display all the ideas for this combination of texts
11 ideas
10794 | The nominalist is tied by standard semantics to first-order, denying higher-order abstracta [Marcus (Barcan)] |
Full Idea: The nominalist finds that standard semantics shackles him to first-order languages if, as nominalists are wont, he is to make do without abstract higher order objects. | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.166) | |
A reaction: Aha! Since I am pursuing a generally nominalist strategy in metaphysics, I suddenly see that I must adopt a hostile attitude to higher-order logic! Maybe plural quantification is the way to go, with just first-order objects. |
11026 | Classical logic is deliberately extensional, in order to model mathematics [Fitting] |
Full Idea: Mathematics is typically extensional throughout (we write 3+2=2+3 despite the two terms having different meanings). ..Classical first-order logic is extensional by design since it primarily evolved to model the reasoning of mathematics. | |
From: Melvin Fitting (Intensional Logic [2007], §1) |
10786 | Anything which refers tends to be called a 'name', even if it isn't a noun [Marcus (Barcan)] |
Full Idea: The tendency has been to call any expression a 'name', however distant from the grammatical category of nouns, provided it is seen as referring. | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.162) |
10788 | Nominalists see proper names as a main vehicle of reference [Marcus (Barcan)] |
Full Idea: For a nominalist with an ontology of empirically distinguishable objects, proper names are seen as a primary vehicle of reference. | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.162) |
11028 | λ-abstraction disambiguates the scope of modal operators [Fitting] |
Full Idea: λ-abstraction can be used to abstract and disambiguate a predicate. De re is [λx◊P(x)](f) - f has the possible-P property - and de dicto is ◊[λxP(x)](f) - possibly f has the P-property. Also applies to □. | |
From: Melvin Fitting (Intensional Logic [2007], §3.3) | |
A reaction: Compare the Barcan formula. Originated with Church in the 1930s, and Carnap 1947, but revived by Stalnaker and Thomason 1968. Because it refers to the predicate, it has a role in intensional versions of logic, especially modal logic. |
10799 | Nominalists should quantify existentially at first-order, and substitutionally when higher [Marcus (Barcan)] |
Full Idea: For the nominalist, at level zero, where substituends are referring names, the quantifiers may be read existentially. Beyond level zero, the variables and quantifiers are read sustitutionally (though it is unclear whether this program is feasible). | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.167) |
10791 | Substitutional semantics has no domain of objects, but place-markers for substitutions [Marcus (Barcan)] |
Full Idea: On a substitutional semantics of a first-order language, a domain of objects is not specified. Variables do not range over objects. They are place markers for substituends (..and sentences are true-for-all-names, or true-for-at-least-one-name). | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.165) |
10790 | Quantifiers are needed to refer to infinitely many objects [Marcus (Barcan)] |
Full Idea: An adequate language for referring to infinitely many objects would seem to require variables and quantifiers in addition to names. | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.164) |
10785 | Maybe a substitutional semantics for quantification lends itself to nominalism [Marcus (Barcan)] |
Full Idea: It has been suggested that a substitutional semantics for quantification theory lends itself to nominalistic aims. | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.161) |
10795 | Substitutional language has no ontology, and is just a way of speaking [Marcus (Barcan)] |
Full Idea: Translation into a substitutional language does not force the ontology. It remains, literally, and until the case for reference can be made, a façon de parler. That is the way the nominalist would like to keep it. | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.166) |
10798 | A true universal sentence might be substitutionally refuted, by an unnamed denumerable object [Marcus (Barcan)] |
Full Idea: Critics say if there are nondenumerably many objects, then on the substitutional view there might be true universal sentences falsified by an unnamed object, and there must always be some such, for names are denumerable. | |
From: Ruth Barcan Marcus (Nominalism and Substitutional Quantifiers [1978], p.167) | |
A reaction: [See Quine 'Reply to Prof. Marcus' p.183] The problem seems to be that there would be names which are theoretically denumerable, but not nameable, and hence not available for substitution. Marcus rejects this, citing compactness. |