Indeterminacy is metaphysical (or worldly) if it has its source in the way the world is (rather than how it is represented or known). There are two questions we could ask about indeterminacy. First: does it exist? Second: is indeterminacy derivative? I focus on the second question. Specifically, I argue that (at least some) metaphysical indeterminacy can be derivative, where this roughly means that facts about indeterminacy are metaphysically grounded in facts about what is determinate.

According to the objection from positive duties, Kant's Formula of Universal Law is flawed because it cannot be used to derive any affirmative moral requirements. This paper offers a response to that objection and proposes a novel way to derive positive duties from Kant's formula. The Formula of Universal Law yields positive duties to adopt our own perfection and others’ happiness as ends because we could not rationally fail to will those ends as universal ends.

The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics _S__T_ and _T__S_. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that in (...) these systems derivability can be characterized in terms of a notion we call absolute global validity. However, arriving at these results doesn’t lead us to disregard local validity. First, because we discuss the conditions under which local, and also global validity, can be expected to coincide with derivability. Secondly, because we show how taking into account certain families of valuations can be useful to describe derivability for different calculi used to present _S__T_ and _T__S_. (shrink)

On the currently dominant reading of the Groundwork, Kant’s derivation of ‘imperatives of duty’ exemplifies a decision procedure for the derivation of concrete duties in moral deliberation. However, Kant’s response to an often-misidentified criticism of the Groundwork by G. A. Tittel suggests that Kant was remarkably unconcerned with arguing for the practicality of the categorical imperative as a decision procedure. Instead, I argue that the main aim of Kant’s derivation of imperatives of duty was to show how (...) his analysis of the form of moral judgement is indeed presupposed in the four types of moral imperative that philosophers of his time recognized. (shrink)

At the heart of Rik Peels’s Responsible Belief: A Theory in Ethics and Epistemology is the idea that responsibility for belief ought to be understood on the model of responsibility for states of affairs that are subject to our influence but not under our intentional control, or what he calls derivative responsibility. In this article, I argue that reflection on the nature and scope of derivative responsibility reveals important lacunae in Peels’s account of responsible belief and his account of responsibility (...) for belief. (shrink)

This chapter argues that quantum indeterminacy can be construed as a merely derivative phenomenon. The possibility of merely derivative quantum indeterminacy undermines both a recent argument against quantum indeterminacy due to David Glick, and an argument against the possibility of merely derivative indeterminacy due to Elizabeth Barnes.

This chapter derives and refines a novel normative moral theory and descriptive theory of moral psychology--Rightness as Fairness--from the theory of prudence defended in Chapter 2. It briefly summarizes Chapter 2’s finding that prudent agents typically internalize ‘moral risk-aversion’. It then outlines how this prudential psychology leads prudent agents to want to know how to act in ways they will not regret in morally salient cases, as well as to regard moral actions as the only types of actions that satisfy (...) this prudential interest. It then uses these findings to defend a new derivation of my (2016) theory of morality, Rightness as Fairness, showing how the derivation successfully defends Rightness as Fairness against a variety of objections. The chapter also details how this book’s theory helps to substantiate the claim that Rightness as Fairness unifies a variety of competing moral frameworks: deontology, consequentialism, contractualism, and virtue ethics. Finally, the chapter shows how Chapter 2’s theory of prudence entails some revisions to Rightness as Fairness, including the adoption of a series of Rawlsian original positions to settle moral and social-political issues under ideal and nonideal circumstances—thus entailing a unified normative and descriptive psychological framework for prudence, morality, and justice. (shrink)

