Ignoring primitive terms leads to an infinite regress. The alternative is to account for an intuitive understanding into the meaning of such terms. The current investigation proceeds on the basis of an idea of the structure of the various modes of being within which concrete entities function. Examples of primtive terms are given from disciplines such as mathematics, physics and logic and they are related to the general idea of a modal aspect. It is argued that (...) primitive terms are not isolated but reveal their meaning only through their interconnections with other primitive terms that are embedded in other modal aspects. However, although primitive terms are found within the various aspects, the meaning of an aspect only comes to expression through its coherence with other aspects, evinced in modal analogies that are qualified by the core meaning of an aspect. There appears to be two options, either reduce what is irreducible or merely provide synonymous terms for given primitives. The former happens when other unique terms are used to define a specific one and the latter when the attempted ‘definitions’ revert to terms with which the original terms could be meaningfully replaced. It is been pointed out that the coherence between primitives invites every academic discipline to account for the meaning attached to the analogies of primitive terms it is employing, without exploring this additional theme any further. (shrink)

We first present an edition of the manuscript LH VII, B 2, 39 in which Leibniz develops a new formalism in order to give rigorous definitions of positive, of privative, and of primitive terms.This formalism involves a symbolic treatment of conceptual quantification which differs quite considerably from Leibniz’s “standard” theory of “indefinite concepts” as developed, e.g., in the “General Inquirles” In the subsequent commentary we give an interpretation and a critical evaluation of Leibniz’s symbolic apparatus. It turns out (...) that the definition of privative terms and primitive terms lead to certain inconsistencies which, however, can be avoided by slight modifications. (shrink)

The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to (...) the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments. (shrink)

The termination of rewrite systems for parameter recursion, simple nested recursion and unnested multiple recursion is shown by using monotone interpretations both on the ordinals below the first primitive recursively closed ordinal and on the natural numbers. We show that the resulting derivation lengths are primitive recursive. As a corollary we obtain transparent and illuminating proofs of the facts that the schemata of parameter recursion, simple nested recursion and unnested multiple recursion lead from primitive recursive functions to (...) primitive recursive functions. (shrink)

Eternalists believe that there is no ontological difference between the past, present and future. Thus, a challenge arises: in virtue of what does time have a direction? Some eternalists, Oaklander and Tegtmeier ) argue that the direction of time is primitive. A natural response to positing primitive directionality is the suspicion that said posit is too mysterious to do any explanatory work. The aim of this paper is to relieve primitive directionality of some of its mystery by (...) offering a novel way to understand the phenomenon in terms of the recently popularised notion of grounding. (shrink)

I argue that McDowell-style disjunctivism, as the position is often cashed out, goes wrong because it takes the good epistemic standing of veridical perception to be grounded in “manifest” facts which do not necessarily satisfy any epistemic constraints. A better form of disjunctivism explains the difference between good and bad cases in terms of epistemic constraints that the states satisfy. This view allows us to preserve McDowell’s thesis that good cases make facts manifest, as long as manifest facts must (...) satisfy epistemic constraints. (shrink)

Primitive ontology is a program which seeks to make explicit the ontological commitments of physical theories in terms of a distribution of matter in ordinary space-time. This program targets wave-function realism, which interprets the high-dimensional configuration space on which wave-functions are defined as our fundamental physical space. Wave-function realism allegedly fails to account for a correspondence between the ontology it postulates and the ‘manifest image’ of the world in which experimental tests of the theory are performed, and therefore (...) the wave-function must be completed with an additional structure which describes what fundamentally exists in ordinary space-time: the ‘primitive ontology’. However primitive ontologies face some difficulties, in particular concerning the ontological status of the wave-function. In this paper, I defend a realist interpretation of the wave-function as describing objects in ordinary space-time, which does not require supplementing the theory with additional structure. The main difference between this proposal and other primitive ontology proposals is that the fundamental constituents of reality are not conceived of as localised objects, but as primitive relations. This interpretation purports to share the advantages of both wave-function realism and primitive ontologies without facing the same difficulties. I argue that the need for an additional structure stems from a commitment to the locality of the fundamental constituents of reality, and that such commitment is unnecessary for recovering the manifest image of the world. (shrink)

