Published Article / Language and Mathematics are both so-called "tools" that are used by other disciplines to explain / describe phenomena in those disciplines, but they are scientific disciplines in their own right. Language is a system of symbols, but so is Mathematics. These symbols carry meaning or value. Both originate in the human mind and are then translated into messages of logic. What is important are the relationships between units that are inherent to both disciplines. In practicing the two disciplines, there are elements that correspond. These are a vocabulary, grammar, a community and meaning. Psycholinguists and psychologists are interested in the role that language might have in enabling other functions in the human cognitive repertoire. Some argue that language is a prerequisite for a whole range of intellectual activities, including mathematics. They claim that mathematical structures are, in a way, parasitic on the human linguistic faculty. Some evidence for the language: maths connection comes from neurology. Functional imaging studies of the brain show increased activation of the language areas as certain mathematical tasks / challenges are performed. Lesions to a certain part of the brain impair both the linguistic as well as the mathematical ability. We are looking at a fundamentally shared enterprise, a deeply interwoven development of numerical and linguistic aspects. This co-evolution of number concepts and number words suggests that it is no accident that the same species that possesses the language faculty as a unique trait, should also be the one that developed a systematic concept of number.

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This thesis proposes a generalisation of pre-logical predicates to simply typed formal systems and their categorical models. We analyse the three elements involved in pre-logical predicates -- syntax, semantics and predicates -- within a categorical framework for typed binding syntax and semantics. We then formulate generalised pre-logical predicates and show two distinguishing properties: a) equivalence with the basic lemma and b) closure of binary pre-logical relations under relational composition. To test the adequacy of this generalisation, we derive pre-logical predicates for various calculi and their categorical models including variations of lambda calculi and non-lambda calculi such as many-sorted algebras as well as first-order logic. We then apply generalised pre-logical predicates to characterising behavioural equivalence. Examples of constructive data refinement of typed formal systems are shown, where behavioural equivalence plays a crucial role in achieving data abstraction.

I defend an understanding of Kant's theory of Geschmacksurteil as detailing an operation of the faculties that does not violate the cognitive structure laid out in the first Critique, even though one would not easily anticipate it from the standpoint of that work, nor would one initially expect aesthetic judgment to be of transcendental interest to Kant. My orientation is primarily epistemological, elaborating the determinations that govern the activity of pure aesthetic judging so as to specify it as a bestimmte type of judgment without transforming it into einem bestimmenden Urteil. I focus on identifying how the logical functions from the table of judgments operate in the pure aesthetic judgment of taste to reveal “the moments to which this power of judgment attends in its reflection” (Critique of the Power of Judgment, §1, 5:203). In the course of doing so, a picture emerges of how the world is not just cognizable in a Kantian framework but also charged with human feeling, acquiring the inexhaustible, inchoate meaningfulness that incites “much thinking” (Critique of the Power of Judgment, §49, 5:315). The universal communicability of aesthetic pleasure serves as the foundation that grounds robust intersubjective relations, enabling genuine connection to others through a shared a priori feeling. / McAnulty College and Graduate School of Liberal Arts; / Philosophy / PhD; / Dissertation;

This thesis provides a model-theoretic semantic analysis of aspects of the LF logical framework

It is widely agreed that some concepts can be possessed only by those who have undergone a certain type of phenomenal experience. The orthodox view among contemporary philosophers of mind that these phenomenal concepts provide the key to understanding the dispute between physicalists and their opponents. I reject the orthodox view; I defend an externalist conception of mental content according to which there are no phenomenal concepts. But the fact that there are no phenomenal concepts should not worry the physicalist: there are better accounts of the data that phenomenal concepts are used to explain. / text

Videogame designers hope to sculpt gameplay, but actually work in the concrete medium of computation. What they create is code, artwork, dialogue---everything that goes inside a videogame cartridge. In other materially constrained design domains, design-support tools help bridge this gap by automating portions of a design in some cases, and helping a designer understand the implications of their design decisions in others. I investigate AI-based videogame-design support, and do so from the perspective of putting knowledge-representation and reasoning (KRR) at the front. The KRR-centric approach starts by asking whether we can formalize an aspect of the game-design space in a way suitable for automated or semi-automated analysis, and if so, what can be done with the results. It begins with the question, "what could a computer possibly do here?", attempts to show that the computer actually can do so, and then looks at the implications of the computer doing so for design support. To organize the space of game-design knowledge, I factor the broad notion of game mechanics mechanics into four categories: abstract mechanics, concrete audiovisual representations, thematic mappings, and input mappings. Concretely, I investigate KRR-centric formalizations in three domains, which probe into different portions of the four quadrants of game-design knowledge: 1. using story graphs and story-quality functions for writing interactive stories, 2. automatic game design focused on the "aboutness" of games, which auto-reskins videogames by formalizing generalized spaces of thematic references, and 3. enhancing mechanics-oriented videogame prototypes by encoding the game mechanics in temporal logic, so that they can be both played and queried.

This thesis is a study of G.W. Leibniz’s views on compossibility. Leibniz calls substances that can be brought into existence together “compossible,” and he says that substances that cannot be brought into existence together are “incompossible.” Incompossibility and compossibility together divide substances into sets of individual substances that make up possible worlds. God then chooses from these possible worlds the best one to bring into existence. Thus without compossibility, the contingency of the world, and even God’s choice could have no rational basis. It is on these grounds that Leibniz thought compossibility was the most powerful—and perhaps, only—defense against the position that the actual world is the only possible world. This is a position that was powerfully argued for by Benedict de Spinoza. For largely theological reasons Spinoza’s position was unacceptable to Leibniz. Since Leibniz’s own time thinkers have found it difficult to see why all the substances are not compossible with one another given certain other philosophical and theological claims Leibniz is committed to. This state of affairs has been exacerbated by the fact that Leibniz himself seems not to have been concerned with providing a clear answer to this conundrum. In an attempt to fill in this omission, and to justify Leibniz’s intuition philosophers have proposed varying accounts of compossibility. Unfortunately, all of these accounts fall short of upholding a comprehensive rational explanation of the world’s contingency based on the objective rational choice of God. My dissertation presents a picture that is multi-faceted in its sensitivity to Leibniz’s theological, physical and logical concerns while nevertheless harmonizing with other tenets of Leibniz’s overall philosophy. I seek to achieve this end by defending the view that compossibility is based on the logical properties of the complete concepts of substances understood as embedded within networks of mutual intelligibility. / Thesis (Ph.D, Philosophy) -- Queen's University, 2014-04-09 13:03:19.752