In a rather old paper, Mario Liu described a hydrodynamic Maxwell equations. While he also discussed potential implications of these new approaches to superconductors, such a discussion of electrodynamics of superconductors is made only after Tajmar’s paper. Therefore, in this paper we present for the first time a derivation of fluidic Maxwell-Proca equations. The name of fluidic Maxwell-Proca is proposed because the equations were based on modifying Maxwell-Proca and Hirsch’s theory of electrodynamics of superconductor. It is hoped that this (...) paper may stimulate further investigations and experiments in superconductor. It may be expected to have some impact to cosmology modeling too, for instance we consider a hypothetical argument that photon mass can be origin of gravitation. Then, after combining with the so-called chiral modification of Maxwell equations (after Spröessig), then we consider chiral Maxwell-Proca equations as possible alternative of gravitation theory. Such a hypothesis has never considered in literature to the best of our knowledge. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, (...) in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

Veritists hold that only truth has fundamental epistemic value. They are committed to explaining all other instances of epistemic goodness as somehow deriving their value through a relation to truth, and in order to do so they arguably need a non-instrumental relation of epistemic value derivation. As is currently common in epistemology, many veritists assume that the epistemic is an insulated evaluative domain: claims about what has epistemic value are independent of claims about what has value simpliciter. This paper (...) argues that the insulation approach to epistemic value is incompatible with non-instrumental epistemic value derivation. Veritsts who want to avail themselves of this important explanatory resource should therefore abandon the insulation approach. (shrink)

This paper explores the charge by Bruce Aune and Allen Wood that a gap exists in Kant's derivation of the Categorical Imperative. I show that properly understood, no such gap exists, and that the deduction of the Categorical Imperative is successful as it stands.

We show that the physical meaning of the wave function can be derived based on the established parts of quantum mechanics. It turns out that the wave function represents the state of random discontinuous motion of particles, and its modulus square determines the probability density of the particles appearing in certain positions in space.

I give a pedagogical derivation of the Cramer-Rao Bound, which gives a lower bound on the variance of estimators used in statistical point estimation, commonly used to give numerical estimates of the systematic uncertainties in a measurement.

Many philosophers of physics think that physical rates of change, like velocity or acceleration in classical physics, are extrinsic. Many philosophers of mind think that phenomenal properties, which characterize what it’s like to be an agent at a time, are intrinsic. I will argue that these two views can’t both be true. Given that these two views are in tension, we face an explanatory challenge. Why should there be any interesting connection between these physical quantities and consciousness in the first (...) place? In a speculative spirit, I close by developing a panpsychist view which promises to explain this connection in a particularly satisfying way. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated (...) labelled calculus. (shrink)

Four simple postulates are presented, from which we derive a (3+1)‑dimensional structure, interpreted as ordinary space and time. We then derive further properties of space: isotropy and homogeneity; a rapid expansion within the first instant of time (i.e. inflation); and a continual and uniform expansionary pressure, due to a continual influx of (non-zero-point) energy that is uniformly distributed (i.e. dark energy). In addition, the time dimension is shown to have an "arrow". These results suggest that the four postulates may be (...) fundamental to the construction of the physical universe. (shrink)

I pedagogically show that the momentum operator in quantum mechanics, in the position representation, commonly known to be a derivative with respect to a spatial x-coordinate, can be derived by identifying momentum as the generator of space translations.

Animal-derived constituents are frequently used in anaesthesia and surgery, and patients are seldom informed of this. This is problematic for a growing minority of patients who may have religious or secular concerns about their use in their care. It is not currently common practice to inform patients about the use of animal-derived constituents, yet what little empirical data does exist indicates that many patients want the opportunity to give their informed consent. First, we review the nature and scale of the (...) problem by looking at the groups who may have concerns about the use of animal-derived constituents in their care. We then summarise some of the products used in anaesthesia and surgery that can contain such constituents, such as anaesthetic drugs, surgical implants and dressings. Finally, we explore the problem of animal-derived constituents and consent using Beauchamp and Childress’ four principles approach, examining issues of autonomy, beneficence, nonmaleficence and justice. Disclosing the use of animal-derived constituents in anaesthesia and surgery is warranted under Beauchamp and Childress’ four principles approach to the problem. Although there exist systemic and practical challenges to implementing this in practice, the ethical case for doing so is strong. The Montgomery ruling presents additional legal reason for disclosure because it entails that patients must be made aware of risks associated with their treatment that they attach significance to. (shrink)

It is shown that the heuristic "derivation" of the Schrödinger equation in quantum mechanics textbooks can be turned into a real derivation by resorting to spacetime translation invariance and relativistic invariance.