David Lewis's account of the de se has two parts. The first part involves treating the objects of the attitudes, not as propositions but as properties. The second part involves treating our attitude to these properties as that of self‐ascription. In particular, much recent literature has tried to incorporate his account simply by treating the objects of the attitudes as centered worlds, where a centered world is an ordered pair of a possible world together with a spatiotemporal location. The explanation (...) of the account in terms of centered worlds originates with Lewis himself, in his development of some comments from Quine. This chapter examines some of other potential costs of Lewis's approach, those that stem from the idea of primitive self‐ascription. Lewis's account of the de se is both more radical, and more unintuitive, than has been appreciated. (shrink)

Conceptual primitivism is the view that truth is among our most basic and fundamental concepts. It cannot be defined, analyzed, or reduced into concepts that are more fundamental. Primitivism is opposed to both traditional attempts at defining truth (in terms of correspondence, coherence, or utility) and deflationary theories that argue that the notion of truth is exhausted by means of the truth schema. Though primitivism might be thought of as a view of last resort, I believe that the view (...) is independently attractive, and can be argued for directly. In this paper I offer what I take to be the strongest argument in favor of conceptual primitivism, which relies upon the Fregean doctrine of the omnipresence of truth. (shrink)

In this dissertation I defend the claim, long held by Donald Davidson, that truth is a primitive concept that cannot be correctly or informatively defined in terms of more basic concepts. To this end I articulate the history of the primitive thesis in the 20th century, working through early Moore, Russell, and Frege, and provide improved interpretations of their reasons for advancing and eventually abandoning the primitive thesis. I show the importance of slingshot-style arguments in the (...) work of Frege, Church, Davidson, and Gödel for resisting certain versions of the correspondence theory of truth. I argue that most slingshots fail to convincingly establish a collapsing conclusion, but that a Gödelian version of the slingshot is terminal to certain varieties of the correspondence theory of truth. I then provide a Davidsonian theory of truth and interpretation that is consistent with and makes use of the primitive thesis. Finally, I provide an account of predication, properties, and universals that I argue is both serviceable and consistent with Davidson’s overall program. (shrink)

Let the chain antichain principle (CAC) be the statement that each partial order on $\mathbb{N}$ possesses an infinite chain or an infinite antichain. Chong, Slaman, and Yang recently proved using forcing over nonstandard models of arithmetic that CAC is $\Pi^1_1$-conservative over $\text{RCA}_0+\Pi^0_1\text{-CP}$ and so in particular that CAC does not imply $\Sigma^0_2$-induction. We provide here a different purely syntactical and constructive proof of the statement that CAC (even together with WKL) does not imply $\Sigma^0_2$-induction. In detail we show using a (...) refinement of Howard's ordinal analysis of bar recursion that $\text{WKL}_0^\omega+\text{CAC}$ is $\Pi^0_2$-conservative over PRA and that one can extract primitive recursive realizers for such statements. Moreover, our proof is finitary in the sense of Hilbert's program. CAC implies that every sequence of $\mathbb{R}$ has a monotone subsequence. This Bolzano-Weierstraß}-like principle is commonly used in proofs. Our result makes it possible to extract primitive recursive terms from such proofs. We also discuss the Erdős-Moser principle, which—taken together with CAC—is equivalent to $\text{RT}^2_2$. (shrink)

In several places we have argued that ‘fitness’ is a primitive term with respect to the theory of evolution properly understood. These arguments have relied heavily on the axiomatization of the theory provided by one of us. In contrast, both John Beatty and Robert Brandon have separately argued for a “propensity“ interpretation of “fitness” ; and in Brandon and Beatty they attack our view that “fitness“ is a primitive term in evolutionary theory, concluding that a definition by way (...) of propensities is possible and preferable. Here we reply to their criticisms, and argue that, at most, the view that fitness is a statistical propensity is a terminological variant on our thesis that it is a primitive in evolutionary theory. (shrink)

A critical examination of the history of theories and uses of concepts such as ‘primitive’ and ‘savage’ in the academic study of religion in imperial, colonial and postcolonial contexts is particularly urgent in our time with its demands to decolonise Western models of knowledge production. In Savage Systems (1996) and Empire of Religion (2014), David Chidester has contributed to this project by relating the invention and use of terms such as ‘religion’, ‘primitive’ and ‘savage’ by theorists of (...) religion in European imperial metropoles to South African colonial and indigenous contexts. This article intends to take Chidester’s project further by relating Gerardus Van der Leeuw’s phenomenological analysis of ‘primitive mentality’ (particularly in De primitieve mensch en de religie, 1937) to Chidester’s analysis and postcolonial critique of imperial theories of religion. By taking animism and dreams in Chidester’s and Van der Leeuw’s works as example, it is argued that in spite of the latter’s decontextualised use of ethnological material, a fundamental shift occurred in the judgement of ‘primitive’ religion from Tylor’s evolutionary to Van der Leeuw’s phenomenological analysis, which is contrary to claims according to which modern theories are unanimously denigratory of indigenous religions. (shrink)

