Is the truthmaker principle a development of the correspondence theory of truth? So Armstrong introduced the truthmaker principle to us, but Lewis (2001. Forget about the ‘correspondence theory of truth’. Analysis 61: 275–80.) influentially argued that it is neither a correspondence theory nor a theory of truth. But the truthmaker principle can be correctly understood as a development of the correspondence theory if it’s conceived as incorporating the insight that truth is a relation between truth-bearers and something worldly. And we (...) strengthen rather than weaken the plausibility of the truthmaker principle if we conceive of truth as performing a substantial rather than deflationary role in the truthmaker principle. (shrink)
There are three different degrees to which we may allow a systematic theory of the world to embrace the idea of relatedness?supposing realism about non-symmetric relations as a background requirement. (First Degree) There are multiple ways in which a non-symmetric relation may apply to the things it relates?for the binary case, aRb ? bRa. (Second Degree) Every such relation has a distinct converse?for every R such that aRb there is another relation R* such that bR*a. (Third Degree) Each one of (...) them applies in an order to the things it relates?with regard to the state that results from R's applying to a and b, either R applies to a first and b second, or it applies to b first and a second. Whereas the first degree is near-indubitable, embracing the second or third generates unwholesome consequences. The second degree embodies a commitment to the existence of a superfluity of distinct converses and states to which such relations give rise. The third degree embodies commitment to recherché facts of the matter about how the states that arise from the application of one non-symmetric relation compare to any other. It is argued that accounts that purport to offer an analysis of the first degree generate unwelcome second or third degree consequences. This speaks in favour of our adopting an account of the application of relations that's not an analysis at all, an account that takes the first degree as primitive. (shrink)
According to one creation myth, analytic philosophy emerged in Cambridge when Moore and Russell abandoned idealism in favour of naive realism: every word stood for something; it was only after “the Fall,” Russell's discovery of his theory of descriptions, that they realized some complex phrases (“the present King of France”) didn't stand for anything. It has become a commonplace of recent scholarship to object that even before the Fall, Russell acknowledged that such phrases may fail to denote. But we need (...) to go further: even before the Fall, Russell had taken an altogether more discerning approach to the ontology of logic and relations than is usually recognized. (shrink)
Can Bradley's Regress be solved by positing relational tropes as truth-makers? No, no more than Russell's paradox can be solved by positing Fregean extensions. To call a trope relational is to pack into its essence the relating function it is supposed to perform but without explaining what Bradley's Regress calls into question, viz. the capacity of relations to relate. This problem has been masked from view by the (questionable) assumption that the only genuine ontological problems that can be intelligibly raised (...) are those that can be answered by providing a schedule of truthmakers. (shrink)
Ante rem structuralism is the doctnne that mathematics descubes a realm of abstract (structural) universab. According to its proponents, appeal to the exutence of these universab provides a source distinctive insight into the epistemology of mathematics, in particular insight into the so-called 'access problem' of explaining how mathematicians can reliably access truths about an abstract realm to which they cannot travel andfiom which they recave no signab. Stewart Shapiro offers the most developed version of this view to date. Through an (...) examination of Shapiro's proposed structuralist epistemology for mathematics I argue that ante rem structuralism faib to provide the ingredients for a satisfactory resolution of the access problem for infinite structures (whether small or large). (shrink)
The eleven new papers in this volume address fundamental and interrelated philosophical issues concerning modality and identity, issues that were pivotal to the development of analytic philosophy in the twentieth century, and remain a key focus of debate in the twenty-first. Identity and Modality brings together leading researchers in metaphysics, the philosophy of mind, the philosophy of science, and the philosophy of mathematics.
Is the assumption of a fundamental distinction between particulars and universals another unsupported dogma of metaphysics? F. P. Ramsey famously rejected the particular–universal distinction but neglected to consider the many different conceptions of the distinction that have been advanced. As a contribution to the (inevitably) piecemeal investigation of this issue three interrelated conceptions of the particular–universal distinction are examined: (i) universals, by contrast to particulars, are unigrade; (ii) particulars are related to universals by an asymmetric tie of exemplification; (iii) universals (...) are incomplete whereas particulars are complete. It is argued that these conceptions are wanting in several respects. Sometimes they fail to mark a significant division amongst entities. Sometimes they make substantial demands upon the shape of reality; once these demands are understood aright it is no longer obvious that the distinction merits our acceptance. The case is made via a discussion of the possibility of multigrade universals. (shrink)
Frege attempted to provide arithmetic with a foundation in logic. But his attempt to do so was confounded by Russell's discovery of paradox at the heart of Frege's system. The papers collected in this special issue contribute to the on-going investigation into the foundations of mathematics and logic. After sketching the historical background, this introduction provides an overview of the papers collected here, tracing some of the themes that connect them.
