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In analytic philosophy, anti-realism is a position which encompasses many varieties such as metaphysical, mathematical, semantic, scientific, moral and epistemic. The term was first articulated by British philosopher Michael Dummett in an argument against a form of realism Dummett saw as 'colorless reductionism'.
The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives.
A proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as being the kind of thing that declarative sentences denote. For instance the sentence "The sky is blue" denotes the proposition that the sky is blue. However, crucially, propositions are not themselves linguistic expressions. For instance, the English sentence "Snow is white" denotes the same proposition as the German sentence "Schnee ist weiß" even though the two sentences are not the same. Similarly, propositions can also be characterized as the objects of belief and other propositional attitudes. For instance if one believes that the sky is blue, what one believes is the proposition that the sky is blue. A proposition can also be thought of as a kind of idea: Collins Dictionary has a definition for proposition as "a statement or an idea that people can consider or discuss whether it is true."
Moral skepticism is a class of meta-ethical theories all members of which entail that no one has any moral knowledge. Many moral skeptics also make the stronger, modal claim that moral knowledge is impossible. Moral skepticism is particularly opposed to moral realism: the view that there are knowable and objective moral truths.
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
Ruth Barcan Marcus was an American academic philosopher and logician best known for her work in modal and philosophical logic. She developed the first formal systems of quantified modal logic and in so doing introduced the schema or principle known as the Barcan formula. Marcus, who originally published as Ruth C. Barcan, was, as Don Garrett notes "one of the twentieth century's most important and influential philosopher-logicians". Timothy Williamson, in a 2008 celebration of Marcus' long career, states that many of her "main ideas are not just original, and clever, and beautiful, and fascinating, and influential, and way ahead of their time, but actually – I believe – true".
David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton University from 1970 until his death. He is closely associated with Australia, whose philosophical community he visited almost annually for more than 30 years.
Ethical subjectivism is the meta-ethical view which claims that:
- Ethical sentences express propositions.
- Some such propositions are true.
- The truth or falsity of such propositions is ineliminably dependent on the attitudes of people.
Moral nihilism is the meta-ethical view that nothing is morally right or morally wrong and that morality doesn't exist.
Hartry H. Field is an American philosopher. He is Silver Professor of Philosophy at New York University; he is a notable contributor to philosophy of science, philosophy of mathematics, epistemology, and philosophy of mind.
Modal realism is the view propounded by philosopher David Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It is based on four tenets: possible worlds exist, possible worlds are not different in kind from the actual world, possible worlds are irreducible entities, and the term actual in actual world is indexical, i.e. any subject can declare their world to be the actual one, much as they label the place they are "here" and the time they are "now".
Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism had a profound effect on Western thought. In its most basic fundamentals, Platonism affirms the existence of abstract objects, which are asserted to exist in a third realm distinct from both the sensible external world and from the internal world of consciousness, and is the opposite of nominalism. This can apply to properties, types, propositions, meanings, numbers, sets, truth values, and so on. Philosophers who affirm the existence of abstract objects are sometimes called Platonists; those who deny their existence are sometimes called nominalists. The terms "Platonism" and "nominalism" also have established senses in the history of philosophy. They denote positions that have little to do with the modern notion of an abstract object.
Quietism in philosophy sees the role of philosophy as broadly therapeutic or remedial. Quietist philosophers believe that philosophy has no positive thesis to contribute; rather, it defuses confusions in the linguistic and conceptual frameworks of other subjects, including non-quietist philosophy. For quietists, advancing knowledge or settling debates is not the job of philosophy, rather philosophy should liberate the mind by diagnosing confusing concepts.
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterisation, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.
Modal fictionalism is a term used in philosophy, and more specifically in the metaphysics of modality, to describe the position that holds that modality can be analysed in terms of a fiction about possible worlds. The theory comes in two versions: Strong and Timid. Both positions were first exposed by Gideon Rosen starting from 1990.
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the number 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any natural number is defined by its respective place in that theory. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra.
Logical consequence is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises? All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth.
The Quine–Putnam indispensability argument is an argument in the philosophy of mathematics for the existence of abstract mathematical objects such as numbers and sets, a position known as mathematical platonism. It was named after the philosophers Willard Quine and Hilary Putnam, and is one of the most important arguments in the philosophy of mathematics.
In semantics, pragmatics, and philosophy of language, the common ground of a conversation is the set of propositions that the interlocutors have agreed to treat as true. For a proposition to be in the common ground, it must be common knowledge in the conversational context. The set of possible worlds compatible with the common ground is often called the context set.
This is a glossary of logic. Logic is the study of the principles of valid reasoning and argumentation.
References
- ↑ Field, Hartry, Science Without Numbers, Blackwell, 1980.
- 1 2 Gericke, Jaco (2012). The Hebrew Bible and Philosophy of Religion. Atlanta, GA: Society of Biblical Literature. p. 366. ISBN 9781589837072.
- ↑ Nolan, Daniel (2002). Topics in the Philosophy of Possible Worlds . New York: Routledge. pp. 95. ISBN 9780815340515.
- 1 2 Irvine, Andrew, ed. (2009). Philosophy of Mathematics . Burlington, MA: Elsevier. pp. 345. ISBN 9780444515551.