_ Source: _Page Count 25 The familiar challenges to historiographical knowledge turn on epistemological concerns having to do with the unobservability of historical events, or with the problem of establishing a sufficiently strong inferential connection between evidence and the historiographical claim one wishes to convert from a true belief into knowledge. This paper argues that these challenges miss a deeper problem, viz., the lack of obvious truth-makers for historiographical claims. The metaphysical challenge to historiography is that reality does not appear (...) to co-operate in our cognitive endeavours by providing truth-makers for claims about historical entities and events. Setting out this less familiar, but more fundamental, challenge to the very possibility of historiography is the first aim of this paper. The various ways in which this challenge might be met are then set out, including ontologically inflationary appeals to abstract objects of various kinds, or to “block” theories of time. The paper closes with the articulation of an ontologically parsimonious solution to the metaphysical challenge to historiography. The cost of this approach is a revision to standard theories of truth. The central claim here is that the standard theories of truth have mistaken distinct causes of truth for truth itself. This mistake leads to distorted expectations regarding truth-makers for historiographical claims. The truth-makers of historiographical claims are not so much the historical events themselves but atemporal modal facts about the order of things of which those events were a part. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...) propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the interaction between Elohim's hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of $\Omega$-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{12} avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents a new mathematical trick in which first-order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{14} examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

This essay accounts for the notion of _Lebensform_ by assigning it a _logical _role in Wittgenstein’s later philosophy. Wittgenstein’s additions of the notion to his manuscripts of the _PI_ occurred during the initial drafting of the book 1936-7, after he abandoned his effort to revise _The Brown Book_. It is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity as it figures within the notion of logical analysis. Next, a reconstruction of his later (...) remarks on _Lebensformen_ is offered which factors in his reading of Alan Turing’s “On computable numbers, with an application to the _Entscheidungsproblem_“, as well as his discussions with Turing 1937-1939. An interpretation of the five occurrences of _Lebensform_ in the PI is then given in terms of a logical “regression” to _Lebensform_ as a fundamental notion. This regression characterizes Wittgenstein’s mature answer to the question, “What is the nature of the logical?”. (shrink)

A widespread assumption in current philosophy of mind is that a conscious state’s phenomenal properties vary with its representational contents. In this paper, I present (rather dogmatically) an alternative picture that recognizes two kinds of phenomenal properties that do not vary concomitantly with content. First, it admits phenomenal properties that vary rather with attitude: what it is like for me to see rain is phenomenally different from what it is like for me to remember (indistinguishable) rain, which is different again (...) from what it is like for me to visualize (indistinguishable) rain – where these differences cannot be traced back to variations in content. Secondly, there is a kind of phenomenal property that varies neither with content nor with attitude but is altogether invariant across all conscious states: a substantive phenomenal commonality among what it is like for me to see, remember, and visualize rain, cats, or dogs. This substantive commonality, I will suggest, is the for-me-ness component of what it is like for me to have any of these experiences. I will close by discussing the interrelations among these three concentric layers of phenomenality: content-based, attitude-based, and for-me-ness. (shrink)

This book describes a novel conception of reality, one that uniquely incorporates an idealistic view of existence with an account of objectivity. It introduces a general model of conceptual analysis and demonstrates its effectiveness in exposing and establishing the existence of conceptual ties. The book begins by introducing the tools and principles needed for the conceptual analysis undertaken in chapters that follow. Next, it presents a detailed examination into existence, contingency, idealism, self-consciousness and natural laws. In the process, the author (...) critically examines the conceptions of existence held by Kant, Frege and Russell; argues that the determinations of past, present and future are subjective in the sense that they imply the existence of consciousness in relation to which they are fixed; shows that every possible reality includes sufficient conditions for self-consciousness; and confronts the question of the "uniformity of nature," which states that reality is subject to natural laws. In the end, the idealistic conception of reality developed in this book implies that existence is relative, rather than absolute, in the sense that it is determined in relation to a point of view internal to reality. This view of existence implies that reality necessarily exists. (shrink)