In this paper, we develop a mathematical model of awareness based on the idea of plurality. Instead of positing a singular principle, telos, or essence as noumenon, we model it as plurality accessible through multiple forms of awareness (“n-awareness”). In contrast to many other approaches, our model is committed to pluralist thinking. The noumenon is plural, and reality is neither reducible nor irreducible. Nothing dies out in meaning making. We begin by mathematizing the concept of awareness by appealing to the (...) mathematical formalism of higher category theory. The beauty of higher category theory lies in its universality. Pluralism is categorical. In particular, we model awareness using the theories of derived categories and (infinity, 1)-topoi which will give rise to our meta-language. We then posit a “grammar” (“n-declension”) which could express n-awareness, accompanied by a new temporal ontology (“n-time”). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? Another question which could be re-conceptualized in our model is one of soteriology related to this pluralism: what is a self in this context? A new model of “personal identity over time” is thus introduced. (shrink)

Sennett (1999) and Pawl & Timpe (2009; 2013) attempt to show how we can praise heavenly agents for things they inevitably do in heaven by appealing to the notion of derivative freedom. Matheson (2017) has criticized this use of derivative freedom. In this essay I show why Matheson's argument is inconclusive but also how the basic point may be strengthened to undermine the use Sennett and Pawl & Timpe make of derivative freedom. I then show why Matheson is mistaken to (...) claim that the value of free choice depends on an agent retaining the ability to change their mind; in so doing I demonstrate that some choices which result in fixed outcomes - a feature of the choices leading to impeccability - can indeed be valuable even if they cannot be undone. (shrink)

A thorough critique (extracted from the author’s 1979 doctoral dissertation) of Kripke’s purported derivation, in footnote 56 of his philosophical masterpiece /Naming and Necessity/, of nontrivial modal essentialism from the theory of rigid designation.

In this paper, we deal with the computation of Lie derivatives, which are required, for example, in some numerical methods for the solution of differential equations. One common way for computing them is to use symbolic computation. Computer algebra software, however, might fail if the function is complicated, and cannot be even performed if an explicit formulation of the function is not available, but we have only an algorithm for its computation. An alternative way to address the problem is to (...) use automatic differentiation. In this case, we only need the implementation of the algorithm that evaluates the function in terms of its analytic expression in a programming language, but we cannot use this if we have only a compiled version of the function. In this paper, we present a novel approach for calculating the Lie derivative of a function, even in the case where its analytical expression is not available, that is based on the In finity Computer arithmetic. A comparison with symbolic and automatic differentiation shows the potentiality of the proposed technique. (shrink)

We give the derivation, as opposed to justification, of the Presentist Fragmentalist interpretation of quantum mechanics in perhaps its most basic form, and then several other considerations.

The reason for physics’ failure to find a final theory of the universe is examined. Problems identified are: the lack of unequivocal definitions for its fundamental elements (time, length, mass, electric charge, energy, work, matter-waves); the danger of relying too much on mathematics for solutions; especially as philosophical arguments conclude the universe cannot have a mathematical basis. It does not even need the concept of number to exist. Numbers and mathematics are human inventions arising from the human predilection for measurement. (...) Following Aristotle, a single fundamental cause is proposed to explore the efficacy of using pure non-mathematical philosophy to explain the universe, contrary to current quantum physical views. The cause is taken as Time, which is then defined, surprisingly leading automatically to a definition of a three-dimensional space answering the question into what can a universe be placed (space before space seems non-sensical). This enables the philosophical arguments to derive a universal rule giving clear-cut descriptions (definitions) of force (both gravitational and electromagnetic), motion, energy, and particles. The formation of atomic nuclei and atomic properties together with an unexpected role for neutrinos follow. In particular, a Popper-test can be prepared by introducing the concept of measurement to allow the philosophy arguments to be tested in another discipline - mathematics. The solution agrees with human physical observations to a remarkable degree of accuracy, automatically explaining and predicting values for Planck’s and the fine-structure constants. Although mathematical, it is included as confirming the efficacy of philosophy in attaining a final theory. (shrink)

