Glossary

a se:

Latin expression for self-existence; lit., by itself

absolute creationism:

the view that God has created all abstract objects

abstract objects:

immaterial entities which are essentially causally powerless

abstracta:

Latin word for abstract objects

alethicity:

being truth-apt; capable of being true or false

analytic philosophy:

a method of philosophizing, dominant in Anglophone philosophy, that places a high value on clear definitions, analysis of concepts, logical rigour, and careful argumentation

analytic truth:

a statement which is true simply in virtue of the meaning of its terms

anti-Platonism:

the view that abstract objects do not exist

anti-realism:

the view with respect to a certain thing that the thing does not exist

applicability of mathematics:

mathematics’ utility in describing the physical world

arché:

Greek word for beginning or ultimate source

arealism:

the view that there is no fact of the matter concerning something’s existence

Arianism:

a third-century heresy which held that God the Father is alone uncreated and therefore Christ is not God, but a created thing

aseity:

self-existence

aspectual shape:

the particular way in which propositional content is grasped, e.g. from a first-person or third-person perspective

asymmetric: not symmetric

axiomatization:

a method of avoiding the paradoxes of naïve set theory by postulating a series of axioms, while leaving ‘set’ undefined; more generally, stating a mathematical theory in terms of basic axioms from which theorems may be derived

axioms of mathematics:

basic postulates of a mathematical theory

bare particular:

a thing logically prior to its exemplifying any properties

biblical theology:

exegetical theology aimed at determining the view of the biblical author

bootstrapping objection:

an objection alleging a vicious circularity

 (p.210) class:

a mathematical set-like object which is even more comprehensive than a set

composite:

made up of more fundamental parts

conceptual:

pertaining to the intellect, to ideas

conceptualism:

the view that supposedly abstract objects are really concrete thoughts of God

concrete objects:

objects which have causal powers, such as minds and material objects

conservation:

God’s preserving things in being moment by moment

constant:

a logical term which stands for an individual, typically, ‘a’, ‘b’, ‘c’, etc.; constants may be substituted for variables, typically ‘x’, ‘y’, ‘z’, in order to form statements about specific individuals

contingent:

possible but not necessary

contingentism:

the view that some things exist contingently

conventionalism:

the view that answers to metaphysical questions are wholly arbitrary, having no truth value

counterfactuals:

conditional statements in the subjunctive mood; e.g. ‘If I were rich, I would buy a Mercedes.’

creatio ex nihilo:

Latin expression for creation without a material cause (lit., creation out of nothing)

criterion of ontological commitment:

a criterion revealing to us just what existential commitments our assertions have; it tells us what we have to believe exists in order to hold to the truth of our assertion

deductivism:

the view that mathematical statements have the (disguised) logical form of conditional statements; also called If-thenism

deflationary:

minimalist; reducing one’s ontological commitments; opposite of inflationary

demiurge:

in Plato’s dialogue Timaeus, a god-like being who looks to the Forms as his model for creating the sensible world

denote:

a term’s singling out some object which has the properties predicated by the statement in which the term occurs; the object is the denotation of the term

domain of quantification:

in logic, the class of things over which one is quantifying; one says something about either all the members of the domain or some of the members of the domain

doxastic attitudes:

attitudes towards some propositional content, such as belief, doubt, hope, expectation

doxasticity:

capable of being the object of doxastic attitudes

(p.211) dual domain semantics:

in free logic, a semantics featuring two domains, one over which the quantifiers range and the other containing the referents of singular terms which fail to refer to things in the first domain

eliminative structuralism:

anti-realist view of mathematical structures

emanationism:

the view that things proceed from the being of God independent of His will

entity:

a thing; a being; an object

epistemic:

cognitive; knowledge related

essential:

belonging to a thing’s very nature

eternal:

having neither beginning nor end in time; permanent

eternalism:

a view of time as tenseless

ex nihilo:

see creatio ex nihilo

exemplification:

a relation between a thing and a property which the thing has; e.g. Fido exemplifies the property of brownness

exemplify:

to have (a property)

Existential Generalization:

a logical rule permitting us to infer from ‘a is F’ that ‘There is something that is F’ (or, ‘Something is F’)

existential quantifier:

a logical operator which makes a statement an existentially quantified statement. Ordinary language expressions like ‘there is/are’, ‘some’, ‘at least one’, and so forth, are informal quantifiers; in formal or symbolic logic, the operator ‘∃’ is a formal quantifier symbolizing such informal expressions

existential sentence:

an existentially quantified sentence

existentially loaded:

carrying ontological commitment

existentially quantified statement:

an assertion about some of the members of a class, usually indicated by words like ‘some’, ‘there is/are’, ‘at least one’, and so forth

extensional context:

sentence phrases which have two characteristics: (i) singular terms referring to the same entity can be switched without affecting the sentence’s truth value; (ii) one can quantify into such contexts from the outside

external questions:

questions posed in a language not used in an adopted linguistic framework

fictionalism:

the view that abstract object discourse is false or untrue

fictionally true:

prescribed to be imagined as true

figuralism:

the view that abstract object discourse is figurative language

figurative language:

non-literal language, e.g. metaphorical language

 (p.212) Form:

for Plato, transcendent, abstract objects on which God patterns the sensible world; for Aristotle, immaterial entities which imbue matter to make it into some specific thing, such as a rock or a horse

free logic:

a logic which holds that the quantifiers of first-order logic are ontologically committing but denies that singular terms are devices of ontological commitment

genus and species:

ancient categories for classifying things into kinds

heavyweight Platonism:

the view that abstract objects are fundamental features of reality

Hellenistic Judaism:

