Euclid (350,325-275 BC)

Major Ideas – A rigorous, systematic treatment of mathematics requires the statement of all assumptions and the proof of all propositions by means of uniform methodology. – All mathematical quantities can be expressed by geometrical figures, either lines, areas, or solids. – Physical events can be modeled using mathematical expressions. – Space is infinite

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Law of excluded middle

One of the traditional three laws of thought (along with the laws of identity and contradiction). Every proposition is either true or not true. This is weaker than the law of bivalence (every proposition is true or false), since if there is a third truth value excluded middle can still hold, though bivalence will fail. (However, bivalence is sometimes treated as

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Existentialism

Movement originating with Soren Kierkegaard(1813-1855) and continuing later with Karl Jaspers(1883-1969), Gabriel Marcel (1889-1973), Martin Heidegger (1889-1976), Jean-Paul Sartre (1905-1980), and various others, though it has had little influence in English-speaking philosophy. Fyodor Dostoevsky (1812-1881) and Friedrich Nietzsche(1844-1900) are sometimes included. The main idea is to distinguish the kind of being possessed by humans – called Dasein (Heidegger) or être-pour-soi (Sartre) – from

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Extensionality thesis

Thesis beloved of logical atomists, logical positivists, and various kinds of nominalists and reductionists. It says that apparent exceptions to Leibniz’s law can be dispensed with; that is, intensions can be reduced to extensions, or roughly, what holds true of objects does not depend on how they are described. For logical atomism in particular the thesis says that

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Externalism

Any view claiming that to analyze a certain phenomenon reference must be made to something outside a certain sphere within which the phenomenon might have been thought to be confined. In particular, externalism appears in certain analyses of mental notions such as belief and knowledge. An externalist view of belief holds, for example, that

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Fact / value distinction

Claim that a sharp distinction can be drawn between factual statements and value judgments, only the former being regarded as stating anything and as being true or false; the latter having meaning by doing something other than stating (for example, expressing attitudes: see speech act theories). The claim underlies emotivist and prescriptivist – as against descriptivist –

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Fallibilism

Doctrine that nothing can be known for certain; that is, there is no infallible knowledge, but there can still be knowledge. We need not have logically conclusive justifications for what we know. This was particularly insisted on by the American pragmatist Charles Sanders Peirce (1839-1914) in his opposition to foundationalism. Also see: relevant alternatives theory, epistemic closure Usage The

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Falsificationism

Claim associated especially with Austrian philosopher Karl Raimund Popper (1902-1994) that science should aim not to verify or confirm hypotheses – as verificationists and inductivists in general claim – but to falsify them. This is because science is interested (in Popper’s view) in universal affirmative conclusions, of the form ‘All As are Bs’, and if the

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Fatalism

The view – beloved of Greek oracles and their adherents – that the future, or part of it, will be what it will be, irrespective of our desires and actions. If we try to evade what is destined, our actions will always be frustrated and somehow turned so as to bring about the fated

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Fideism

The idea that religious faith stands apart from orthodox reason and can never be reconciled with it. Such religious thinkers as St Augustine (354-430) have argued that reason itself plays a subsidiary role to faith; while others (including Danish philosopher Soren Aaby Kierkegaard (1813-1855)) have maintained that acceptance of various aspects of religious belief requires actual

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Fido-fido theories

Fido-fido theories which explain some concept in terms of a direct relation to an object. The ‘Fido-fido theories of meaning says that the meaning of a word is an object it stands for (the name ‘Fido’ means the dog Fido); the term is thus a nickname for a naming theory of meaning. The ‘Fido’-Fido

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Finalism

View that there are final causes (see Aristotle’s four causes) in nature; that is, that at least some things other than the products of deliberate human activity can be explained in terms of their end or purpose. The idea that the world, or certain features of it, were amenable to such explanation goes back at

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Finitism

Usually regarded as a form of CONSTRUCTIVISM in the philosophy of mathematics, emphasizing that the construction in question must be possible in finitely many steps with finitely many elements. The views that the construction must be possible in practice (not just in principle), and that a mathematical statement only gets its sense from the

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Five ways (13TH CENTURY)

The five methods employed by St Thomas Aquinas (c. 1225-1274) in his attempt to prove the existence of God by reference to natural facts about the universe, in Summa Theologiae. The five ways were: argument from design; the cosmological argument; the degrees of perfection argument; the First Cause theory; the First Mover theory; and

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Folk psychology

Term used in recent philosophy of mind for the view that beliefs, desires and so on exist and operate much as common sense assumes they do; that is, the operations of the mind can be adequately explained in terms of such notions, or (more strongly) that they cannot be adequately explained without them. Strictly

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Formalism

Any doctrine emphasizing form as against matter or content, especially in aesthetics, ethics, and philosophy of mathematics. (The term is not, however, normally used of a metaphysical preoccupation with Platonic or Aristotelian forms.) In ethics formalism sees the value or rightness of an action in what kind of action it is (what formal description

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Foundationalism

Doctrine that knowledge must have foundations; that is, if we are to know anything at all there must be some things that we can know incorrigibly, so that it is impossible – or perhaps does not even make sense – for us to be mistaken. The usual candidates for such knowledge have been facts

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Four humors

Four bodily juices (blood, phlegm, black bile, yellow bile) whose balance or imbalance in the body was commonly regarded in Ancient Greek medicine as the source of health or disease. The doctrine was made influential for later thought by Galen (129-C.AD 199), though its origins are much earlier in the Hippocratic tradition (see the

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Frequency theory of probability

Theory due to German philosopher and mathematician Richard von Mises (1883-1954) in Probability, Statistics and Truth (1928, 2nd edition translated 1939). Here he defined the probability of something in terms of the relative frequency of its occurrence on occasions when it might occur. Von Mises limits his definition to cases where we have a collective, or potentially

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Functionalism

Any theory analyzing something in terms of its function; that is, any theory claiming that the best, or only, way of defining something is in terms of what it does or the role it plays in the ongoing course of events. Functionalism tends to define things in terms of their causes and effects, and,

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