In this paper I provide a state of the art survey and assessment of the contemporary debate about relations. After (1) distinguishing different varieties of relations, symmetric from non-symmetric, internal from external relations etc. and relations from their set-theoretic models or sequences, I proceed (2) to consider Bradley’s regress and whether relations can be eliminated altogether. Next I turn (3) to the question whether relations can be reduced, bringing to bear considerations from the philosophy of physics as well as metaphysics. (...) Finally, (3) I consider in what sense relations have order, and whether to make sense of this we are required to conceive of relations as having direction or argument positions. (shrink)

This paper aims to vindicate the thesis that cognitive computational properties are abstract objects implemented in physical systems. I avail of the equivalence relations countenanced in Homotopy Type Theory, in order to specify an abstraction principle for epistemic intensions. The homotopic abstraction principle for epistemic intensions provides an epistemic conduit into our knowledge of intensions as abstract objects. I examine, then, how intensional functions in Epistemic Modal Algebra are deployed as core models in the philosophy of mind, Bayesian perceptual psychology, (...) and the program of natural language semantics in linguistics, and I argue that this provides abductive support for the truth of homotopic abstraction. Epistemic modality 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)

I present and defend a reliabilist explanation of a priori knowledge which fulfils seven plausibility requirements.

Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...) framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams. (shrink)

Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new category of entity, (...) are we theoreticians epistemically justified in holding that there are such entities? This would hardly seem sufficient. To be epistemically justified, the ontology to which we theoreticians are committed must pass strict standards: the entities must be of the sort required by our best comprehensive theory of the world. The thesis of this paper is that fine-grained type-free intensional entities are like this. If the thesis is right, these entities have a special objective status perhaps not possessed by some of the other ontological categories associated with special syntactic constructions in natural language. In fact, it is plausible to hold that fine-grained type-free intensional entities provide the proper minimal framework for constructing logical and linguistic theories. In this paper my strategy will be to survey the competing conceptions of fine-grained type-free intensionality and to present arguments in support of one of them. Following this narrowing down process, I will go on to the indicated epistemological considerations. (shrink)

The paper presents a two-level approach to an assessment of meaning theories. To begin with, language is distinguished from lan guage-model and, analogously, meaning is discerned from a model of meaning. The first level of a theory assessment is presented as dealing with the relation of a model of meaning to intra-theoretical aims and assumptions of a theory with specific language-model. The second level of assessment concerns ontological, epistemological, logical and other assumptions underlying the respective language-model. Finally, several questions are (...) set forth as methodological directives for elucidating hidden assumptions behind the theories of meaning. (shrink)

The purpose of this paper can be described as follows. The contemporary philosophical logic cannot work without using some terms well-known from mathematics and logic. Among such terms that play an important role in logical and philosophical analyses of language, meaning and the like we can find function, procedure and construction. One problem is that various authors use these terms in various ways, another problem consists in the well-known fact that many philosophers do not have any idea of what those (...) and similar terms could mean. The present paper tries to explain why an exact explication of the three mentioned terms can contribute to understanding and even solving many problems with semantics of natural language, which a philosopher should be interested in. (shrink)

The doctrine of the Trinity is central to mainstream Christianity. But insofar as it posits “three persons” (Father, Son and Holy Spirit), who are “one God,” it appears as inconsistent as the claim that 1+1+1=1. -/- Much of the literature on “The Logical Problem of the Trinity,” as this has been called, attacks or defends Trinitarianism with little regard to the fourth century theological controversies and the late Hellenistic and early Medieval philosophical background in which it took shape. I argue (...) that this methodol- ogy, which I call “the Puzzle Approach,” produces obviously invalid arguments, and it is unclear how to repair it without collapsing into my preferred method- ology, “the Historical Approach,” which sees history as essential to the debate. I also discuss “mysterianism,” arguing that, successful or not, it has a different goal from the other approaches. I further argue that any solution from the His- torical Approach satisfies the concerns of the Puzzle Approach and mysterianism anyway. -/- I then examine the solution to the Logical Problem of the Trinity found in St. Gregory of Nyssa’s writings, both due to his place in the history of the doctrine, and his clarity in explicating what I call “the metaphysics of synergy.” I recast his solution in standard predicate logic and provide a formal proof of its consistency. I end by considering the possibilities for attacking the broader philosophical context of his defense and conclude that the prospects for doing so are dim. In any case, if there should turn out to be any problem with the doctrine of the Trinity at all, it will not be one of mere logical inconsistency in saying that “These Three are One.”. (shrink)

It is my intention in this thesis to demonstrate that there exists a clear and explicit formal relationship between the seemingly exclusive descriptions of spatio-temporal and purely temporal continuity, and further, that this relationship manifests itself within our most fundamental understanding of the physical world itself, namely; within our understanding of the identity, diversity and re-identification of material bodies. It may therefore be claimed that behind that cultural understanding which leads us to imagine that the physical world is located in (...) both space and time, whereas our thoughts and feelings are located in time alone, there lies a formal logical framework, or an explicit formal description of how being in space and time relates to being in time alone - leading us to wonder, perhaps, whether these two things are really as distinct as we might at first imagine. That I should then go on to apply to this analysis a philosophical interpretation of Bergson's conception of the relationship between the intuition and the intellect is of lesser importance - indicating as it does little more than my own philosophical inclinations. However, something will be gained, I hope, from this further exercise. Along the way it will allow me to clarify a number of technical points of which the general philosopher may be unaware; for example the unobservable nature of numerical identity and re-identification, the importance of the principle of special relativity to the topic of mind and the technical difficulties of claiming that mental events are 'in time' at all. Notwithstanding these latter points, however, the intentions of this work are predominantly analytical and are adequately described as an attempt to consolidate spatio-temporal and purely temporal description under a unified logical framework. (shrink)