Judaism which bore the imprint of Greek thinking and culture. Though it is sometimes distinguished from Palestinian Judaism, in fact, Greek influence was strong in the Jewish homeland.

hermeneutic nominalism:

the view that mathematicians themselves do not take their mathematical sentences to be ontologically committing to mathematical objects

ideal:

non-physical, conceptual

idealization:

a fictitious entity in a scientific theory which real objects approximate, e.g. ideal gases or ideal fluids

impredicative:

pertaining to something’s being a member or constituent of itself

indispensability of mathematics:

the necessity of using mathematical terms in describing the physical world

instantiation:

the relation between a thing and its essence, whereby the essence is particularized; the thing is an instance of its essence; e.g. Paul and John instantiate or are instances of humanity

instrumental:

not descriptive of reality, but nevertheless useful for various practical purposes, such as making predictions

instrumentalism:

the view that a certain type of discourse is not to be taken as descriptive of reality, but merely as useful for various purposes

intellective activity: thinking

intelligible realm/world:

in ancient Platonism, the realm of the Ideas; a static, conceptual realm

intensional context:

a non-extensional context (see extensional context)

intentional attitude:

an object-directed attitude; an attitude about something

intentionality:

about-ness; object-directedness; being of something; ‘intentional’ must not be confused with ‘intensional’

internal questions:

questions posed in the language of an adopted linguistic framework

(p.213) intransitive: not transitive

intuitionism:

the view that mathematics is a construction of human minds; it denies the Law of Excluded Middle: p or not-p

Law of Excluded Middle:

for any proposition p, either p or not-p is true

lightweight Platonism:

the view that abstract objects merely serve as the semantic referents of certain terms and as values of the variables of quantification

linguistic framework:

an object language involving terms for certain kinds of objects to which one is not ontologically committed when speaking from a standpoint outside the framework

literally true:

true; not metaphorically true

logically prior:

prior in the order of explanation

logicians:

persons who specialize in the study of logic

logicism:

an early twentieth-century attempt to derive set theory from logic alone

LXX:

the Septuagint, an ancient Greek translation of the Old Testament

mereological nihilism:

the view that there are no composite objects

mereological universalism:

the view that any plurality whatsoever compose an object

mereology:

area of metaphysics which studies parts and wholes

metalanguage:

language used to talk about a lower level language

meta-ontological anti-realism:

the view that there are no objective answers to certain ontological questions

meta-ontology:

a higher level philosophical discipline about how to settle questions of ontology

metaphysical:

pertaining to metaphysics; beyond the physical world; what is ultimately real

metaphysical necessity/possibility:

what must be actual/what could be actual

metaphysics:

a branch of philosophy exploring reality in its various aspects

Middle Platonism:

a school of philosophical thought which evolved from classical Platonism and flourished from the first century BC until the third century; Middle Platonists identified Plato’s Ideas with God’s thoughts

mind-independent:

not products of human thinking or imagination; objectively existing

modal:

having to do with something’s possibility or necessity

modal operator:

a logical prefix which serves to give a modal status to a statement, like ‘Necessarily,…’ or ‘Possibly,…’

(p.214) nature:

the essence of a thing, or those properties without which the thing would not exist

necessary:

having to be certain way; being impossible to be otherwise

necessitism:

the view that everything that exists exists necessarily

neo-Meinongianism:

the view deriving from Alexius Meinong that there are (in a neutral sense) nonexistent objects bearing properties

neo-Quinean:

deriving from the view of the influential American philosopher W. V. O. Quine

neutralism:

the view that existential quantification and use of singular terms are not ontologically committing

nominalism:

in medieval debates, the view that universals do not exist; in the contemporary debate, the view either that abstract objects do not exist or that objects of a certain sort normally taken to be abstract, such as mathematical objects, do not exist

nominalistic content:

the non-Platonistic contents of scientific theories

nominalistic scientific realism:

the view that the nominalistic content of scientific theories is mostly true, while its Platonistic content is untrue

nominalization:

finding a noun or noun phrase to express a notion; gerunds are often used for this purpose

object language:

ground level language about the objects in one’s quantificational domain

objectual semantics for quantificational logic:

a theory of quantification according to which the variables which lie within the scope of the quantifiers range over a specified domain of objects to pick out various objects in the domain

occurrent:

present in consciousness

Ockham’s Razor:

the principle that, all things being equal, simpler explanations are to be preferred; causes should not be multiplied unnecessarily