Following W.V. Quine’s lead, many metaphysicians consider ontology to be concerned primarily with existential questions of the form, “What is there?”. Moreover, if the position advanced by Rudolf Carnap, in his seminal essay, “Empiricism, Semantics, and Ontology ”, is correct, then many of these existential ontological questions ought to be classified as either trivially answerable or as “pseudo-questions”. One may justifiably wonder, however, whether the Quinean and Carnapian perspective on ontology really does justice to many of the most central concerns (...) of this discipline. This chapter argues, by considering a particular ontological dispute between two different kinds of trope theorists, that some of the most interesting and important debates which properly belong to the study of being, whether we call it “metaphysics” or “ ontology ”, do not concern existential questions at all; rather, such disputes in some cases focus on non-existential disagreements over questions of fundamentality. (shrink)

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...) proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

I defend the claim that Kant held a wide-scope view of hypothetical imperatives, against objections raised by Mark Schroeder [2005]. There is an important objection, now commonly known as the ‘bootstrapping’ problem, to the alternative, narrow-scope, view which Schroeder attributes to Kant. Schroeder argues that Kant has sufficient resources to reply to the bootstrapping problem, and claims that this leaves us with no good reason to attribute to Kant the wide-scope view. I show that Schroeder's Kantian reply to the bootstrapping (...) problem cannot fully answer it. Schroeder also offers three main textual arguments for attributing to Kant the narrow-scope view: from Kant's claim that the moral imperative is unique in virtue of its categoricity, from Kant's distinction between ‘problematic’ and ‘assertoric’ hypothetical imperatives, and from Kant's conception of analyticity together with his claim that hypothetical imperatives are analytic. I argue that each of these views can be understood as cohering with the.. (shrink)

This paper argues that Carnap both did not view and should not have viewed Frege's project in the foundations of mathematics as misguided metaphysics. The reason for this is that Frege's project was to give an explication of number in a very Carnapian sense — something that was not lost on Carnap. Furthermore, Frege gives pragmatic justification for the basic features of his system, especially where there are ontological considerations. It will be argued that even on the question of the (...) independent existence of abstract objects, Frege and Carnap held remarkably similar views. I close with a discussion of why, despite all this, Frege would not accept the principle of tolerance. (shrink)

I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

Name der Zeitschrift: Nordic Wittgenstein Review Jahrgang: 2 Heft: 1 Seiten: 33-56.

In Sein und Zeit Heidegger makes several claims about the nature of ‘assertion’ [Aussage]. These claims are of particular philosophical interest: they illustrate, for example, important points of contact and divergence between Heidegger's work and philosophical movements including Kantianism, the early Analytic tradition and contemporary pragmatism. This article provides a new assessment of one of these claims: that assertion is connected to a ‘present-at-hand’ ontology. I also indicate how my analysis sets the stage for a new reading of Heidegger's further (...) claim that assertion is an explanatorily derivative phenomenon. I begin with a loose overview of Heidegger's position and then develop a sharper formulation of the key premises. I go on to argue that existing treatments of the supposed link between assertion and the ‘present-at-hand’ are unsatisfactory, and advance a new, ‘methodological’, interpretation of that link. Finally, I sketch the implications of my interpretation for the further claim that assertion is explanatorily derivative. (shrink)

The Linda paradox is a key topic in current debates on the rationality of human reasoning and its limitations. We present a novel analysis of this paradox, based on the notion of verisimilitude as studied in the philosophy of science. The comparison with an alternative analysis based on probabilistic confirmation suggests how to overcome some problems of our account by introducing an adequately defined notion of verisimilitudinarian confirmation.

Deliberate contextual vocabulary acquisition (CVA) is a reader’s ability to figure out a (not the) meaning for an unknown word from its “context”, without external sources of help such as dictionaries or people. The appropriate context for such CVA is the “belief-revised integration” of the reader’s prior knowledge with the reader’s “internalization” of the text. We discuss unwarranted assumptions behind some classic objections to CVA, and present and defend a computational theory of CVA that we have adapted to a new (...) classroom curriculum designed to help students use CVA to improve their reading comprehension. (shrink)

In this work I first develop, motivate, and defend the view that mereological composition, the relation between an object and all its parts collectively, is a relation of identity. I argue that this view implies and hence can explain the logical necessity of classical mereology, the formal study of the part-whole relation. I then critically discuss four contemporary views of the same kind. Finally, I employ my thesis in a recent discussion of whether the world is fundamentally one in number.

