Extensive and persistent variability causes (...) both of these difficulties, so further attempts to describe natural selection as a mechanism are also unlikely to succeed. (shrink)

This is a response to Macleod 2012's argument that the history of unjust property acquisitions requires rich libertarians to give away everything in excess of equality. At first, problematic questions are raised. How much property is usually inherited or illegitimate? Why should legitimate inheritance be affected? What of the burden of proof and court cases? A counterfactual problem is addressed. Three important cases are considered: great earned wealth; American slavery; land usurpation. All are argued to be problematic for Macleod 2012's (...) thesis. Various problems are explained concerning using the Nozickian argument to decide the alleged excess that rich libertarians own. The essay's main error is the presupposition that free markets do not help the worst-off. The majority of unjust holdings today are not the result of historical injustices but arise through continuing transfers enabled by taxation and state-regulation. More study of libertarian contributions to the social sciences and philosophy would appear to be desirable "personal behavior" among socialists. (shrink)

Goldman, though still a reliabilist, has made some recent concessions to evidentialist epistemologies. I agree that reliabilism is most plausible when it incorporates certain evidentialist elements, but I try to minimize the evidentialist component. I argue that fewer beliefs require evidence than Goldman thinks, that Goldman should construe evidential fit in process reliabilist terms, rather than the way he does, and that this process reliabilist understanding of evidence illuminates such important epistemological concepts as propositional justification, ex ante justification, and defeat.

This article examines a fundamental question of justice in global health. Is it ethically preferable to provide a larger number of people with cheaper treatments that are less effective (or more toxic), or to restrict treatments to a smaller group to provide a more expensive but more effective or less toxic alternative? We argue that choosing to provide less effective or more toxic interventions to a larger number of people is favored by the principles of utility, equality, and priority for (...) those worst-off. Advocates are mistaken to demand that medical care provided in low-income and middle-income countries should be the same as in high-income countries. (shrink)

In this introduction, before summarizing the contents of the volume, the authors characterize materialism as it is understood within the philosophy of mind, and they identify three respects in which materialism is on the wane.

Klein’s account of epistemic justification, infinitism, supplies a novel solution to the regress problem. We argue that concentrating on the normative aspect of justification exposes a number of unpalatable consequences for infinitism, all of which warrant rejecting the position. As an intermediary step, we develop a stronger version of the ‘finite minds’ objection.

A look at the dynamical concept of space and space-generating processes to be found in Kant, J.F. Herbart and the mathematician Bernhard Riemann's philosophical writings.

The positions of Frege, Russell and Wittgenstein on the priority of complexes over (propositional) functions are sketched, challenging those who take the "judgment centered" aspects of the Tractatus to be inherited from Frege not Russell. Frege's views on the priority of judgments are problematic, and unlike Wittgenstein's. Russell's views on these matters, and their development, are discussed in detail, and shown to be more sophisticated than usually supposed. Certain misreadings of Russell, including those regarding the relationship between propositional functions and (...) universals, are exposed. Wittgenstein's and Russell's views on logical grammar are shown to be very similar. Russell's type theory does not countenance types of genuine entities nor metaphysical truths that cannot be put into words, contrary to conventional wisdom. I relate this to the debate over "inexpressible truths" in the Tractatus. I lastly comment on the changes to Russell's views brought about by Wittgenstein's influence. (shrink)

Skeptics of the moral case against industrial farming often assert that harm to animals in industrial systems is limited to isolated instances of abuse that do not reflect standard practice and thus do not merit criticism of the industry at large. I argue that even if skeptics are correct that abuse is the exception rather than the rule, they must still answer for two additional varieties of serious harm to animals that are pervasive in industrial systems: procedural harm and institutional (...) oppression. That procedural and institutional harms create conditions under which abuse is virtually inevitable only increases the skeptic's burden. (shrink)

Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.

Many biologists and philosophers have worried that importing models of reasoning from the physical sciences obscures our understanding of reasoning in the life sciences. In this paper we discuss one example that partially validates this concern: part-whole reductive explanations. Biology and physics tend to incorporate different models of temporality in part-whole reductive explanations. This results from differential emphases on compositional and causal facets of reductive explanations, which have not been distinguished reliably in prior philosophical analyses. Keeping these two facets distinct (...) facilitates the identifi cation of two further aspects of reductive explanation: intrinsicality and fundamentality. Our account provides resources for discriminating between different types of reductive explanation and suggests a new approach to comprehending similarities and differences in the explanatory reasoning found in biology and physics. (shrink)

I trace changes to Frege's understanding of numbers, arguing in particular that the view of arithmetic based in geometry developed at the end of his life (1924–1925) was not as radical a deviation from his views during the logicist period as some have suggested. Indeed, by looking at his earlier views regarding the connection between numbers and second-level concepts, his understanding of extensions of concepts, and the changes to his views, firstly, in between Grundlagen and Grundgesetze, and, later, after learning (...) of Russell's paradox, this position is a natural position for him to have retreated to, when properly understood. (shrink)