Some variants of Object-Oriented Ontology define entities in terms of their powers. Such variants are rooted in Gilles Deleuze and Félix Guattari’s theory of “machinic assemblages”. This article asks whether such entities can be metaphysical primitives with regard to similarity and change. This is the case if no further existents are needed to account for these two features of reality. According to Levi Bryant’s machine-oriented ontology, entities defined in terms of powers are such primitives. According to Manuel DeLanda’s (...) assemblage theory, they are not. DeLanda therefore holds that further metaphysical primitives must exist. After reconstructing the key features of the theories involved, I argue that Bryant’s position is ultimately more parsimonious, and that DeLanda’s theory confuses epistemological models with ontological realities. (shrink)

The contemporary debate about truth is polarized between deflationists and those who offer robust accounts of truth. I present a theory of truth called ‘Primitive Disclosive Alethism’ that occupies the middle ground between these two extremes. Contrary to deflationist claims, truth has a nature beyond its merely linguistic, expressive function. Truth is objective and non-epistemic, yet cannot be characterized in terms of correspondence. Primitive Disclosive Alethism offers a metaphysically satisfying explanation of our correspondence intuitions, while explaining why (...) the concept of truth is an undefined primitive. The theory also explains why the T-schema offers the clearest expression of what makes a sentence true. I distinguish this theory from the Identity Theory of Truth which equates true propositions with facts. (shrink)

There are two parts to Lewis's account of the de se. First there is the idea that the objects of de se thought (and, by extension of de dicto thought too) are properties, not propositions. This is the idea that is center-stage in Lewis's discussion. Second there is the idea that the relation that thinkers bear to these properties is that of self-ascription. It is crucial to LewisÕs account that this is understood as a fundamental, unanalyzable, notion: self-ascription of a (...) property is not ascription of a property to the self, on a par with ascription to someone else. This has been overlooked in much recent discussion, especially when Lewis's account is understood in terms of centered worlds. When it is back in focus it brings problems. An almost Cartesian starting point is required; and first-person plural ascriptions, and those with first person pronouns other than in subject position, become unmanageably complex. (shrink)

Three philosophical questions that are often confused should instead be keep distinct: First, what is a thought? Second, what is that in virtue of which a thought is a thought? Third, what is it that determines of what a thought is a thought? These questions raise very different issues within Ockham’s philosophy. Although Ockham’s views about the first question evolve, he seems to answer the second and the third questions in the same way, maintaining throughout his career that the intentionality (...) of thoughts, which he expresses in terms of signification, is a primitive feature of them. Ockham’s view contrasts sharply with the view that can be found in Aquinas and others that a thought is a form of being present in an immaterial way. This alternative view explains intentionality by reducing it to the co-presence of a number of non-cognitive factors. This latter view offers hope of unifying epistemology and such sciences as optics but at the price of a very peculiar ontology. Ockham avoids this peculiarity, but his way of doing so raises issues about what determines the taxonomy of thoughts, and about whether the items which are thoughts are essentially so or whether by God’s power they could exist without being thoughts. Despite Ockham’s terminology of similitude, the taxonomy of thoughts is not fixed by internal features of the metaphysical items which are thoughts but by the objects of the thoughts, and this suggests a negative answer to the questions whether thoughts are essentially thoughts, an answer that Ockham seems not to draw explicitly but which is explicit in the work of some, like Pierre d’Ailly, who are much influenced by him. (shrink)