According to the standard reading of Kant's formula of universal law (FUL), positive duties can be derived from FUL. In this article, I argue that the standard reading does not work. In the first section, I articulate FUL and what I mean by a positive duty. In the second section, I set out an intuitive version of the standard reading of FUL and argue that it does not work. In the third section, I set out a more rigorous version of (...) the standard reading of FUL and argue that even this more rigorous version does not work. (shrink)

This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines. Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking non-orientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.

Einstein's gravitational redshift derivation in his famous 1916 paper on general relativity seems to be problematic, being mired in what looks like conceptual difficulties or at least contradictions or gaps in his exposition. Was this derivation a blunder? To answer this question, we will consider Einstein’s redshift derivations from his first one in 1907 to the 1921 derivation made in his Princeton lectures on relativity. This will enable to see the unfolding of an interdependent network of concepts (...) and heuristic derivations in which previous ideas inform and condition later developments. The resulting derivations and views on coordinates and clocks are in fact not without inconsistencies. However, we can see these difficulties as an aspect of an evolving network understood as a “work in progress”. (shrink)

The problem of the formal connection between electrodynamics and wave mechanics has attracted the attention of a number of authors, especially there are some existing proofs on Maxwell-Dirac isomorphism. Here the author will review two derivations of Maxwell-Dirac isomorphism i.e. by Hans Sallhofer and Volodimir Simulik. A few plausible extensions will be discussed too.

In this paper I begin by discussing the different ways in which Spinoza’s famous conatus argument has been understood, after which I present my own reconstruction of the derivation: each and every true finite thing is, in itself, an expresser of power (E1p25c, 1p34) that never acts self-destructively (E3p4) but instead strives to drive itself through opponents to produce effects as they follow from the definition of the thing in question (E1p25c, 1p34, and 3p5). This tells us something decisive (...) about the meaning of Spinoza’s doctrine: according to it, things are active causers whose “power to exist and act” has conatus character in temporality, amounting not only to striving to prolong the duration of one’s actualization but also to striving to be as active or autonomous as possible, that is, to attain a state determined by the striving subject’s essence alone. (shrink)

I argue that a reasonable understanding of Leopold’s ‘Land Ethic’ is one that identifies possession of health as being a sufficient condition for moral consideration. With this, Leopold extends morality not only to biotic wholes, but to individual organisms, as both can have their health undermined. My argument centers on explaining why Leopold thinks it reasonable to analogize ecosystems both to an organism and to a community: both have a health. My conclusions undermine J. Baird Callicott’s rhetorical dismissal of the (...) organism analogy’s importance, a dismissal crucially serving his thesis that Leopoldians should hold community membership necessary for moral standing. (shrink)

Imagine a sculptor who molds a lump of clay to create a statue. Hylomorphism claims that the statue and the lump of clay are two different colocated objects that have different forms, even though they share the same matter. Recently, there has been some discussion on the requirements of consistency for hylomorphist theories. In this paper, we focus on an argument presented by Maegan Fairchild, according to which a minimal version of hylomorphism is inconsistent. We argue that the argument is (...) unsound or, at best, it just points to a well-known problem for hylmorphist theories. Additionally, we explore some general consequences of this fact. (shrink)

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

The mathematical formalism of quantum theory has been established for nearly a century, yet its physical foundations remain elusive. In recent decades, connections between quantum theory and information theory have garnered increasing attention. This study presents a physical derivation of the mathematical formalism quantum theory based on information-theoretic considerations in physical systems. We postulate that quantum systems are characterized by single independent adjustable variables. Utilizing this physical postulate along with the conservation of total probability, we derive the standard Hilbert (...) space formalism of quantum theory, including the Born probability rule. This comprehensive derivation of quantum theory offers a clear and concise physical foundation for the mathematical formalism of quantum mechanics. (shrink)

Appendix to lecture notes on "Nominal (re)centering: From Kalaallisut to UC1". Day 2 of advanced course on "Cross-linguistic compositional semantics" at LSA Summer Institute 2009 at UC Berkeley.