Fictionalism in ontology is a mixed bag. Here I focus on three main variants—which I label after the names of Pascal, Berkeley, and Hume—and consider their relative strengths and weaknesses. The first variant is just a version of the epistemic Wager, applied across the board. The second variant builds instead on the fact that ordinary language is not ontologically transparent; we speak with the vulgar, but deep down we think with the learned. Finally, on the Humean variant it’s the structure (...) of the ontological inventory, not its content, that may turn out to involve fictional elements. That is, for the Humean the fiction lies, not in the reality of common-sense ontology, but in the laws—of unity, identity, causation, etc.—in terms of which we articulate our experience of that reality. In the end, this is the kind of fictionalism that I find most interesting, sensible, and tenable. And I argue that it is even compatible with the sort of “naive” realism we have all come to appreciate in the work of Paolo Bozzi, to whom the paper is dedicated. (shrink)

This paper discusses certain problems arising within the treatment of the senses of functions in Alonzo Church's Logic of Sense and Denotation. Church understands such senses themselves to be "sense-functions," functions from sense to sense. However, the conditions he lays out under which a sense-function is to be regarded as a sense presenting another function as denotation allow for certain undesirable results given certain unusual or "deviant" sense-functions. Certain absurdities result, e.g., an argument can be found for equating any two (...) senses of the same type. An alternative treatment of the senses of functions is discussed, and is thought to do better justice to Frege's original theory. (shrink)

Lester‘s reply to the review by Gordon and Modugno of Escape from Leviathan was due to appear in a later edition of the same periodical, but it was eventually dropped without notice or a reason being given. Subsequently, their review has occasionally been cited in isolation as a refutation of that book‘s theory of liberty, the compatibility of such liberty with welfare maximisation, and the use of "Popperian views" as though a complete reply did not exist and were not freely (...) available and easily found online. To make it harder to avoid the reply, whether by accident or design, it is reproduced here (but with sundry small emendations for greater clarity). (shrink)

The way we farm, the kinds of backyards and landscapes we favor, and the way we control patterns of development are creating an invisible crisis through their affects upon soil ecology. The invisibility of soil ecosystems, the seemingly alien properties of the organisms that inhabit them, and the specialized knowledge required to understand them create obstacles to moral concern for these fountains of life. Our treatment of soils has reached the point of crisis. Obstacles to moral thinking about soils might (...) be overcome by supplying the moral imagination with a deeper understanding of our own biological identity as ecosystems analogous in organization and functions to soil ecosystems. Not only have microbes created the conditions necessary for human life, but they have shaped our evolutionary history and helped constitute the human genome. Our biological identity encompasses communities of microbes, such that humans (and all organisms) are most properly understood as ecosystems. For this reason, moral concern for humans implies moral concern for ecosystems. (shrink)

Global climate change is one of the most widely discussed problems of our time. However, many libertarian thinkers have not participated in the ethical dimensions of this discussion due to a narrow focus on the scientific basis for concern about climate change. In this paper, I reject this approach and explore the kind of response libertarians should be offering instead. I frame the climate change problem as one which concerns potential rights-infringements and explore different ways in which climate change might (...) be thought to infringe upon rights. I conclude that there are some ways in which climate change might be expected to result in rights-infringements, but that some of the current concern about climate change cannot be reconciled with a rights-oriented paradigm. I close by outlining future directions for research, emphasizing that much remains to be done in order to formulate a complete libertarian perspective on climate change. (shrink)

Review of Logic as Universal Science: Russell’s Early Logicism and Its Philosophical Context, by Anssi Korhonen (Palgrave Macmillan 2013).

In this short response to Kerstein and Bognar, we clarify three aspects of the complete lives system, which we propose as a system of allocating scarce medical interventions. We argue that the complete lives system provides meaningful guidance even though it does not provide an algorithm. We also defend the investment modification to the complete lives system, which prioritizes adolescents and older children over younger children; argue that sickest-first allocation remains flawed when scarcity is absolute and ongoing; and argue that (...) Kerstein and Bognar are mistaken to base their allocation principles on differences in personhood. (shrink)

I examine Mach's influence on American philosophy from 1890-1910, on Carus, James, Peirce, the American Realists and J.B. Stallo. I also consider the question of whether Mach was a pragmatist in the sense of Peirce and James. I conclude that early pragmatism was a method-centric theory whereas Mach's empiricism prized agreement with experience and downplayed the significance of inductive-scientific methods in general as a guide to discovery.