In her ‘Primitive Normativity and Scepticism about Rules’ (2011b), Hannah Ginsborg proposes a novel solution to Kripke’s sceptical challenge to factualists about meaning (those who think that there is some fact about what you mean or meant by your utterances). According to Ginsborg, the fact in virtue of which you mean, say, addition by ‘plus’ is the fact that ‘you are disposed to respond to a query about (say) “68 plus 57” with “125,” where, in responding in that way, (...) you take that response to be primitively appropriate in light of your previous uses of “plus”’ (Ginsborg 2011b, 244). Ginsborg’s account is at its most compelling when considering what we might call unsophisticated cases of meaning, cases in which a subject means something by their words without their being in a position to identify the relevant rule or provide any sort of justification for their using the term as they do. In this paper, I raise doubts about whether Ginsborg’s account is extendable to sophisticated cases of meaning. Reflection on those cases which generate the doubts brings it into question whether the dispositions that Ginsborg identifies are necessary and jointly sufficient for one’s meaning that p even in unsophisticated cases. (shrink)

This paper develops a statistical approach to the problem of primitive representation. Representation of the kind commonly attributed to litmus paper, fuel gauges and tree rings occurs when, so to speak, there is a sufficiently good correlation between two variables. The fundamental distinction between misrepresentation and non-representation is explained in terms of the notion of an informationally useful correlation. The paper further argues that the statistical approach satisfactorily resolves well known puzzles such as Fodor's disjunction problem.

It is well known that Leibniz believes that the motion of bodies is caused by an internal force.1 Moreover, he distinguishes between two kinds of force that are associated with bodies, which he calls primitive and derivative forces respectively. My aim is to explain Leibniz’s account of the relation between these two kinds of force, and to address a puzzle that arises in connection with this relation. In fact Leibniz speaks of two different kinds of derivative force. The first, (...) and most fundamental, kind of derivative force is the momentary tendency to move from one perception to another within a simple substance, or monad. Sometimes these are called “appetitions”.2 The second kind are the forces of bodies that are found in the mechanical explanations of Leibnizian Dynamics.3 We shall be concerned primarily with the latter in what follows. However, the derivative forces of monads will also play an important role in the discussion. As one might expect, Leibniz holds that derivative forces are derived from the primitive ones. This idea is more usually expressed in terms of the notion of modification. Thus, derivative forces are said to be “nothing but the modifications and results of primitive forces”4 and to “arise as shapes arise from modification of extension”.5 Here it is natural to assume that Leibniz understands the relation between primitive and derivative force in something like the way in which Descartes understood the relation between modes of extended and thinking substances and the substances themselves, namely as particular ways of being an extended or thinking thing that inhere in their subjects.6 Although this account of derivative forces as modifications of primitive forces may seem plausible at first, difficulties arise when we try to understand how it could apply to the derivative forces in Leibnizian bodies. For it seems to be in conflict with two further aspects of Leibniz’s philosophy. Both can be found in the following passage from a letter to De Volder of 1705.. (shrink)

We criticize attempts to define hope in terms of other psychological states and argue that hope is a primitive mental state whose nature can be illuminated by specifying key aspects of its functional profile.

Let R be a real closed field, and X⊆Rm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\subseteq R^m}$$\end{document} semi-algebraic and 1-dimensional. We consider complete first-order theories of modules over the ring of continuous semi-algebraic functions X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X\to R}$$\end{document} definable with parameters in R. As a tool we introduce -piecewise vector bundles on X and show that the category of piecewise vector bundles on X is equivalent to the category of syzygies of (...) finitely generated submodules of free modules. We give an explicit method to determine the Baur–Monk invariants of free modules in terms of pre-piecewise vector bundles. When R is a recursive real closed field this yields the decidability of the theory of free modules. Where it makes sense, we address the same questions for continuous definable functions in o-minimal expansions of a real closed field. From the free module case we are able to deduce generalisations of some results to arbitrary modules over the ring. We present a geometrically motivated quantifier elimination result down to the level of positive primitive formulae with a certain block decomposition of the matrix of coefficients. (shrink)

LetA≤Bbe structures, and${\cal K}$a class of structures. An elementb∈BisdominatedbyArelative to${\cal K}$if for all${\bf{C}} \in {\cal K}$and all homomorphismsg,g':B → Csuch thatgandg'agree onA, we havegb=g'b. Our main theorem states that if${\cal K}$is closed under ultraproducts, thenAdominatesbrelative to${\cal K}$if and only if there is a partial functionFdefinable by a primitive positive formula in${\cal K}$such thatFB =bfor somea1,…,an∈A. Applying this result we show that a quasivariety of algebras${\cal Q}$with ann-ary near-unanimity term has surjective epimorphisms if and only if$\mathbb{S}\mathbb{P}_n \mathbb{P}_u \left$has surjective epimorphisms. (...) It follows that if${\cal F}$is a finite set of finite algebras with a common near-unanimity term, then it is decidable whether the variety generated by${\cal F}$has surjective epimorphisms. (shrink)