According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. (...) The issues discussed include reductionism, rejectionism, the Julius Caesar problem, the Bad Company objections, and the charge that second-order logic is set theory in disguise. The irresistible metaphor is that pure abstract objects [...] are no more than shadows cast by the syntax of our discourse. And the aptness of the metaphor is enhanced by the reflection that shadows are, after their own fashion, real. (Crispin Wright , p. 181-2) But I feel conscious that many a reader will scarcely recognise in the shadowy forms which I bring before him his numbers which all his life long have accompanied him as faithful and familiar friends; (Richard Dedekind , p. 33). (shrink)
There is no single problem of universals but a family of difficulties that treat of a variety of interwoven metaphysical, epistemological, logical and semantic themes. This makes the problem of universals resistant to canonical reduction (to a ‘once-and-for-all’ concern). In particular, the problem of universals cannot be reduced to the problem of supplying truth-makers for sentences that express sameness of type. This is (in part) because the conceptual distinction between numerical and qualitative identity must first be drawn before a sentence (...) is eligible to be supplied with truth-makers. The case is made through a consideration of a recent argument by Gonzalo Rodriguez-Pereyra. (shrink)
The contemporary Humean programme that seeks to combine property realism with the denial of necessary connections between distinct existences is flawed. Objects and properties by their very natures are entangled in such connections. It follows that modal notions cannot be reductively analysed by appeal to the concept property, not even if the reducing theory posits an abundant supply of entities to fall under that concept.
Neo-Ftegeanism contends that knowledge of arithmetic may be acquired by second-order logical reflection upon Hume's principle. Heck argues that Hume's principle doesn't inform ordinary arithmetical reasoning and so knowledge derived from it cannot be genuinely arithmetical. To suppose otherwise, Heck claims, is to fail to comprehend the magnitude of Cantor's conceptual contribution to mathematics. Heck recommends that finite Hume's principle be employed instead to generate arithmetical knowledge. But a better understanding of Cantor's contribution is achieved if it is supposed that (...) Hume's principle really does inform arithmetical practice. More generally, Heck's arguments misconceive the epistemological character of neo-Fregeanism. (shrink)
There cannot be a reductive theory of modality constructed from the concepts of sparse particular and sparse universal. These concepts are suffused with modal notions. I seek to establish this conclusion by tracing out the pattern of modal entanglements in which these concepts are involved. In order to appreciate the structure of these entanglements a distinction must be drawn between the lower-order necessary connections in which particulars and universals apparently figure, and higher-order necesary connections. The former type of connection (...) relates specific entities. By contrast, the latter type of connection is unspecific: it relates entities to some others. I argue that whilst there may be techniques that succeed in providing reductive truth conditions for sentences that say particulars and universals figure in lower-order necessary connections, such techniques cannot succeed in providing reductive truth conditions for sentences that say these entities figure in higher-order necessary connections. I conclude that this situation leaves reductionists with a dilemma. If they wish to affirm that there are particulars and universals then the project of reducing modality by positing these entities must be abandoned. Alternatively, they may continue to deploy their usual reductive techniques but then they must abandon the doctrine that there is more than one fundamental category of entity. (shrink)
Is there a particular-universal distinction? Is there a difference of kind between all the particulars on the one hand and all the universals on the other? Can we demonstrate that there is such a difference without assuming what we set out to show? In 1925 Frank Ramsey made a famous attempt to answers these questions. He came to the sceptical conclusion that there was no particularuniversal distinction, the theory of universals being merely “a great muddle”. Following Russell, Ramsey identified three (...) kinds of distinction, psychological, physical and logical, in terms of which the particular-universal distinction might be understood. Ramsey argued that the particular-universal distinction could not be understood in terms of any of these kinds of distinction. Ramsey concluded that the particular-universal distinction, being neither psychological, physical or logical, was no distinction at all. The conclusion that there is no particular-universal distinction cannot be substantiated on the basis of the arguments that Ramsey provides. At least one of these arguments, the argument that the particular-universal distinction cannot be a ‘physical’ distinction, is flawed. (shrink)