Some philosophers working on the metaphysics of agency argue that if agency is understood in terms of settling the truth of some matters, then the power required for the exercise of intentional agency is an irreducible two-way power to either make it true that p or not-p. In this paper, the focus is on two-way powers in decision-making. Two problems are raised for theories of decision-making that are ontologically committed to irreducible two-way powers. First, recent accounts lack an adequate framework (...) for explaining decisions by the reasons of agents. Second, accepting ontologically irreducible two-way powers into one’s metaphysic of agency implies an ontological commitment to substance dualism. An ontologically less-costly alternative to irreducible two-way powers is offered. It is argued that a reductive account of two-way powers in terms of what George Molnar called “derivative powers” should be accepted. The reductive account can provide us with the truthmakers for talk about two-way powers. Moreover, the reductive account does not share the liabilities of accepting irreducible two-way powers. (shrink)

This article presents a generic model for pricing financial derivatives subject to counterparty credit risk. Both unilateral and bilateral types of credit risks are considered. Our study shows that credit risk should be modeled as American style options in most cases, which require a backward induction valuation. To correct a common mistake in the literature, we emphasize that the market value of a defaultable derivative is actually a risky value rather than a risk-free value. Credit value adjustment (CVA) is also (...) elaborated. A practical framework is developed for pricing defaultable derivatives and calculating their CVAs at a portfolio level. (shrink)

The argument that follows has a certain air of prestidigitation about it. I attempt to show that, given a couple of innocent-seeming suppositions, it is possible to derive a positive and complete theory of normative ethics from the Humean maxim "You can't get ought from is." This seems, of course, absurd. If the reasoning isn't completely unhinged, you may be sure, the trick has to lie in those "innocent-seeming" props. And, in fact, you are right. But every argument has to (...) begin somewhere, and, however questionable, those suppositions just don't seem to harbor serious normative import. (shrink)

In this chapter, I argue that Kant can be read as holding that "ought" judgments follow from certain "is" judgments by mere analysis. More specifically, I defend an interpretation according to which (1) Kant holds that “S ought to F” is analytically equivalent to “If, as it can and would were there no other influences on the will, S’s faculty of reason determined S’s willing, S would F” and (2) Kant’s notions of reason, the will, and freedom are all fundamentally (...) non-normative. Not only does this reading have significant textual support, but, I claim, it also sheds light on why Kant takes freedom and morality to mutually imply one another. Moreover, while Kant does take there to be a gap between moral judgments and empirical descriptive statements, that gap is consistent with the analysis in question. I conclude by arguing that this rejection of the is-ought gap is not as philosophically implausible as it might seem, with a focus on G.E. Moore and Hume’s arguments for certain ‘gaps’ between the normative and the non-normative. (shrink)

The purpose of this paper is to show that, if Kant’s universalization formulations of the Categorical Imperative are our only standards for judging right from wrong and permissible from impermissible, then we have no obligations. I shall do this by examining five different views of how obligations can be derived from the universalization formulations and arguing that each one fails. I shall argue that the first view rests on a misunderstanding of the universalization formulations; the second on a misunderstanding of (...) the concept of an obligation; the third on a misunderstanding of the concept of a maxim; the fourth on a misunderstanding of the limits of action description; and the fifth on a misunderstanding of the universalization formulations again. (shrink)