John Searle’s account of collective intentions in action appears to have all the theoretical pros of the non-reductivist view on collective intentionality without the metaphysical cons of committing to the existence of group minds. According to Searle, when we collectively intend to do something together, we intend to cooperate in order to reach a collective goal. Intentions in the first-person plural form therefore have a particular psychological form or mode, for the we-intender conceives of his or her intended actions as (...) singular contributions by means of which – or: by way of which – a collective goal is pursued. Accordingly, we-intentions are held to have a psychological mode with a “collective goal by means of singular contribution” structure, which makes them primitive and irreducible to intentions in the I-form. It is further contended that, albeit primitive and irreducible, we-intentions are not the mental states of an alleged group mind but always of an individual’s mind. This paper targets Searle’s claim of irreducibility by developing an argument whose aim is to show that, pace Searle, it is possible to track the idea of intentions with a psychological mode structured in terms of “collective goal by means of singular contribution” back to the concept of intentions in the I-form. The argument mainly relies on the idea that Searle’s technical expressions “being a collective goal by means of singular contribution intention in action” or “being a collective goal by way of singular contribution intention in action” are susceptible to conceptual analysis. The upshot of this analysis is that we-intentions can be reduced to complex bundles of mental states, all of which come in the first-person singular form. If this argument is sound, Searlean we-intentions do not belong to a primitive kind of mental states. (shrink)

Many metaphysicians posit primitives. These vary with respect to the theoretical work that they perform, but are all undefinable in more basic terms. I argue against the existence of metaphysical primitives on the grounds that, if they existed, they would be essentially primitive. However, if primitives were essentially primitive, then they would have an essence. Because they are primitive, they lack an essence, which undermines the original supposition that they are primitive. I close by mentioning (...) some implications this has both for metaphysicians and for metaphysics more generally. (shrink)

Recently scholars have been claiming that Aristotle’s biological explanations treat “facts about matter”—facts such as the degree of heat or amount of fluidity in an organism’s material constitution—as explanatorily basic or “primitive.” That is, these facts about matter are taken to be unexplained, brute facts about organisms, rather than ones that are explained by the organism’s form or essence, as we would have expected from Aristotle’s general commitment to the causal and explanatory priority of form over matter. In this (...) paper, I present three considerations for rejecting the view that facts about matter are primitive. First, there is evidence that those putative unexplained facts about degrees of heat, dryness, fluidity, etc. are, in fact, explained. Second, there are certain cases, such as human intelligence, where it would be quite implausible to consider the explanation in terms of degrees of heat to be starting from what Aristotle considers primitive facts. Third, the idea that facts about matter are as explanatorily primitive as facts about form requires a particular conception of the causal processes that the explanations mirror. But this conception of the causal processes conflicts with the way Aristotle characterizes them in Generation of Animals. There, heat is not treated as a causal factor that works “independently” of soul. In my view, these three considerations provide compelling reason to reject the claim that Aristotle’s biology treats facts about matter as primitive. (shrink)

If conceptual analysis is possible for finite thinkers, then there must ultimately be a distinction between complex and primitive or irreducible and unanalyzable concepts, by which complex concepts are analyzed as relations among primitive concepts. This investigation considers the advantages of categorizing intentionality as a primitive rather than analyzable concept, in both a historical Brentanian context and in terms of contemporary philosophy of mind. Arguments in support of intentionality as a primitive relation are evaluated relative (...) to objections, especially a recent criticism by Jerry A. Fodor. Against this background, the relation between qualia and intentionality in the understanding of consciousness is explored. (shrink)

The article sets out a primitive ontology of the natural world in terms of primitive stuff—that is, stuff that has as such no physical properties at all—but that is not a bare substratum either, being individuated by metrical relations. We focus on quantum physics and employ identity-based Bohmian mechanics to illustrate this view, but point out that it applies all over physics. Properties then enter into the picture exclusively through the role that they play for the dynamics (...) of the primitive stuff. We show that such properties can be local, as well as holistic, and discuss two metaphysical options to conceive them, namely, Humeanism and modal realism in the guise of dispositionalism. 1 Introduction2 Primitive Ontology: Primitive Stuff3 The Physics of Matter as Primitive Stuff4 The Humean Best System Analysis of the Dynamical Variables5 Modal Realism about the Dynamical Variables6 Conclusion. (shrink)