Although culturally prominent modernist influences account for much of Skinner's early behaviorism, the subsequent changes in his views are appropriately considered as postmodern and are indebted to other sources. These changes are strikingly apparent in his 1945 publication. "The Operational Analysis of Psychological Terms." In that publication. Skinner introduced a probabilistic three-term contingency for verbal behavior with an expanded contextualism and an increased emphasis on consequence with a clear alignment to pragmatism. Instead of reaffirming the mechanistic and necessitarian values of (...) modernism that he had previously embraced, Skinner was aligning himself with the postmodern values of pragmatism and selectionism. (shrink)

In the Twentieth Century, Logic and Philosophy of Language are two of the few areas of philosophy in which philosophers made indisputable progress. For example, even now many of the foremost living ethicists present their theories as somewhat more explicit versions of the ideas of Kant, Mill, or Aristotle. In contrast, it would be patently absurd for a contemporary philosopher of language or logician to think of herself as working in the shadow of any figure who died before the Twentieth (...) Century began. Advances in these disciplines make even the most unaccomplished of its practitioners vastly more sophisticated than Kant. There were previous periods in which the problems of language and logic were studied extensively (e.g. the medieval period). But from the perspective of the progress made in the last 120 years, previous work is at most a source of interesting data or occasional insight. All systematic theorizing about content that meets contemporary standards of rigor has been done subsequently. (shrink)

In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.

Non-empirical principles have always been a subject of interest of philoso-phers. Authors from different times and traditions agree that principles such as analogy or simplicity are present in the scientific practice. The disagreement comes out when these authors affirm that these principles have an epistemic function, and when they try to present reasons in order to found this state-ment. The first goal of this paper is to describe these principles and to point out their methodological importance. The second goal is (...) to introduce the discussion between the two most important models of philosophical fundamentation – it means, the logicism and the psychologism. The last goal – the main one – is to defend that the non-empirical principals have, legitimately, an epistemic role in the scientific investigation. (shrink)

The article first rehearses three deflationary theories of reference, (1) disquotationalism, (2) propositionalism (Horwich), and (3) the anaphoric theory (Brandom), and raises a number of objections against them. It turns out that each corresponds to a closely related theory of truth, and that these are subject to analogous criticisms to a surprisingly high extent. I then present a theory of my own, according to which the schema “That S(t) is about t” and the biconditional “S refers to x iff S (...) says something about x” are exhaustive of the notions of aboutness and reference. An account of the usefulness of “about” is then given, which, I argue, is superior to that of Horwich. I close with a few considerations about how the advertised theory relates to well-known issues of reference, the conclusions of which is (1) that the issues concern reference and aboutness only insofar as the words “about” and “refer” serve to generalise over the claims that are really at issue, (2) that the theory of reference will not settle the issues, and (3) that it follows from (2) that the issues do not concern the nature of aboutness or reference. (shrink)

Much of the debate about identity in recent decades has been about personal identity, and specifically about personal identity over time, but identity generally, and the identity of things of other kinds, have also attracted attention. Various interrelated problems have been at the centre of discussion, but it is fair to say that recent work has focussed particularly on the following areas: the notion of a criterion of identity; the correct analysis of identity over time, and, in particular, the disagreement (...) between advocates of perdurance and advocates of endurance as analyses of identity over time; the notion of identity across possible worlds and the question of its relevance to the correct analysis of de re modal discourse; the notion of contingent identity; the question of whether the identity relation is, or is similar to, the composition relation; and the notion of vague identity. A radical position, advocated by Peter Geach, is that these debates, as usually conducted, are void for lack of a subject matter: the notion of absolute identity they presuppose has no application; there is only relative identity. Another increasingly popular view is the one advocated by Lewis: although the debates make sense they cannot genuinely be debates about identity, since there are no philosophical problems about identity. Identity is an utterly unproblematic notion. What there are, are genuine problems which can be stated using the language of identity. But since these can be restated without the language of identity they are not problems about identity. (For example, it is a puzzle, an aspect of the so-called “problem of personal identity”, whether the same person can have different bodies at different times. But this is just the puzzle whether a person can have different bodies at different times. So since it can be stated without the language of personal “identity”, it is not a problem about identity, but about personhood.) This article provides an overview of the topics indicated above, some assessment of the debates and suggestions for further reading. (shrink)

