I investigate the role of geometric intuition in Frege’s early mathematical works and the significance of his view of the role of intuition in geometry to properly understanding the aims of his logicist project. I critically evaluate the interpretations of Mark Wilson, Jamie Tappenden, and Michael Dummett. The final analysis that I provide clarifies the relationship of Frege’s restricted logicist project to dominant trends in German mathematical research, in particular to Weierstrassian arithmetization and to the Riemannian conceptual/geometrical tradition at Göttingen. (...) Concurring with Tappenden, I hold that Frege’s logicism should not be understood as a continuing a project of reductionist arithmetization. However, Frege does not quite take up the Riemannian banner either. His logicism supports a hierarchical understanding of the structure of mathematical knowledge, according to which arithmetic is applicable to geometry but not vice versa because the former is more general, as revealed by the strictly logical nature of its objects in comparison to the intuitional nature of geometric objects. I suggest, in particular, that Frege intended that foundational work would show the use of geometric intuition in complex analysis, a source of error for Riemann that Weierstrass was proud to have uncovered, to be inessential. (shrink)

An argument for pro-choice advocates engaging the ethical arguments about abortion, and more. Public philosophy on abortion and the value of philosophy. With Jonathan Dudley, MD.

Nathan Salmon; XII*—How to Measure the Standard Metre, Proceedings of the Aristotelian Society, Volume 88, Issue 1, 1 June 1988, Pages 193–218.

According to cultural evolutionary theory in the tradition of Boyd and Richerson, cultural evolution is driven by individuals' learning biases, natural selection, and random forces. Learning biases lead people to preferentially acquire cultural variants with certain contents or in certain contexts. Natural selection favors individuals or groups with fitness-promoting variants. Durham (1991) argued that Boyd and Richerson's approach is based on a "radical individualism" that fails to recognize that cultural variants are often "imposed" on people regardless of their individual decisions. (...) Fracchia and Lewontin (2005) raised a similar challenge, suggesting that the success of a variant is often determined by the degree of power backing it. With power, a ruler can impose beliefs or practices on a whole population by diktat, rendering all of the forces represented in cultural evolutionary models irrelevant. It is argued here, based on work by Boehm (1999, 2012), that, from at least the time of the early Middle Paleolithic, human bands were controlled by powerful coalitions of the majority that deliberately guided the development of moral norms to promote the common good. Cultural evolutionary models of the evolution of morality have been based on false premises. However, Durham (1991) and Fracchia and Lewontin's (2005) challenge does not undermine cultural evolutionary modeling in nonmoral domains. (shrink)

This paper is about Poincaré’s view of the foundations of geometry. According to the established view, which has been inherited from the logical positivists, Poincaré, like Hilbert, held that axioms in geometry are schemata that provide implicit definitions of geometric terms, a view he expresses by stating that the axioms of geometry are “definitions in disguise.” I argue that this view does not accord well with Poincaré’s core commitment in the philosophy of geometry: the view that geometry is the study (...) of groups of operations. In place of the established view I offer a revised view, according to which Poincaré held that axioms in geometry are in fact assertions about invariants of groups. Groups, as forms of the understanding, are prior in conception to the objects of geometry and afford the proper definition of those objects, according to Poincaré. Poincaré’s view therefore contrasts sharply with Kant’s foundation of geometry in a unique form of sensibility. According to my interpretation, axioms are not definitions in disguise because they themselves implicitly define their terms, but rather because they disguise the definitions which imply them. (shrink)

In mid-2019, the controversy regarding South African runner Caster Semenya’s eligibility to participate in competitions against other female runners culminated in a Court of Arbitration for Sport judgement. Semenya possessed high endogenous testosterone levels (arguably a performance advantage), secondary to a disorder of sexual development. In this commentary, Aristotelean teleology is used to defend the existence of ‘male’ and ‘female’ as discrete categories. It is argued that once the athlete’s sex is established, they should be allowed to compete in the (...) category of their sex without obligatory medical treatment. Indeed, other athletes who possess advantageous genetic or phenotypic traits that fall outside of the human norm have been allowed to compete as humans without restraint. In both cases, if an athlete possesses the essential attributes of being a human or being male or female they should be permitted to compete in those respective categories; athletes’ eligibilities should not be based upon accidental attributes. (shrink)