This paper is an attempt to argue that there existed a very prominent view of signs and signification in late sixteenth- and seventeenth-century Europe which can help us to understand several puzzling aspects of baroque culture. This view, called here "pansemioticism," constituted a fundamental part of the baroque conception of the world. After sketching the content and importance of pansemioticism, I will show how it can help us to understand the (from a modern perspective) rather puzzling concept of the polymath, (...) or polyhistor, which constituted the ideal of the baroque scientist. In this context I will also discuss a seventeenth century phenomenon essentially connected with polyhistorism, namely that of the early modem polyhistorical collections, the Wunderkamnmern. Since such a study needs a clearly determined focal point, we will concentrate on the last three quarters of the seventeenth century and will mainly discuss works by German authors of the time. (shrink)

Charles Murray describes himself as a libertarian, most notably in his short book, What it Means to be a Libertarian. He might more accurately have described himself as having libertarian tendencies. My reading of Simple Justice is that the views it espouses are far more traditionalist than libertarian. Neither traditionalist state-retribution nor modernist state-leniency is libertarian. Nor does either provide as just or efficient a response to crime as does libertarian restitution, including restitutive retribution. Here, I shall respond directly only (...) to Murray's views, rather than also deal with state-leniency. This is because I accept Murray's thesis, without endorsing his specific arguments for it, that state-leniency is disastrous as a response to crimes against persons and their justly acquired property. (shrink)

Abstract. As a general theory of reasoning—and as a general theory of what holds true under every possible circumstance—logic is supposed to be ontologically neutral. It ought to have nothing to do with questions concerning what there is, or whether there is anything at all. It is for this reason that traditional Aristotelian logic, with its tacit existential presuppositions, was eventually deemed inadequate as a canon of pure logic. And it is for this reason that modern quantification theory, too, with (...) its residue of existentially loaded theorems and patterns of inference, has been claimed to suffer from a defect of logical purity. The law of non-contradiction rules out certain circumstances as impossible—circumstances in which a statement is both true and false, or perhaps circumstances where something both is and is not the case. Is this to be regarded as a further ontological bias? (shrink)

Virtue, the centerpiece of ancient ethics, has come under attack by virtue skeptics impressed by results of psychology experiments including Milgram’s obedience studies. The virtue skeptic argues that experimental findings suggest that character structures are so fragile vis-à-vis situational factors as to be explanatorily superfluous: virtues and robust character traits are a myth, and should be replaced by situation-specific “narrow dispositions” (Gilbert Harman) or “local traits” (John Doris). This paper argues that the virtue skeptics’ sweeping claims are ill-founded. First, blending (...) Aristotelian and contemporary insights about virtue, I reach adecision about a reasonable, nonstraw defmition of “virtue” and of “character trait.” Next, I argue that explanations give by Lee Ross and Richard Nisbett for the Milgram findings covertly invoke character traits. Reflection reveals that more robust, crosssituationally consistent traits are needed for explanation of subject behavior, and that it is reasonable to suppose that such traits were in place. (shrink)

The theory according to which most ordinary objects are mere “entia successiva”—sequences of distinct mereological aggregates, whose unity resides exclusively in our minds—is a variant of the standard, three-dimensional conception of objects. For the aggregates are, at bottom, endurants, i.e., entities that persist through time by being fully present at any time at which they exist. In this paper I compare this theory with the so-called “stage view”, according to which ordinary objects—indeed, all objects—are sequences of momentary entities that cannot (...) truly be said to persist through time. Both theories face a number of intuitive difficulties but the stage view, I argue, has a lot more to offer in return. (shrink)

From the dictum "ought implies can", it has been argued that no account of belief's normativity can avoid the unpalatable result that, for unbelievable propositions such as "It is raining and nobody believes that it is raining", one ought not to believe them even if true. In this article, I argue that this move only succeeds on a faulty assumption about the conjunction of doxastic "oughts.".

The thesis that rationality consists in the straight-forward maximization of utility has not lacked critics. Typically, however, detractors reject the Humean picture of rationality upon which it seems based; they seek to emancipate reason from the tyranny of the passions. It is, then, noteworthy when an attack on this thesis comes from ‘within the ranks.’David Gauthier's paper ‘Reason and Maximization’ is just such an attack; and for this reason, among others, it is interesting. It is not successful, though. In defense (...) of this conclusion, we shall begin by relating the essentials of Gauthier's argument. Then we shall examine in some detail Gauthier's claim that the principle of straighforward max-imization fails to be self-supporting. We shall argue that Gauthier's defense of this claim is at best incomplete. Finally, we shall show that the fact that a normative principle is self-subverting or non-self-supporting does not entail that the principle is defective. (shrink)