This paper concerns the formal semantic analysis of imperative sentences. It is argued that such an analysis cannot be deferred to the semantics of propositions, under any of the three commonly adopted strategies: the performative analysis, the sentence radical approach to propositions, and the (nondeclarative) mood-as-operator approach. Whereas the first two are conceptually problematic, the third faces empirical problems: various complex imperatives should be analysed in terms of semantic operators over simple imperatives. One particularly striking case is the Dutch (...) pluperfect imperative. It is argued that this construction should be analysed as a genuine counterfactual imperative. On the constructive side, in the last part of the paper a formal semantic analysis of imperatives is presented, in the framework of Update Semantics. On this analysis, imperatives are sui generis semantic entities, on a par with propositions. The analysis also includes an account of the counterfactual imperatives. (shrink)

In my dissertation I analyze the structure of fundamental physical theories. I start with an analysis of what an adequate primitive ontology is, discussing the measurement problem in quantum mechanics and theirs solutions. It is commonly said that these theories have little in common. I argue instead that the moral of the measurement problem is that the wave function cannot represent physical objects and a common structure between these solutions can be recognized: each of them is about a clear (...) three-dimensional primitive ontology that evolves according to a law determined by the wave function. The primitive ontology is what matter is made of while the wave function tells the matter how to move. One might think that what is important in the notion of primitive ontology is their three-dimensionality. If so, in a theory like classical electrodynamics electromagnetic fields would be part of the primitive ontology. I argue that, reflecting on what the purpose of a fundamental physical theory is, namely to explain the behavior of objects in three--dimensional space, one can recognize that a fundamental physical theory has a particular architecture. If so, electromagnetic fields play a different role in the theory than the particles and therefore should be considered, like the wave function, as part of the law. Therefore, we can characterize the general structure of a fundamental physical theory as a mathematical structure grounded on a primitive ontology. I explore this idea to better understand theories like classical mechanics and relativity, emphasizing that primitive ontology is crucial in the process of building new theories, being fundamental in identifying the symmetries. Finally, I analyze what it means to explain the word around us in terms of the notion of primitive ontology in the case of regularities of statistical character. Here is where the notion of typicality comes into play: we have explained a phenomenon if the typical histories of the primitive ontology give rise to the statistical regularities we observe. (shrink)

We use the primitive ontology framework of Allori et al. to analyze the quantum information-theoretic interpretation of Bub and Pitowsky. There are interesting parallels between the two approaches, which differentiate them both from the more standard realist interpretations of quantum theory. Where they differ, however, is in terms of their commitments to an underlying ontology on which the manifest image of the world supervenes. Employing the primitive ontology framework in this way makes perspicuous the differences between the (...) quantum information-theoretic interpretation, and the various realist interpretations of quantum theory. It also allows us to identify a sense in which the commitments of quantum information-theoretic interpretation are underspecified. Several possible ways of completing the interpretation are presented, and it is suggested that the most likely strategy would leave the information-theoretic interpretation such that it would fail to qualify as a theory, according to the primitive ontology approach. (shrink)

This seems to me to be a metaphysically significant feature of CEM. If CEM is correct — if all its theorems are true, then metaphysicians have a choice to make in how we understand the mereological nature of the world. We may think of the mereological relation either as a relation of part to whole, or as a relation of overlap; for if we give a metaphysical theory about one, we thereby give a metaphysical theory about the other. We may (...) choose which we think of as more metaphysically fundamental, for the they are interdefinable. However, if CEM is not correct, then perhaps we do not have this choice. Perhaps part-whole cannot be defined in terms of overlap; in which case we must choose part-whole as the metaphysical fundamental mereological relation (if any relation is). (shrink)

The paper presents a phenomenological approach to recent debates in the philosophy of language about rule-following and the normativity of meaning, a debate that can be traced to Ludwig Wittgenstein’s Philosophical Investigations but that was given new life with Saul Kripke’s Wittgenstein on Rules and Private Language. Taking a cue from Hannah Ginsborg’s recent work on “primitive normativity,” I use some of Husserl’s own comments about meaning and the status of rules to sketch a solution to Kripke’s rule-following paradox (...) by appealing to a kind of normativity at the level of perception and intersubjective embodiment. This level of normativity arises, like Ginsborg’s, via a primitive kind of judgment that does not presuppose linguistic or conceptual mastery. Unlike for Ginsborg, however, for Husserl this level should still be understood in terms of meaning—just not in the standard linguistic or conceptual senses prominent in the Anglo-American philosophical tradition in which the rule-following debates have occurred. My interpretation thus also demonstrates how Husserl’s account bypasses certain presuppositions about meaning common in the period of the linguistic turn—presuppositions also questioned, in different ways, by Wittgenstein, by Kripke, and by Ginsborg. (shrink)

