On the philosophy of logic

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Epistemic Modalities : Knowledge and belief.

Paper 8 - Philosophical Logic

Although Aristotle 's logic is almost entirely concerned with categorical syllogisms , he did anticipate modal logic to some extent, and its connection with potentiality and time. Lewis - and then Saul Kripke - who established System K , the form of Modal Logic that most scholars use today. Propositional Logic or Sentential Logic is concerned only with sentential connectives and logical operators such as "and", "or", "not", "if In propositional logic, the simplest statements are considered as indivisible units.

The Stoic philosophers in the late 3rd century B. This system was also studied by Medieval logicians, although propositional logic did not really come to fruition until the midth Century, with the advent of Symbolic Logic in the work of logicians such as Augustus DeMorgan , George Boole and Gottlob Frege. Predicate Logic allows sentences to be analyzed into subject and argument in several different ways , unlike Aristotelian syllogistic logic, where the forms that the relevant part of the involved judgments took must be specified and limited see the section on Deductive Logic above.

Predicate Logic is also able to give an account of quantifiers general enough to express all arguments occurring in natural language , thus allowing the solution of the problem of multiple generality that had perplexed medieval logicians. Predicate logic was designed as a form of mathematics , and as such is capable of all sorts of mathematical reasoning beyond the powers of term or syllogistic logic. In first-order logic also known as first-order predicate calculus , a predicate can only refer to a single subject, but predicate logic can also deal with second-order logic , higher-order logic , many-sorted logic or infinitary logic.

It is also capable of many commonsense inferences that elude term logic, and along with Propositional Logic - see below has all but supplanted traditional term logic in most philosophical circles. Predicate Logic was initially developed by Gottlob Frege and Charles Peirce in the late 19th Century, but it reached full fruition in the Logical Atomism of Whitehead and Russell in the 20th Century developed out of earlier work by Ludwig Wittgenstein. A logical fallacy is any sort of mistake in reasoning or inference, or, essentially, anything that causes an argument to go wrong.

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There are two main categories of fallacy, Fallacies of Ambiguity and Contextual Fallacies :. These are just some of the most commonly encountered types, the Internet Encyclopedia of Philosophy page on Fallacies lists ! A paradox is a statement or sentiment that is seemingly contradictory or opposed to common sense and yet is perhaps true in fact. Conversely, a paradox may be a statement that is actually self-contradictory and therefore false even though it appears true.

Typically, either the statements in question do not really imply the contradiction , the puzzling result is not really a contradiction , or the premises themselves are not all really true or cannot all be true together. The recognition of ambiguities , equivocations and unstated assumptions underlying known paradoxes has led to significant advances in science, philosophy and mathematics. But many paradoxes e. Curry's Paradox do not yet have universally accepted resolutions. It can be argued that there are four classes of paradoxes:.

Paradoxes often result from self-reference where a sentence or formula refers to itself directly , infinity an argument which generates an infinite regress, or infinite series of supporting references , circular definitions in which a proposition to be proved is assumed implicitly or explicitly in one of the premises , vagueness where there is no clear fact of the matter whether a concept applies or not , false or misleading statements assertions that are either willfully or unknowingly untrue or misleading , and half-truths deceptive statements that include some element of truth.

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History of Logic. Types of Logic.

Paper 8 - Philosophical Logic — Faculty of Philosophy

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Course description

Propositional Logic. Predicate Logic. Teaching methods include: - Lectures - In-class discussion - One to one consultation with the module coordinator Learning activities include: - Attending lectures - Contributing to class discussion - Preparing for and completing the assessment tasks. Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

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Undergraduate Postgraduate taught Postgraduate research Foundation Years Pre-sessional English language courses How to apply Clearing Free online learning Continuing professional development Prospectuses. Module Overview Philosophical logic provides tools for the rigorous study of some of the most central notions of philosophy and of ordinary thought - for instance, necessity and possibility modal logic , time temporal logic , moral obligation deontic logic , and knowledge and belief epistemic logic. Aims and Objectives Learning Outcomes Knowledge and Understanding Having successfully completed this module, you will be able to demonstrate knowledge and understanding of: to learn advanced techniques of philosophical logic, including translating natural language expressions into logical formulae, building counter-models, and constructing proofs.

Subject Specific Intellectual and Research Skills Having successfully completed this module you will be able to: Ability to employ advanced techniques of philosophical logic in formulating and evaluating arguments. Ability to articulate and defend your own views in philosophical logic and relate the issues they concern to issues in other areas of philosophy, such as metaphysics, epistemology and ethics. Transferable and Generic Skills Having successfully completed this module you will be able to: Ability to identify, analyse and assess arguments in a sophisticated way.

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