If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case (...) with respect to the objects that are studied in mathematics. In addition to that, the methods of investigation of mathematics differ markedly from the methods of investigation in the natural sciences. Whereas the latter acquire general knowledge using inductive methods, mathematical knowledge appears to be acquired in a different way, namely, by deduction from basic principles. The status of mathematical knowledge also appears to differ from the status of knowledge in the natural sciences. The theories of the natural sciences appear to be less certain and more open to revision than mathematical theories. For these reasons mathematics poses problems of a quite distinctive kind for philosophy. Therefore philosophers have accorded special attention to ontological and epistemological questions concerning mathematics. (shrink)

Recently, I’ve championed the doctrine that fundamentally different sorts of things exist in fundamentally different ways.1 On this view, what it is for an entity to be can differ across ontological categories.2 Although historically this doctrine was very popular, and several important challenges to this doctrine have been dealt with, I suspect that contemporary metaphysicians will continue to treat this view with suspicion until it is made clearer when one is warranted in positing different modes of existence.3 I address this (...) concern here. The question of when to posit ways of being is closely related to a more general question: when should one think that some philosophically interesting expression is analogous? Accordingly, my strategy here is as follows. First, I briefly explain my interpretation of ontological pluralism, the doctrine that there are ways of being.4 Second, I introduce the notion of an analogous term, and show how, on most ways of implementing ontological pluralism, “existence” is analogous. Third, I discuss two sufficient conditions for when one is warranted in claiming that a philosophically interesting term is analogous. Fourth, I present a series of ontological schemes, each of which satisfies at least one of the sufficient conditions. The upshot is this: if you are attracted to one of these ontologies, you have reason to believe in ways of being. The careful reader will have noted the apparent modesty of my conclusion. Unfortunately, I do not believe that one could ever be rationally required to believe in ways of being. Still, in general a metaphysic is a live option to the extent that it is shown to be rationally permissible to believe. Since the apparent consensus among contemporary analytic metaphysicians is that believing that things can exist in different ways is silly or confused, establishing the rational permissibility of belief in ways of being is a non-trivial task. Let us begin. (shrink)

The traditional understanding of analyticity in terms of concept containment is revisited, but with a concept explicitly understood as a certain kind of mental representation and containment being read correspondingly literally. The resulting conception of analyticity avoids much of the vagueness associated with attempts to explicate analyticity in terms of synonymy by moving the locus of discussion from the philosophy of language to the philosophy of mind. The account provided here illustrates some interesting features of representations and explains, at least (...) in part, the special epistemic status of analytic judgments. (shrink)

Speech acts are a staple of everyday communicative life, but only became a topic of sustained investigation, at least in the English-speaking world, in the middle of the Twentieth Century.[1] Since that time “speech act theory” has been influential not only within philosophy, but also in linguistics, psychology, legal theory, artificial intelligence, literary theory and many other scholarly disciplines.[2] Recognition of the importance of speech acts has illuminated the ability of language to do other things than describe reality. In the (...) process the boundaries among the philosophy of language, the philosophy of action, the philosophy of mind and even ethics have become less sharp. In addition, an appreciation of speech acts has helped lay bare an implicit normative structure within linguistic practice, including even that part of this practice concerned with describing reality. Much recent research aims at an accurate characterization of this normative structure underlying linguistic practice. (shrink)

The distinction between analytic and synthetic propositions, and with that the distinction between a priori and a posteriori truth, is being abandoned in much of analytic philosophy and the philosophy of most of the sciences. These distinctions should also be abandoned in the philosophy of mathematics. In particular, we must recognize the strong empirical component in our mathematical knowledge. The traditional distinction between logic and mathematics, on the one hand, and the natural sciences, on the other, should be dropped. Abstract (...) mathematical objects, like transcendental numbers or Hilbert spaces, are theoretical entities on a par with electromagnetic fields or quarks. Mathematical theories are not primarily logical deductions from axioms obtained by reflection on concepts but, rather, are constructions chosen to solve some collection of problems while fitting smoothly into the other theoretical commitments of the mathematician who formulates them. In other words, a mathematical theory is a scientific theory like any other, no more certain but also no more devoid of content. (shrink)

Crispin Wright and Bob Hale have defended the strategy of defining the natural numbers contextually against the objection which led Frege himself to reject it, namely the so-called ‘Julius Caesar problem’. To do this they have formulated principles (called sortal inclusion principles) designed to ensure that numbers are distinct from any objects, such as persons, a proper grasp of which could not be afforded by the contextual definition. We discuss whether either Hale or Wright has provided independent motivation for a (...) defensible version of the sortal inclusion principle and whether they have succeeded in showing that numbers are just what the contextual definition says they are. (shrink)

