## Vocabulary Important for Study of Analytic Philosophy

by Dr. Jan Garrett

Last revised on October 14, 2009

### Aristotelian logical and metaphysical vocabulary

Category – an Aristotelian term for a class of objects that objectively possess common features; more specifically, the broadest classes of objects that possess common features, such as substance, quality, quantity, relation, place, time, action, etc. (In the second sense, all individual living beings belong to the category of substance; so do the species and genera of individual living beings, such as human beings, warm-blooded animal, and animal itself.)

Predication – roughly, applying a predicate (e.g., horse, human being, tallest man in Rome, student of Plato) to something, e.g., an individual person or thing, as in "Bucephalus is a horse," or a group of objects, as in "all living beings in this room are human beings."

### Vocabulary of 20th century symbolic logic

For a very careful description of the basic grammar of a symbolic language, see this material from Benson Mates, Elementary Logic (1972). The definitions in this grammar may be necessary to understand some of the undefined terms in the vocabulary of symbolic logic below.

First-order Predicate Logic – See Predicate logic below. Predicate logic that permits quantifications over individual objects, but not over predicates. (x)(if Ax then Bx), "for all x, if x is an A then x is a B." 'x' here is a variable that can be "satisfied" by constants representing individual objects.

One-place Predicate – A predicate that requires only a constant, referring to an individual, to create a well-formed sentence.

Predicate logic – an enhancement of truth-functional logic that permits some analysis of simple sentences, for instance, "Pa," which states that object a has the predicate P and might represent "Socrates is bald," or "Rab," which states that objects a and b stand in relation R and might represent "a is to the right of b."

Quantifier – (x) or (E*x), "for all x" or "there is an x".
I have used E* instead of the backwards E that cannot be expressed in html (the website language).

Satisfaction of a variable – the substitution of a constant for a variable that ranges over it. For instance, a, which represents Socrates, satisfies Mx, if M represents the predicate 'is mortal'.

Second-Order Predicate Logic – a form of symbolic logic, based on truth-functional logic and first-order predicate logic, but going beyond them and permitting variables for predicates. For instance, "for all properties P there is some individual x that possess all of them." (P might have been defined to vary over a limited set of predicates, say, intellectual and moral perfections.)

Truth conditions of a sentence – the conditions under which a sentence is true, either its direct fit with the world or the rules for combining its components such that the combination will be true. A simple or atomic sentence will be true if it directly fits the world. A compound sentence will be true if the truth-values of its component sentences make it true (according to the principles of truth-functional logic).

Truth-functional logic – the logic governing sentences that claim to directly fit reality or consist of such sentences linked by truth-functional connectives, such as NOT, OR, AND, and IF-THEN.

Truth-value – There are two truth-values, true and false.

Two-placed predicate – A predicate that requires two constants (representing two individuals), or two bound variables, or one of each, to generate a sentence in the symbolic language of first-order predicate calculus.

Value of a variable – In first-order predicate logic, the value of a variable is an item (the constant naming the object) that can be substituted for the variable. See variable, constant.

Variable – a symbol in predicate logic that can vary over a set of entities. In first order predicate logic, it can vary over individuals. Typically, u, v, … z are used. In second order predicate logic, predicate symbols can be variables.

### Fregean vocabulary

Meaning – For Frege, our ordinary term "meaning" must be disambiguated as either reference or sense.

Psychologism – the view that some of our concepts, say mathematical concepts, result from the structure of the human mind. Frege opposes psychologism, especially but probably not only in the philosophy of mathematics. He was attacking John Stuart Mill in particular.

Reference – the way in which proper names (like Socrates), singular personal and demonstrative pronouns (he, she, this, that) and expressions containing the definite article ("the first President of the U.S.") pick out or refer to individuals. Contrasted with Sense. The individual picked out by a term is its referent. General nouns refer by having an extension, that is, a set of real individuals to which they refer. "Horse," for instance, refers to the nonhuman winners of the Kentucky Derby, Alexander of Macedon's Bucephalus, Napoleon's Nicole, and other members of the same species.

Sense(s) (=disembodied meaning(s), 441) – the meaning of a term that it seems to have apart from its extension. For instance, although "the morning star" and "the evening star" both refer to the same object (namely, the planet Venus), the description "the morning star" clearly has a different meaning or sense from the description "the evening star." Another term for "sense" is intension.

### Logical Positivism

Logical positivism (Vienna Circle and A. J. Ayer in the 1930's) – The movement of formalist yet empiricist analytic philosophy most strikingly characterized by its rejection of sentences that could not be confirmed empirically. Such "cognitively meaningless" sentences are found in ethics, aesthetics, and theology. They contain value terms (like beautiful and ugly, good and bad, morally right and wrong, and holy and unholy), which are considered "cognitively meaningless" expressions of likes and dislikes because there is no objective feature of the world to which they could refer.

Observation sentence – a sentence that objectively and uncontroversially describes the physical world. (The whole idea assumes "normal" observers and "normal" conditions of observation.) Quine borrows this concept from logical positivism. Observation sentences supposedly make it possible to confirm scientific hypotheses.

### W. V. O. Quine

Meaning holism – Quine's conclusion based on the principles of formalist analytic philosophy that the arbitrary symbols of a formal language can only be meaningfully interpreted in a fixed way as whole all at once.

Natural kinds – A 20th century version of the old philosophical idea of really existing species and genera. For a long time, this idea was bound up with Aristotelian metaphysics, according to which individuals were grouped into species, e.g., felines, canines, and humans, whose members shared a specific essence (and definition). Species were then grouped into genera (plural of genus), e.g., mammals and reptiles, whose members shared a somewhat less specific definition. By the 20th century, natural kind had been extended to include elements (like oxygen or gold) and chemical entities (like water), the sorts of things we tend to assume scientific knowledge is about. It is generally granted that natural kinds can be known only as a result of empirical research. Natural kinds are typically distinguished from artifact kinds (automobiles, toasters), and mathematical entities. As LJ say, Quine "assumes that there is an objective similarity in the world between objects of the same kind, that humans have innate abilities to notice similarities more or less accurately . . . " (460).

Naturalized epistemology – Quine's epistemology for explaining how we can acquire true observation sentences by use of behaviorist psychology (psychology that regards observation as having to do with the publicly observable behavior of the observer, not his "subjective" consciousness.)

Occam's Razor – A metaphysical principle first stated by William of Ockham in the Middle Ages to the effect that metaphysicians ought to keep the number of entities postulated to a minimum. This principle tends to support anti-Platonist ontologies.

Ontological relativity – Quine's thesis that what one can count as existing is relative to the interpretation of one's entire language, when the variables of one's language are all assigned referents.