The paper deals with the semantics and ontology of ordinary discourse about properties. The main focus lies on the following thesis: A simple predication of the form ‘a is F’ is synonymous with the corresponding explicit property-attribution ‘a has F-ness’. An argument against this Synonymy Thesis is put forth which is based on the thesis that simple predications and property-attributions differ in their conditions of understanding. In defending the argument, the paper accounts for the way in which we come to (...) adopt the conceptual framework of properties. (shrink)

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional contexts.) One (...) rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

I take some initial steps toward a theory of real definition, drawing upon recent developments in higher-order logic. The resulting account allows for extremely fine- grained distinctions (i.e., it can distinguish between any relata that differ in their syntactic structure, while avoiding the Russell-Myhill problem). It is the first account that can consistently embrace three desirable logical principles that initially appear to be incompatible: the Identification Hypothesis (if F is, by definition, G then F is the same as G), Irreflexivity (...) (there are no reflexive definitions) and Leibniz’s Law. Additionally, it possesses the resources to resolve the paradox of analysis. (shrink)

In a 1997 paper Jennifer Saul adduces various examples of simple sentences in which the substitution of one co-referential singular term for another appears to be invalid. I address the question of whether anti-substitution is logically justified by examining the validity and soundness of substitution of co-referential singular terms in three simple-sentence arguments each exhibiting a different logical structure. The result is twofold. First, all three arguments are valid, provided Leibniz’s Law is valid with respect to simple sentences . Thus, (...) as far as these arguments are concerned, there is no logical problem with substitution in simple sentences. Second, two of the arguments cannot be sound, because their respective sets of premises are inconsistent. Thus, it would be logically irrational to commit oneself to all the premises of the respective arguments. To the extent that the origin of Saul’s puzzles is in logic , I suggest, tentatively, that substitution may appear to be invalid because the issues of validity and soundness have not been kept separate. I then consider in depth Saul’s first sentence, “Clark Kent enters a phone booth and Superman exits”. Obviously, two-way substitution is trivially valid, if the expressions are co-referential semantically proper names, the conclusion being but a rephrasing of the premise. However, I argue that a non-trivial semantic analysis of this sentence should take account of the diachronicity of Clark Kent’s entrance and Superman’s exit while preserving the internal link between being Superman and being Clark Kent. I propose the following. ‘Superman’ and ‘Clark Kent’ refer to two distinct individual concepts. “Superman is Clark Kent” then no longer expresses the self-identity of an individual bearing two names, but that two named concepts are held together by the requisite relation: wherever and whenever someone falls under the concept of Superman the same individual also falls under the Clark Kent concept, whereas there are exceptions to the converse. This semantic analysis always validates the substitution of ‘Clark Kent’ for ‘Superman’, but validates the substitution of ‘Superman’ for ‘Clark Kent’ only if the additional condition is met that somebody should fall under the Superman concept when Clark Kent. (shrink)

So selbstverständlich es klingt, vom Geist, der Psyche oder auch der Seele eines Menschen zu reden, und so vertraut uns wissenschaftliche Disziplinen sind, die sich philosophisch oder empirisch damit beschäftigen, so schwer fällt es, ein einheitliches Merkmale dafür anzugeben, wann etwas ein psychisches Phänomen ist. Viele der potentiellen Merkmale decken eben nur einen Teil des Spektrums dessen ab, was wir gewöhnlich als psychisch bezeichnen würden, und sind damit bestenfalls hinreichende, aber sicher keine notwendigen Bedingungen des Psychischen. Im Mittelpunkt des folgenden (...) Artikels wird dagegen ein Merkmal stehen, von dem feststeht, daß es nicht hinreichend ist, von dem man aber vermuten kann, es sei zumindest notwendig: die Individualität psychischer Phänomene. Die Frage, mit der ich mich beschäftigen werde, ist, ob sich diese Vermutung mit Bezug auf eine Grnppe paradigmatisch psychischer Phänomene aufrecht erhalten läßt, die intentionalen Einstellungen. (shrink)

The paper is based on transparent intensional logic. A sentence denotes a proposition and expresses a construction in the sense of Tichý´s definition . ‘Belief sentences’ refer to an attitude of some individual to the sense of the dependent clause, i.e., to the respective construction, which eliminates such problems as ‘paradox of omniscience’. In the case of empirical dependent clauses we can observe that at least besides this relation to a construction one can define a relation of the subject to (...) the state-of-affairs, represented by a proposition, i.e., by the denotation of the sentence. To stipulate such a kind of attitudes is justified by such cases where X says that he believes that Chicago is smaller than Prague and Y refers to this X’s belief saying that X believes that Prague is larger than Chicago. (shrink)