Expressivism’s central idea is that normative sentences bear the same relation to non-cognitive attitudes that ordinary descriptive sentences bear to beliefs: the expression relation. Allan Gibbard teIls us that “that words express judgments will be accepted by almost everyone” - the distinctive contribution of expressivism, his claim goes, is only a view about what kind of judgments words express. But not every account of the expression relation is equally suitable for the expressivist’s purposes. In fact, what I argue in this (...) paper, considering four possible accounts of expression, is that how suitable each account is for the expressivist’s purpose varies in proportion to how controversial it is. So Gibbard is wrong - if expression is to get expressivism off the ground, then it will be enormously controversial whether words do express judgments. And thus expressivism is committed to strong claims about the semantics of non-normative language. (shrink)

This entry focuses on two of the more historically important monisms: existence monism and priority monism . Existence monism targets concrete objects and counts by tokens. This is the doctrine that exactly one concrete object exists. Priority monism also targets concrete objects, but counts by basic tokens. This is the doctrine that exactly one concrete object is basic, which will turn out to be the classical doctrine that the whole is prior to its parts.

There are two principles which bear the name Frege''sprinciple: the principle of compositionality, and the contextprinciple. The aim of this contribution is to investigate whether thisis justified: did Frege accept both principles at the same time, did hehold the one principle but not the other, or did he, at some moment,change his opinion? The conclusion is as follows. There is a developmentin Frege''s position. In the period of Grundlagen he followed to a strict form of contextuality. He repeatedcontextuality in later (...) writings, but became less strict. From 1914 on,pushed by the needs of research, he comes close to compositionality. Buthe could never make the final step toward compositionality forprincipled reasons, therefore he always would reject compositionality. (shrink)

Neo-Fregeanism in the philosophy of mathematics consists of two main parts: the logicist thesis, that mathematics (or at least branches thereof, like arithmetic) all but reduce to logic, and the platonist thesis, that there are abstract, mathematical objects. I will here focus on the ontological thesis, platonism. Neo-Fregeanism has been widely discussed in recent years. Mostly the discussion has focused on issues specific to mathematics. I will here single out for special attention the view on ontology which underlies the neo-Fregeans’ (...) claims about mathematical objects, and discuss this view in a broader setting. (shrink)

The notion of a "mental representation" is, arguably, in the first instance a theoretical construct of cognitive science. As such, it is a basic concept of the Computational Theory of Mind, according to which cognitive states and processes are constituted by the occurrence, transformation and storage (in the mind/brain) of information-bearing structures (representations) of one kind or another.

This essay is a critical examination of how Edmund Husserl, in his appropriation of Franz Brentano’s concept of intentionality into his phenomenology, deals with the very issues that shaped Brentano’s theory of intentionality. These issues concern the proper criterion for distinguishing mental from physical phenomena and the right explanation for the independence of the intentionality of mental phenomena from the existence or non-existence of their objects. Husserl disagrees with Brentano’s views that intentionality is the distinguishing feature of all mental phenomena (...) and that the mental status of intentional objects is what explains the said independence. The crucial concept in Husserl’s theory of intentionality is the noema of consciousness, which functions in the same way as Gottlob Frege’s sense in his theory of semantics. This essay argues that Husserl’s alternative solutions to the problems of Brentano run in conflict either with the desired rigor of his phenomenology or with the actual workings of language. (shrink)

Brandom's book Making It Explicit defends Davidson's claim that conceptual thought can arise only on the background of a practice of mutual interpretation, without endorsing the further view that one can be a thinker only if one has the concept of a concept. This involves giving an account of conceptual content in terms of what Brandom calls practical deontic attitudes. In this paper, I make a plea for the conclusion that these practical attitudes are best seen as intentional, but non-conceptually (...) contentful. In particular, I argue that the hypothesis that Brandom's practical deontic attitudes are non-conceptually contentful wouldn't conflict with his view that non-conceptual intentionality is merely derivative. I then explore some of the implications which this hypothesis might have with respect to various forms of «intentional ascent». (shrink)