In this review essay, I raise three principal concerns relating to Schulting’s project of deriving the categories from apperception as elaborated in his recent book Kant’s Deduction and Apperception (Palgrave Macmillan, 2012). First, I claim that Schulting overlooks a key ambiguity relating to ‘ableiten’ and which contrasts with his strictly logical understanding of that term. Second, I dispute on textual and philosophical grounds Schulting’s characterization of the subject’s consciousness of its own identity in terms of the analytic unity of apperception. (...) Finally, I raise an objection to Schulting’s account of the derivation of the concept of substance from apperception, as I claim that at best Kant allows that the logical function underlying this category (rather than the category itself) can be so derived, and I note that this objection can be extrapolated to apply to the other derivations of the categories Schulting offers. (shrink)

The additive presupposition of particles like "too"/"even" is uncontested, but usually stipulated. This paper proposes to derive it based on two properties. (i) "too"/"even" is cross-linguistically focus-sensitive, and (ii) in many languages, "too"/"even" builds negative polarity items and free-choice items as well, often in concert with other particles. (i) is the source of its existential presupposition, and (ii) offers clues regarding how additivity comes about. (i)-(ii) together demand a sparse semantics for "too/even," one that can work with different kinds of (...) alternatives (focus, subdomain, scalar) and invoke suitably different further operators. (shrink)

This paper offers a sketch of welfarist pluralism, a view that is intended to resolve a difficulty for non-derivative pluralists about normative reasons for belief. Welfarist pluralism is the view that all reasons for belief are rooted in wellbeing, and that wellbeing has as one of its components being in a positive epistemic state. The paper explores how this view can explain various pluralist intuitions and why it offers a plausible basis for combinatorial pluralists who believe that alethic and pragmatic (...) reasons for belief combine to determine what one ought to believe. The paper also considers the relationship between theoretical rationality and wellbeing, and provides a partial argument for the derivative normativity of at least some requirements of theoretical rationality. (shrink)

Medicines and medical devices containing animal-derived ingredients are frequently used on patients without their informed consent, despite a significant proportion of patients wanting to know if an animal-derived product is going to be used in their care. Here, I outline three arguments for why this practice is wrong. First, I argue that using animal-derived medical products on patients without their informed consent undermines respect for their autonomy. Second, it risks causing nontrivial psychological harm. Third, it is morally inconsistent to respect (...) patients’ dietary preferences and then use animal-derived medicines or medical devices on them without their informed consent. I then address several anticipated objections and conclude that the continued failure to address this issue is an ethical blind spot that warrants applying the principles of respect for autonomy and informed consent consistently. There are no data in this work. (shrink)

a simple derivation of the effect induced from repeated measurements on quantum unstable systems is obtained by using the regularized incomplete beta - function .

Ever since Hegel famously objected to Kant’s universalization formulations of the Categorical Imperative on the grounds that they are nothing but an empty formalism, there has been continual debate about whether he was right. In this paper I argue that Hegel got things at least half-right: I argue that even if negative duties (duties to omit actions or not to adopt maxims) can be derived from the universalization formulations, positive duties (duties to commit actions or to adopt maxims) cannot. The (...) paper is divided into three main sections. In the first, I set out the procedures generally accepted among Kantians for deriving positive duties from the universalization formulations. In the second, I set out the arguments from section 1 in more detail and explain why they do not work. In the third, I examine a strategy that might be used to supplement the arguments from section 2 and I argue that it also does not work. (shrink)

Vehicle externalism maintains that the vehicles of our mental representations can be located outside of the head, that is, they need not be instantiated by neurons located inside the brain of the cogniser. But some disagree, insisting that ‘non-derived’, or ‘original’, content is the mark of the cognitive and that only biologically instantiated representational vehicles can have non-derived content, while the contents of all extra-neural representational vehicles are derived and thus lie outside the scope of the cognitive. In this paper (...) we develop one aspect of Menary’s vehicle externalist theory of cognitive integration—the process of enculturation—to respond to this longstanding objection. We offer examples of how expert mathematicians introduce new symbols to represent new mathematical possibilities that are not yet understood, and we argue that these new symbols have genuine non-derived content, that is, content that is not dependent on an act of interpretation by a cognitive agent and that does not derive from conventional associations, as many linguistic representations do. (shrink)