Online research in philosophy

In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined, notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional theory, as well as defined syntactic counterparts, of the semantic notions of a possible world and the Routley-Meyer * operator.

Laws of nature are puzzling because they have a 'modal character'—they seem to be 'necessary-ish'—even though they also seem to be metaphysically contingent. And it is hard to understand how contingent truths could have such a modal character. Scientific essentialism is a doctrine that seems to dissolve this puzzle, by showing that laws of nature are actually metaphysically necessary. I argue that even if the metaphysics of natural kinds and properties offered by scientific essentialism is correct, there are still some metaphysically contingent truths that share the modal character of the laws of nature. I argue that these contingent truths should be considered laws of nature. So even if scientific essentialism is true, at least some laws of nature are metaphysically contingent.

Generics and frequency statements are puzzling phenomena: they are lawlike, yet contingent. They may be true even in the absence of any supporting instances, and extending the size of their domain does not change their truth conditions. Generics and frequency statements are parametric on time, but not on possible worlds; they cannot be applied to temporary generalizations, and yet are contingent. These constructions require a regular distribution of events along the time axis. Truth judgments of generics vary considerably across speakers, whereas truth judgments of frequency statements are much more uniform. A generic may be false even if the vast majority of individuals in its domain satisfy the predicated property, whereas a frequency statement using, e.g., usually would be true. This paper argues that all these seemingly unrelated puzzles have a single underlying cause: generics and frequency statements express probability judgments, and these, in turn, are interpreted as statements of hypothetical relative frequency.

Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘π is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and according to fictionalists there are no such entities. Fictionalism is a nominalist (or anti-realist) account of mathematics in that it denies the existence of a realm of abstract mathematical entities. It should be contrasted with mathematical realism (or Platonism) where mathematical statements are taken to be true, and, moreover, are taken to be truths about mathematical entities. Fictionalism should also be contrasted with other nominalist philosophical accounts of mathematics that propose a reinterpretation of mathematical statements, according to which the statements in question are true but no longer about mathematical entities. Fictionalism is thus an error theory of mathematical discourse: at face value mathematical discourse commits us to mathematical entities and although we normally take many of the statements of this discourse to be true, in doing so we are in error (cf. error theories in ethics).

I argue against both relation-ascription views: the object-view, on which identity statements ascribe a relation borne by all objects to themselves, and the name-view, on which 'a is b' says that the names 'a' and 'b' codesignate. In philosophy since Frege, the object- and name-views are usually treated as if they exhaust the field. I make a case for treating identity statements as being sui generis. My contention is that once we do this, no analysis is required.

I do not wish to insist that we stop saying that identity statements ascribe a relation. The point is that there is a fundamental disanalogy between identity statements and other two-termed statements, which we overlook to our peril. This will be seen to parallel the more recognized disanalogy between existence statements and other one-termed statements. One way of registering the fundamental disanalogy is to say that identity statements are not relational, but this is not essential. Following my negative arguments in section 2, I employ some simple diagrammatical models in section 3 to exhibit the fundamental disanalogy. In a final section, I respond to some possible objections which may be raised against this kind of approach.

Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement. The most thoroughly researched branch of propositional logic is classical truth-functional propositional logic, which studies logical operators and connectives that are used to produce complex statements whose truth-value depends entirely on the truth-values of the simpler statements making them up, and in which it is assumed that every statement is either true or false and not both. However, there are other forms of propositional logic in which other truth-values are considered, or in which there is consideration of connectives that are used to produce statements whose truth-values depend not simply on the truth-values of the parts, but additional things such as their necessity, possibility or relatedness to one another.

Rieber 1998 proposes an account of "S knows that p" that generates a contextualist solution to Closure. In this paper, I’ll argue that Rieber’s account of "S knows that p" is subject to fatal objections, but we can modify it to achieve an adequate account of "S knows that p" that generates a unified contextualist solution to all four puzzles. This is a feat that should matter to those philosophers who have proposed contextualist solutions to Closure: all of them have motivated their contextualism by appeal to the fact that they can explain the plausibility of each of the statements in Closure taken individually, and they can do this without having to deny that each of those statements is true, at least in the context in which it is plausible. But notice that this consideration would equally well motivate a contextualist approach to the other puzzles. Nonetheless, no contextualist has yet suggested how a contextualist solution to the other puzzles might go.

The Yale Shooting Problem introduced by Steve Hanks & Drew McDermott (1987) is a well-known test case of non-monotonic temporal reasoning. There is a sequence of situations. In the initial situation a gun is not loaded and the target is alive. In the next situation the gun is loaded. Eventually, a shot is fired, perhaps with fatal consequences. In this scenario there are two "fluents", alive and loaded, and two actions, load and shoot. Being loaded and being alive are inert propositions in the sense that if they are true at a given moment, they will be true at the next moment unless some action such as..

We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones.

Ontology is the study of what there is, what kinds of things make up reality. Ontology seems to be a very difficult, rather speculative discipline. However, it is trivial to conclude that there are properties, propositions and numbers, starting from only necessarily true or analytic premises. This gives rise to a puzzle about how hard ontological questions are, and relates to a puzzle about how important they are. And it produces the ontologyobjectivity dilemma: either (certain) ontological questions can be trivially answered using only uncontroversial premises, or the uncertainties of ontology are really a threat to the truth of basically everything we say or believe. The main aim of this dissertation is to resolve these puzzles and to shed some light on the discipline of ontology. I defend a view inspired by Carnap’s internal-external distinction about what there is, but one according to which both internal and external questions are fully factual and meaningful. In particular, I argue that the trivial arguments are valid, but they do not answer any ontological questions. Furthermore, I propose an account of the function of our talk about properties, propositions and natural numbers. According to this account our talk about them has no ontological presuppositions for its literal and objective truth. This avoids the ontology-objectivity dilemma, and solves the puzzles about ontology. To do this I look at quantification and noun phrases in general, and at their relation to ontology. I argue that quantifiers are semantically underspecified in a certain respect, and play two different roles in communication. I discuss the relation between syntactic form and information structure, the function of certain non-referential, non-quantificational noun phrases, the uses of bare number determiners, and how arithmetic truths are learned and taught. The more metaphysical issues discussed include: inexpressible properties, logicism about arithmetic, nominalism, Carnap’s view about ontology, the problem of universals, the relationship between ontology and objectivity, different projects within ontology, non-existent....