Toward a theory of n-tuples of individuals and concepts as surrogates for Russellian singular propositions and singular concepts. Alonzo Church proposed a powerful and elegant theory of sequences of functions and their arguments as singular-concept surrogates. Church’s account accords with his Alternative (0), the strictest of his three competing criteria for strict synonymy. The currently popular objection to strict criteria like (0) on the basis of the Russell-Myhill paradox is misguided. Russell-Myhill is not a problem specifically for Alternative (0). Rather (...) it is a disproof of unrestricted concept comprehension. Unrestricted comprehension is also inconsistent with facts about sets of properties. It is demonstrated furthermore that the principal rival conception of propositions, as classes of possible worlds, is subject to a fatal philosophical collapse: It follows on that conception, given that each of us is fallible, that everyone believes everything. Although it is far superior to its principal rival conception, Church’s proposed theory is vulnerable under (0) to a version of Russell’s notorious Gray’s /Elegy/ objection. Some amendments to Church’s proposal are proffered that address Russell’s objection, including an amendment first proposed in the present author’s /Frege’s Puzzle/ (1986). Church’s response (personal correspondence) is considered. (shrink)

Charles Carlini interviews Nathan Salmón about the philosophical work of his mentor and friend, the late Saul Kripke, one of the foremost philosophers of the 20th Century.

This article evaluates an emerging element in popular debate and inquiry: DYOR. (Haven’t heard of the acronym? Then Do Your Own Research.) The slogan is flexible and versatile. It is used frequently on social media platforms about topics from medical science to financial investing to conspiracy theories. Using conceptual and empirical resources drawn from philosophy and psychology, we examine key questions about the slogan’s operation in human cognition and epistemic culture.

Expressions are synonymous if they have the same semantic content. Complex expressions are synonymously isomorphic in Alonzo Church’s sense if one is obtainable from the other by a sequence of alphabetic changes of bound variables or replacements of component expressions by syntactically simple synonyms. Synonymous isomorphism provides a very strict criterion for synonymy of sentences. Several eminent philosophers of language hold that synonymous isomorphism is not strict enough. These philosophers hold that ‘Greeks prefer Greeks’ and ‘Greeks prefer Hellenes’ express different (...) propositions even if they are synonymously isomorphic. They hold that the very recurrence (multiple occurrence) of ‘Greeks’ contributes to the proposition expressed something that indicates the very recurrence in question. Kit Fine argues that this thesis, which he labels semantic relationism calls for a radically new conception of semantics. I have argued that the relevant phenomenon is wholly pragmatic, entirely non-semantic. Here I supplement the case with a new argument. No cognition without recognition—or almost none. With this observation, standard Millianism has sufficient resources to confront Frege’s puzzle and related problems without injecting pragmatic phenomena where they do not belong. (shrink)

In Frege’s Puzzle (1986), Salmon analyzed ‘a withholds believing p’ in terms of a ternary relation BEL of x believing a proposition p under a guise g. The proposed analysis is the following: There is a proposition guise g such that a grasps p by means of g but a does not stand in BEL to p and g. Sean Crawford has made a proposal for Millians to evade propositional guises through second-order belief. Specifically, in effect, Crawford’s proposes to analyze (...) the crucial notion of withheld belief instead as believing that one does not believe: a believes that a does not believe p. Crawford’s clever proposal thus avoids explicit quantification over guises. However, it is shown that the proposal is inadequate to avoid guises. The resulting notion is too weak to capture the relevant notion of withheld belief. (shrink)

We offer an original argument for the existence of universal fictions—that is, fictions within which every possible proposition is true. Specifically, we detail a trio of such fictions, along with an easy-to-follow recipe for generating more. After exploring several consequences and dismissing some objections, we conclude that fiction, unlike reality, is unlimited when it comes to truth.

Epistemic trespassers judge matters outside their field of expertise. Trespassing is ubiquitous in this age of interdisciplinary research and recognizing this will require us to be more intellectually modest.

