Logic and Foundations of Mathematics Commons^™

A Groundwork For A Logic Of Objects, David Winters

Electronic Thesis and Dissertation Repository

The history of philosophy is rich with theories about objects; theories of object kinds, their nature, the status of their existence, etc. In recent years philosophical logicians have attempted to formalize some of these theories, yielding many fruitful results. My thesis intends to add to this tradition in philosophical logic by developing a second-order logical system that may serve as a groundwork for a multitude of theories of objects (e.g. concrete and abstract objects, impossible objects, fictional objects, and others). Through the addition of what we may call sortal quantifiers (i.e. quantifiers that bind individual variables ranging over objects of …

Maths Living In Social Arenas, From Practice To Foundations, Nigel Vinckier

Journal of Humanistic Mathematics

Maths comes to life in human interaction. This has consequences for the mathematics itself. This paper discusses how this ``coming to life'' of mathematics in different social arenas influences the foundations of maths. We will argue that this influence is profound, to the extent that it is hard to upkeep the idea that there is or should be one foundation on which all mathematics can be built.

The Poetic Function Of Imagination: The Parallel Process Of Poiêsis, Angela Carlson

Expressive Therapies Capstone Theses

In the advent of Postmodernism, modern approaches to understanding the nature of things is being put into question. As the gap between objective and subjective realms of experiences is narrowing, there is an increased need for a more artful approach to science. This paper serves as my attempt to promote the field of Expressive Arts Therapy (ExATh) as a mode of poetic science for understanding the experience of ‘Being’ in the world. Through a critical review of the semantic development of the ancient Greek concepts poiêsis, noêsis, and aisthêsis, the imagination is identified as a function of alêthaic revealing, …

Fatal Attractions, Elective Affinities, And Deadly Epistemologies, Ibpp Editor

International Bulletin of Political Psychology

This article cites film, the novel, and news report to underline the deadly seriousness of the quest for knowledge.

The Systems Of Post And Post Algebras: A Demonstration Of An Obvious Fact, Daviel Leyva

USF Tampa Graduate Theses and Dissertations

In 1942, Paul C. Rosenbloom put out a definition of a Post algebra after Emil L. Post published a collection of systems of many–valued logic. Post algebras became easier to handle following George Epstein’s alternative definition. As conceived by Rosenbloom, Post algebras were meant to capture the algebraic properties of Post’s systems; this fact was not verified by Rosenbloom nor Epstein and has been assumed by others in the field. In this thesis, the long–awaited demonstration of this oft–asserted assertion is given.

After an elemental history of many–valued logic and a review of basic Classical Propositional Logic, the systems given …

Pagan Winter, Samm Willard

Sophia and Philosophia

Isn’t this a lovely place to pick apart your lover’s face
Some say the river bank’s a sacred place
Others think that’s such a silly thing to say
But I would never try to prove them wrong on such a blissful day
The colors of the leaves will soon have changed
The yellows and the greens will fade to gray
But I will lose a quiet hour to the darkest day
A pagan winter’s on its way
I will see the death of God before it’s Christmas day
A pagan winter’s on its way
Well isn’t this some lovely clay …

Haunted By A Memory I Never Lived, Carlos Hiraldo

Sophia and Philosophia

I am haunted by a memory I never lived. My mother and father are sitting in their house in Brooklyn with my baby sister watching the 1969 moon landing. Born in 1971, I wasn’t there. But I spent my toddler years in the waning residue of excitement about the landing and listening to adults talk about where they had watched it. As a child, I was baffled by how vivid this event that occurred without me was to people of my parents’ age. Except for some surviving pictures of the living room, I never knew the house in which they …

Frontiers Of Conditional Logic, Yale Weiss

Dissertations, Theses, and Capstone Projects

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional obligation). Despite the close connections between conditional and modal logic, both the technical development and philosophical exploitation of the …

Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois

Journal of Humanistic Mathematics

Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry …

From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger

Journal of Humanistic Mathematics

The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of solvability is commonly identified with the decision problem. Given this identification, there is not the slightest doubt that Hilbert’s conviction was falsified by Gödel’s proof and by the negative results for the decision problem. On the other hand, Gödel’s theorems do offer a solution, albeit a negative one, in the form of an impossibility proof. In this sense, Hilbert’s optimism may still be justified. Here I argue that …

Recapture, Transparency, Negation And A Logic For The Catuṣkoṭi, Adrian Kreutz

Comparative Philosophy

The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. Cotnoir (2015) has argued that the lattices of Priest and Garfield …

An Introduction To Logic: From Everyday Life To Formal Systems, Albert Mosley, Eulalio Baltazar

Open Educational Resources: Textbooks

An introduction to the discipline of logic covering subjects from the structures of arguments, classical and modern logic, categorical and inductive inferences, to informal fallacies.

• Over 30 years of development provides a sound empirical based pedagogy throughout the text.

• Examples in ordinary language using familiar examples avoids the suggestion of an alien cultural imposition.

• A focus on the basic representational techniques of classical and modern logic.

• Students introduced to basic concepts of set theory, using Venn diagrams to represent statements and evaluate arguments.

• Students introduced to basic concepts of propositional logic and the use of truth-tables.

• Students introduced to basic …

Logical Instrumentalism And Concatenation, Teresa Kouri Kissel

Philosophy Faculty Publications

Logical pluralism is the theory that there is more than one right logic. Logical instrumentalism is the view that a logic is a correct logic if it can be used to fruitfully pursue some deductive inquiry. Logical instrumentalism is a version of logical pluralism, since more than one logic can be used fruitfully. In this paper, I will show that a logical instrumentalist must accept linear logic as a correct logic, since linear logic is useful for studying natural language syntax. I further show that this means that the logical instrumentalist must accept a wide range of connectives, in particular …

Susan Stebbing, Teresa Kouri Kissel

Philosophy Faculty Publications

Susan Stebbing (1885-1943) was a founder of Analysis and had a large influence on philosophy during the early 20th century. Recently, the work of Michael Beaney (2000), Siobhan Chapman (2013) and Frederique Janssen- Lauret (2017), amongst others, has begun a resurgence of interest in Stebbing. This paper serves as a brief introduction to some of the major features of her philosophical work.

Counterfactual Conditional Analysis Using The Centipede Game, Ahmed Bilal

CMC Senior Theses

The Backward Induction strategy for the Centipede Game leads us to a counterfactual reasoning paradox, The Centipede Game paradox. The counterfactual reasoning proving the backward induction strategy for the game appears to rely on the players in the game not choosing that very same backward induction strategy. The paradox is a general paradox that applies to backward induction reasoning in sequential, perfect information games. Therefore, the paradox is not only problematic for the Centipede Game, but it also affects counterfactual reasoning solutions in games similar to the Centipede Game. The Centipede Game is a prime illustration of this paradox in …