endorsed one kind of inverted spectrum hypothesis and rejected another. This paper argues that the kind of inverted spectrum hypothesis that Wittgenstein endorsed is the thin end of the wedge that precludes a Wittgensteinian critique of the kind of inverted spectrum hypothesis he rejected. The danger of the dangerous kind is that it provides an argument for qualia, where qualia are contents of experiential states which cannot be fully captured in natural language. I will pinpoint the difference between the innocuous (...) and dangerous scenarios that matters for the argument for qualia, give arguments in favor of the coherence and possibility of the dangerous scenario, and try to show that some standard arguments against inverted spectra are ineffective against the version of the dangerous scenario I will be advocating. The leading idea of the paper is that an argument for qualia based on spectrum inversion does not require that the inversion be behaviorally indistinguishable. At one crucial point, I will rely on a less controversial version of an argument I gave in Block. Wittgenstein's views provide a convenient starting point for a paper that is much more about qualia than about Wittgenstein. (shrink)

In the past few years, a number of philosophers ; Horgan and Tienson 2002; Pitt 2004) have maintained the following three theses: there is a distinctive sort of phenomenology characteristic of conscious thought, as opposed to other sorts of conscious mental states; different conscious thoughts have different phenomenologies; and thoughts with the same phenomenology have the same intentional content. The last of these three claims is open to at least two different interpretations. It might mean that the phenomenology of a (...) thought expresses its intentional content, where intentional content is understood as propositional, and propositions are understood as mind-and language-independent abstract entities. And it might mean that the phenomenology of a thought is its intentional content—that is, that the phenomenology of a thought, like the phenomenology of a sensation, constitutes its content. The second sort of view is a kind of psychologism. Psychologistic views hold that one or another sort of thing—numbers, sentences, propositions, etc.—that we can think or know about is in fact a kind of mental thing. Since Frege, psychologism has been in bad repute among analytic philosophers. It is widely held that Frege showed that such views are untenable, since, among other things, they subjectivize what is in fact objective, and, hence, relativize such things as consistency and truth to the peculiarities of human psychology. The purpose of this paper is to explore the consequences of the thesis that intentional mental content is phenomenological and to try to reach a conclusion about whether it yields a tenable view of mind, thought and meaning. I believe the thesis is not so obviously wrong as it will strike many philosophers of mind and language. In fact, it can be defended against the standard objections to psychologism, and it can provide the basis for a novel and interesting account of mentality. (shrink)

This essay aims to vindicate the thesis that cognitive computational properties are abstract objects implemented in physical systems. I avail of Voevodsky's Univalence Axiom and function type equivalence in Homotopy Type Theory, in order to specify an abstraction principle for epistemic (hyper-)intensions. The homotopic abstraction principle for epistemic (hyper-)intensions provides an epistemic conduit for our knowledge of (hyper-)intensions as abstract objects. Higher observational type theory might be one way to make first-order abstraction principles defined via inference rules, although not higher-order (...) abstraction principles, computable. The truth of my first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable i.e. Turing computable and the Turing machine being physically implementable. Epistemic modality and hyperintensionality can thus be shown to be both a compelling and a materially adequate candidate for the fundamental structure of mental representational states, comprising a fragment of the language of thought. (shrink)

A perspective in the philosophy of mathematics is developed from a consideration of the strengths and limitations of both logicism and platonism, with an early focus on Frege’s work. Importantly, although many set-theoretic structures may be developed each of which offers limited isomorphism with the system of natural numbers, no one of them may be identified with it. Furthermore, the timeless, ever present nature of mathematical concepts and results itself offers direct access, in the face of a platonist account which (...) generates a supposed problem of access. Crucially too, pure mathematics has its own distinctive method of confirming or validating results - mathematical proof - which supplies a higher level of confidence and objectivity than that available elsewhere. The dichotomy of invention and discovery is too jejune a framework for analysing creative mathematical activity. The Gödelian platonist perspective is evaluated and queried through scrutiny of the part played by mathematical resources and constraints in relation to human activity. It appears that there can be non-causal mathematical explanations and mathematical constraint on purely natural processes. Valuable implications of Quine’s naturalism are explored, but one must be cautious of his thesis of confirmational holism. The distinction between algebraic and non-algebraic mathematical theories usefully contributes to our understanding of the internally differentiated nature of the subject. (shrink)