Standard compositionality is the doctrine that the semantic content of a compound expression is a function of the semantic contents of the contentful component expressions. In 1954 Hilary Putnam proposed that standard compositionality be replaced by a stricter version according to which even sentences that are synonymously isomorphic (in the sense of Alonzo Church) are not strictly synonymous unless they have the same logical form. On Putnam’s proposal, the semantic content of a compound expression is a function of: (i) the (...) contentful component expressions; and (ii) the expression’s logical form. Kit Fine recently expanded and modified Putnam’s idea into a sweeping theory in philosophy of language and philosophy of mind. The present paper is a detailed critique of Fine’s “semantic relationism.” Fine’s notion of coordination is explained in terms of the familiar pragmatic phenomenon of recognition. A serious error in Fine’s formal disproof of standard Millianism is exposed. It is demonstrated furthermore that Church’s original criticism of Putnam’s proposal can be extended to Fine’s semantic relationism. Finally, it is also demonstrated that the positive position Fine proffers to supplant standard Millianism is in fact exactly equivalent to standard Millianism, so that Fine’s overall position not only does not displace standard Millianism but is in fact inconsistent. (shrink)

Rather infamously, Kit Fine provided a series of counter-examples which purport to show that the modalist program of analysing essence in terms of metaphysical necessity is fundamentally misguided. Several would-be modalists have since responded, attempting to save the position from this Finean Challenge. This paper evaluates and rejects a trio of such responses, from Della Rocca, Zalta, and Gorman. But I’m not here arguing for Fine’s conclusion – ultimately, this is a fight amongst friends, with Della Rocca, Zalta, Gorman, and (...) I all wanting to be modalists, but disagreeing on the details. As such, while my primary aim is to show what’s wrong with this trio, the secondary aim is demonstrating how what’s right about them in fact pushes one towards my own sparse modalist account. So while the primary conclusion of this paper is negative, the secondary, positive, conclusion is that modalists shouldn’t give up hope – plausible responses to Fine are still out there. (shrink)

In this essay I consider whether the political perspective of third wave science studies – ‘elective modernism’ – offers a suitable framework for understanding the policy-making contributions that (bio)ethical experts might make. The question arises as a consequence of the fact that I have taken inspiration from the third wave in order to develop an account of (bio)ethical expertise. I offer a précis of this work and a brief summary of elective modernism before considering their relation. The view I set (...) out suggests that elective modernism is a political philosophy and that although its use in relation to the use of scientific expertise in political and policy-making process has implications for the role of (bio)ethical expertise it does not, in the final analysis, provide an account that is appropriate for this latter form of specialist expertise. Nevertheless, it is an informative perspective, and one that can help us make sense of the political uses of (bio)ethical expertise. (shrink)

In this paper I argue that Locke takes sensitive knowledge (i.e. knowledge from sensation) to be genuine knowledge that material objects exist. Samuel Rickless has recently argued that, for Locke, sensitive knowledge is merely an “assurance”, or a highly probable judgment that falls short of certainty. In reply, I show that Locke sometimes uses “assurance” to describe certain knowledge, and so the use of the term “assurance” to describe sensitive knowledge does not entail that it is less than certain. Further, (...) I show that sensitive knowledge includes the perception of a relation between ideas, and thus it satisfies Locke’s definition of knowledge. He also repeatedly claims that sensitive knowledge is certain. So, despite recent challenges to this interpretation raised in the secondary literature, Locke really does take sensitive knowledge to be certain knowledge. (shrink)

The past decade and a half has seen an absolute explosion of literature discussing the structure of reality. One particular focus here has been on the fundamental. However, while there has been extensive discussion, numerous fundamental questions about fundamentality have not been touched upon. In this chapter, I focus on one such lacuna about the modal strength of fundamentality. More specifically, I am interested in exploring the contingent fundamentality thesis - that is, the idea that the fundamentalia are only contingently (...) fundamental (or, in property-terms, that the property of being fundamental is not a (weakly) necessary property). And while I think this thesis is plausible – indeed, I show here that it lurks in the unexamined shadows/assumptions of some fairly prominent positions – as far as I can tell, nothing has been said either for or against it. Here, I hope to fix this by giving the thesis a proper airing. In this way, this chapter represents a first-pass at exploring not only the modal status of fundamentality, but also offers a starting point for examining broader issues about the relationship between fundamentality and modality. (shrink)