This paper continues a thread in Analysis begun by Adam Rieger and Nicholas Denyer. Rieger argued that Frege’s theory of thoughts violates Cantor’s theorem by postulating as many thoughts as concepts. Denyer countered that Rieger’s construction could not show that the thoughts generated are always distinct for distinct concepts. By focusing on universally quantified thoughts, rather than thoughts that attribute a concept to an individual, I give a different construction that avoids Denyer’s problem. I also note that this problem for (...) Frege’s philosophy was discovered by Bertrand Russell as early as 1902 and has been discussed intermittently since. (shrink)

Wall, G. Locke's attack on innate knowledge.--Harris, J. Leibniz and Locke on innate ideas.--Greenlee, D. Locke's idea of idea.--Aspelin, G. Idea and perception in Locke's essay.--Greenlee, D. Idea and object in the essay.--Mathews, H. E. Locke, Malebranche and the representative theory.--Alexander, P. Boyle and Locke on primary and secondary qualities.--Ayers, M. R. The ideas of power and substance in Locke's philosophy.--Allison, H. E. Locke's theory of personal identity.--Kretzmann, N. The main thesis of Locke's semantic theory.--Woozley, A. D. Some remarks on (...) Locke's account of knowledge.--Laudan, L. The nature and sources of Locke's views on hypotheses. (shrink)

The political distinction between left and right remains ideologically muddled. This was not always so, but an immediate return to the pristine usage is impractical. Putting a theory of social liberty to one side, this essay defends the interpretation of left-wing as personal-choice and right-wing as property-choice. This allows an axis that is north/choice (or state-free) and south/control (or state-ruled). This Political Compass clarifies matters without being tendentious or too complicated. It shows that what is called ‘libertarianism’ is north-wing. A (...) quiz gives the reader’s Political Compass reading. (shrink)

Contractarians view justice as being defined by a contract made by rational individuals. No one supposes that this contract is actual, and the fact that it is merely hypothetical raises a number of questions both about the assumptions under which it would be actual and about the force of hypothetical agreement that is contingent on these assumptions.Particular contractarian theories must specify the circumstances of the agreement and the endowments, beliefs, desires, and degree and type of rationality of the agents. How (...) these issues are settled determines the force of the hypothetical agreement. The fact that ignorant people who desired only universal suffering would, under duress, agree to a certain principle gives us no reason to believe the principle is a correct moral principle or to think it rational to accept or act on it: some counterfactual assumptions undermine entirely the moral force of hypothetical agreement. On the other hand, to take people just as they are, with their current beliefs, desires, endowments, and all, is to endorse their ignorance and mistakes as well as any previous injustice that affects their bargaining power. (shrink)

The U.S. Supreme Court regards parental rights as fundamental. Such a status should subject any legal procedure that directly and substantively interferes with the exercise of parental rights to strict scrutiny. On the contrary, though, despite their status as fundamental constitutional rights, parental rights are routinely suspended or revoked as a result of procedures that fail to meet even minimal standards of procedural and substantive due process. This routine and cavalier deprivation of parental rights takes place in the context of (...) divorce where, during the pendency of litigation, one parent is routinely deprived of significant parental rights without any demonstration that a state interest exists—much less that there is a compelling state interest that cannot be achieved in any less restrictive way. In marked contrast to our current practice, treating parental rights as fundamental rights requires a presumption of joint legal and physical custody upon divorce and during the pendency of divorce litigation. The presumption may be overcome, but only by clear and convincing evidence that such an arrangement is harmful to the children. (shrink)

The theory and philosophy of artificial intelligence has come to a crucial point where the agenda for the forthcoming years is in the air. This special volume of Minds and Machines presents leading invited papers from a conference on the “Philosophy and Theory of Artificial Intelligence” that was held in October 2011 in Thessaloniki. Artificial Intelligence is perhaps unique among engineering subjects in that it has raised very basic questions about the nature of computing, perception, reasoning, learning, language, action, interaction, (...) consciousness, humankind, life etc. etc. – and at the same time it has contributed substantially to answering these questions. There is thus a substantial tradition of work, both on AI by philosophers and of theory within AI itself. - The volume contains papers by Bostrom, Dreyfus, Gomila, O'Regan and Shagrir. (shrink)

Along with offering an historically-oriented interpretive reconstruction of the syntax of PM ( rst ed.), I argue for a certain understanding of its use of propositional function abstracts formed by placing a circum ex on a variable. I argue that this notation is used in PM only when de nitions are stated schematically in the metalanguage, and in argument-position when higher-type variables are involved. My aim throughout is to explain how the usage of function abstracts as “terms” (loosely speaking) is (...) not inconsistent with a philosophy of types that does not think of propositional functions as mind- and language-independent objects, and adopts a nominalist/substitutional semantics instead. I contrast PM’s approach here both to function abstraction found in the typed λ-calculus, and also to Frege’s notation for functions of various levels that forgoes abstracts altogether, between which it is a kind of intermediary. (shrink)