The last Episode wasn’t about logic or formal theories at all: it was about common-or-garden arithmetic and the informal notion of computability. We noted that addition can be defined in terms of repeated applications of the successor function. Multiplication can be defined in terms of repeated applications of addition. The exponential and factorial functions can be defined, in different ways, in terms of repeated applications of multiplication. There’s already a pattern emerging here! The main task in the (...) last Episode was to get clear about this pattern. So first we said more about the idea of defining one function in terms of repeated applications of another function. Tidied up, that becomes the idea of defining a function by primitive recursion (Defn. 27). (shrink)

We introduce a system of simply typed lambda terms and show that a rather comprehensive class of recursion equations on streams or non-wellfounded trees can be solved in our system. Moreover certain conditions are presented which guarantee that the defined functionals are primitive recursive. As a major example we give a co-recursive treatment of Mints’ continuous cut-elimination operator.

In his influential article ‘Essence and Modality’, Fine proposes a definition of necessity in terms of the primitive essentialist notion ‘true in virtue of the nature of’. Fine’s proposal is suggestive, but it admits of different interpretations, leaving it unsettled what the precise formulation of an Essentialist definition of necessity should be. In this paper, four different versions of the definition are discussed: a singular, a plural reading, and an existential variant of Fine’s original suggestion and an alternative (...) version proposed by Correia which is not based on Fine’s primitive essentialist notion. The first main point of the paper is that the singular reading is untenable. The second that given plausible background assumptions, the remaining three definitions are extensionally equivalent. The third is that, this equivalence notwithstanding, Essentialists should adopt Correia’s version of the definition, since both the existential variant, which has de facto been adopted as the standard version of the definition in the literature, and the plural reading suffer from problems connected to Fine’s primitive essentialist notion. (shrink)

My modest aim in this piece is to frame and illuminate some of the issues surrounding normative motivation, rather than take a firm position on any of them. I begin by clarifying the key terms in my title of this essay, and unpacking some of the assumptions that underpin its question. I then distinguish four kinds of answers one might give. In this short essay I will not be able to properly develop and evaluate an argument for the view (...) that normative motivations are psychologically primitive, but I will have some comments about what such an argument might look like, and what it would have to show. (shrink)

The main aim of Schonfinkel's paper was methodological: to reduce the primitive logical notions to as few and definite notions as possible. ...

The present paper deals with a systemS of propositional calculus, conjunction, equivalence and falsum being its primitive terms.The only primitive rule inS is the rule of extensionality defined by the scheme: $\frac{{E\alpha \beta ,\Phi (\alpha )}}{{\Phi (\beta )}}$.

Pain is often used as the paradigmatic example of a phenomenal kind with a phenomenal quality common and unique to its instantiations. Philosophers have intensely discussed the relation between the subjective feeling, which unites pains and distinguishes them from other experiences, and the phenomenal properties of sensory, affective, and evaluative character along which pains typically vary. At the center of this discussion is the question whether the phenomenal properties prove necessary and/or sufficient for pain. In the empirical literature, sensory, affective, (...) and evaluative properties have played a decisive role in the investigation of psychophysical correspondence and clinical diagnostics. This paper addresses the outlined philosophical and empirical issues from a new perspective by constructing a multidimensional phenomenal space for pain. First, the paper will construe the phenomenal properties of pains in terms of a property space whose structure reflects phenomenal similarities and dissimilarities by means of spatial distance. Second, philosophical debates on necessary and sufficient properties are reconsidered in terms of whether there is a phenomenal space formed of dimensions along which all and only pains vary. It is concluded that there is no space of this kind and, thus, that pain constitutes a primitive phenomenal kind that cannot be analyzed entirely in terms of its varying phenomenal properties. Third, the paper addresses the utility of continued reference to pain and its phenomenal properties in philosophical and scientific discourses. It is argued that numerous insights into the phenomenal structure of pain can be gained that have thus far received insufficient attention. (shrink)