In this paper, I consider a novel challenge to John Martin Fischer and Mark Ravizza’s reasons-responsiveness theory of moral responsibility. According to their view, agents possess the control necessary for moral responsibility if their actions proceed from a mechanism that is moderately reasons-responsive. I argue that their account of moderate reasons-responsiveness fails to provide necessary and sufficient conditions for moral responsibility since it cannot give an adequate account of the responsibility of individuals with autism spectrum disorder. Empirical evidence suggests that (...) autistic individuals demonstrate impairments in counterfactual thinking, and these impairments, I argue, are such that they cast doubt on Fischer and Ravizza’s construal of moderate reasons-responsiveness. I then argue that modifying the view in order to accommodate individuals with ASD forces them to defend a strong reasons-responsive account despite the fact that they explicitly deny that such an account can adequately characterize what it is to be morally responsible for one’s actions. (shrink)

Over the course of the last four decades, William Leon McBride has distinguished himself as one of the most esteemed and accomplished philosophers of his generation. This volume—which celebrates the occasion of his seventy-fifth birthday—includes contributions from colleagues, friends, and formers students and pays tribute to McBride’s considerable achievements as a teacher, mentor, and scholar.

In recent years there has been an explosion of philosophical work on blame. Much of this work has focused on explicating the nature of blame or on examining the norms that govern it, and the primary motivation for theorizing about blame seems to derive from blame’s tight connection to responsibility. However, very little philosophical attention has been given to praise and its attendant practices. In this paper, I identify three possible explanations for this lack of attention. My goal is to (...) show that each of these lines of thought is mistaken and to argue that praise is deserving of careful, independent analysis by philosophers interested in theorizing about responsibility. (shrink)

A distinction is drawn among predicates, open sentences (or open formulas), and general terms, including general-term phrases. Attaching a copula, perhaps together with an article, to a general term yields a predicate. Predicates can also be obtained through lambda-abstraction on an open sentence. The issue of designation and semantic content for each type of general expression is investigated. It is argued that the designatum of a general term is a universal, e.g., a kind, whereas the designatum of a predicate is (...) a class (or its characteristic function) and the designatum of an open sentence is a truth-value. Predicates and open sentences are therefore typically non-rigid designators. It is argued further that certain general terms, including phrases, are invariably rigid designators, whereas certain others (general definite descriptions) are typically non-rigid. Suitable semantic contents for predicates, open sentences, and general terms are proposed. Consequences for the thesis of compositionality are drawn. (shrink)

This paper presents a deductive proof for the necessary existence of objective truth and reality, addressing core philosophical challenges across multiple frameworks, including modernism, postmodernism, relativism, and radical skepticism. By starting with the undeniable fact of subjective experience, the argument demonstrates that rationality presupposes subjectivity, which in turn relies on the classical laws of logic. These laws cannot be grounded within subjectivity or rationality without falling into circular reasoning. Therefore, the proof establishes that objective reality must serve as the ground (...) for these logical laws, while objective truth provides their validation. This foundational framework resolves key philosophical problems, including infinite regress and self-justification, allowing for coherent philosophical thought. Furthermore, the paper explores conceptual parallels between this proof and elements of mysticism, pragmatism, and religious notions of divinity, suggesting a unified foundation that can empower individual contributions to the collective pursuit of truth. (shrink)

Pensare in modo critico sull'aborto: Perché la maggior parte degli aborti non sono moralmente sbagliati; Perché tutti gli aborti dovrebbero essere legali: "Thinking Critically About Abortion" in Italian.

The Counterfactual Comparative Account of Harm says that an event is overall harmful for someone if and only if it makes her worse off than she otherwise would have been. I defend this account from two common objections.

The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that no effective procedure is possible for ascertaining whether a given procedure is effective. This (...) undecidability result is proved directly from the notion itself of an effective procedure, without reliance on any (partly) mathematical lemma, conjecture, or thesis invoking recursiveness or Turing-computability. In fact, there is no reliance on anything very mathematical. The proof does not even appeal to a precise definition of ‘effective procedure’. Instead, it relies solely and entirely on a basic grasp of the intuitive notion of an effective procedure. Though the result that effectiveness is undecidable is not surprising, it is also not without significance. It has the consequence, for example, that the solution to a decision problem, if it is to be complete, must be accompanied by a separate argument that the proposed ascertainment procedure invariably terminates with the correct verdict. (shrink)

Arguments for moral nihilism—the view that there are no moral truths—are criticized by showing that their major premises suggest epistemic or intellectual nihilism—the view that no beliefs are reasonable, justified, ought to be believed, and so on. Insofar as intellectual nihilism ought be rejected, this shows that the major premises of arguments for moral nihilisms ought to be rejected also.

Error Management Theory (EMT) suggests that cognitive adaptations evolve to minimize the cost of false negative and false positive errors in detections of consequential environmental conditions. These adaptations manifest as biases tailored to specific environmental conditions. This paper proposes that the same selection pressure fostered the evolution of a self-biasing ability, allowing us to minimize such costs based on experience and culturally transmitted information. The research indicates that this ability specifically applies to productions of belief or doubt about the existence (...) of an environmental condition that is not adequately perceptible to the senses, e.g., doubt that the man is being honest. A model of this self-biasing process, rooted in signal detection theory, is developed and its explanatory reach is demonstrated through many diverse examples from epistemological and social psychological literatures. These examples feature an evidentiary standard for belief that appears too high or low, or seems to have modulated. This study aims to correct and to significantly enhance EMT by introducing this evolved self-biasing ability. (shrink)

While it is tempting to suppose that an act has moral worth just when and because it is motivated by sufficient moral reasons, philosophers have, largely, come to doubt this analysis. Doubt is rooted in two claims. The first is that some facts can motivate a given act in multiple ways, not all of which are consistent with moral worth. The second is the orthodox view that normative reasons are facts. I defend the tempting analysis by proposing and defending a (...) heterodox account of both normative and motivating reasons that is inspired by Donald Davidson’s primary reasons. We should adopt the heterodox view, I argue, because it addresses an overlooked but fatal defect in the orthodox conception of reasons, of which challenges to the tempting analysis are a special case. (shrink)

In the Republic, Socrates argues that morality (justice) is valuable both for itself and for what comes from it. In contemporary moral theory, this view is not widely accepted. However, contemporary empirical research in psychology reveals that what we experience is also what we come to expect. It follows from this that if we act in an immoral fashion, we will expect the same from others. The more often we act immorally, the more suspicion will be ingrained within us. Suspicion (...) quickly pervades our minds, corrodes our relationships, and increases our levels of stress, thereby dramatically decreasing our quality of life. Moral action, on the other hand, has the ability to strengthen our faith in others and create strong human relationships. Therefore,morality should be classified as having the highest type of value, just as Socrates contends.Moral behavior allows for healthy relations between persons (intrinsic value) and the wellbeing of the individual (extrinsic value). (shrink)

This is a research report in which we present examples which should be of interest to those working on clausal embedding and dubitative verbs. Examples are presented which are relevant to the evaluation of claims and arguments in: (Karttunen 1977), (Uegaki 2021), (Huddleston 1994), (Biezma & Rawlins 2012), (Roelofsen; Herbstritt; & Aloni 2019), (Suñer 1993), and (Rawlins 2008). The examples are mostly from English, but we also present some examples from Italian, Spanish, and German.

In this candid autobiographical essay, Nathan Salmon recounts and assesses the impact of various philosophers and events on his philosophical development.

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

Kit Fine has replied to my criticism of a technical objection he had given to the version of Millianism that I advocate. Fine evidently objects to my use of classical existential instantiation in an object-theoretic rendering of his meta-proof. Fine’s reply appears to involve both an egregious misreading of my criticism and a significant logical error. I argue that my rendering is unimpeachable, that the issue over my use of classical EI is a red herring, and that Fine’s original argument (...) commits the straw-man fallacy. I argue further that contrary to Fine’s gratuitous attribution, what Kripke’s Pierre lacks and a typical bilingual has is not knowledge of a “manifest-making” premise, but the capacity to recognize London when it is differently designated. Fine’s argument refutes a preposterous theory no one advocates while leaving standard Millianism unscathed. The failure of his argument threatens to render Fine’s central notion of “coordination” redundant or empty. (shrink)