One over Many:

an ancient philosophical problem of explaining the resemblance of particular objects to each other; what is the one thing that they have in common that accounts for their resemblance?

ontically relevant:

carrying ontological implications

onticity: ontological reality

ontological:

pertaining to being or existence

ontological assay:

an account of the metaphysical constituents of a thing

ontological commitment:

something that one must regard as real or existent

ontological dependence:

dependence in being (regardless of temporal beginning)

(p.215) ontological dispute:

a disagreement over what exists or is real

ontologically inflationary:

carrying gratuitous ontological commitments

ontologists:

philosophers who study ontology

ontology:

the study of what exists; an account of what exists

ontology, constituent:

an ontology which takes things to be metaphysically composed of other entities; e.g. a substratum and its properties

ontology, relational:

an ontology which takes things to be metaphysically simple, i.e. lacking any metaphysical constituents

paradigms: representative examples

paraphrastic strategies:

anti-realist strategies for paraphrasing sentences involving quantification over, or singular terms referring to, abstract objects, so that their ontological commitments are eliminated

particular quantifier:

an ontologically neutral existential quantifier

patristic:

pertaining to the Church Fathers

personification:

the portrayal of some property or aspect of a thing as a person, e.g. Lady Luck

Platonism:

the view that there exist abstract objects

possible worlds:

ways reality might have been; maximal states of affairs

postulationalism:

the view which treats the axioms of competing mathematical theories as postulates whose consequences may be explored

presentism:

the view that the present is ontologically privileged; the past and future do not exist

pretence theory:

a theory of fiction according to which statements of fiction are prescribed to be imagined true

principle of universal comprehension:

the principle according to which any property serves to determine a set of things having that property

property:

a universal quality which is exemplified by particulars

property instance:

the particular exemplification of a property, as the redness of this rose; property instances are particulars, not universals

proposition:

the information content expressed by sentences

quantification:

see existentially quantified statement, universally quantified statement

quantifier:

see existential quantifier, universal quantifier

quantify over (something):

to take (something) as the value of the variable lying within the scope of the quantifier

realism:

the view with respect to a certain thing that that thing exists

referent:

what one refers to

(p.216) referentialism:

the doctrine that singular terms successfully refer only if there are mind-independent objects in the world which are the denotations or referents of the terms

reify:

to construe something as a thing by nominalizing an expression for it; e.g. if one hunts deer, one might say that one is engaged in deer-hunting

revolutionary nominalism:

the view that mathematics needs to be revised in such a way that its sentences are not ontologically committing to abstract objects

Second Temple period:

the time when King Herod’s temple in Jerusalem was still standing

self-existent:

existing independently of anything else

semantic ascent:

talking about a claim rather than simply making the claim itself

semantic descent:

simply making a claim rather than talking about the claim

semantic theory:

theory concerning the meaning of linguistic expressions

sensible realm/world:

in ancient Platonism, the realm of temporal becoming and concrete objects

simple:

having no parts; uncomposed

simplicity:

the property of being simple

single domain semantics:

in free logic, a semantics featuring a single domain, typically everything that exists

singular term:

a word (or words) which serves to pick out a specific individual, typically proper names like ‘John’ or ‘USS Constitution’, definite descriptions like ‘the coin in my pocket’ or ‘your left arm’, and demonstratives like ‘this’ and ‘that’

socially constructed reality:

objects dependent upon social conventions

sole ultimate reality:

the only self-existent, uncreated thing

Sophia:

a female personification of God’s wisdom in Jewish Wisdom literature

sovereignty:

God’s control over all things

speaker’s reference:

what the person using certain terms intends to refer to

special composition question:

a question in mereology as to what conditions have to be met in order for a plurality to compose an object

Stoicism:

an ancient Greco-Roman philosophy originating in the third century BC that included an impersonal logos principle which supplied the world with rational structure

structuralism:

the view which takes numbers to be no more than positions in a certain kind of structure or pattern

(p.217) substances:

things which exist in their own right and not as modifications of something else

substitutional semantics for quantified logic:

a theory of quantification according to which the variables within the scope of the quantifier serve as dummy letters which may be replaced by linguistic expressions in order to form sentences

symmetric:

a relation > is symmetric just in case A > B, and B > A

systematic theology:

reflection upon the data of Scripture using philosophical and other tools

temporal: located in time

tense operator:

a logical prefix which serves to give a tenseless statement a tense, like ‘It was the case that …’ or ‘It will be the case that …’

tensed theory of time:

a view of time which holds that the tense of moments or events in time is objective and so the distinction between past, present, and future is an objective feature of the world

tenseless:

lacking any relation to the present and so neither past, present, nor future

tenseless theory of time:

a view of time which implies that all moments or events in time are equally real and the distinction between past, present, and future is merely a subjective feature of consciousness

theistic activism:

the view that modality is at least partly grounded in God’s free will

theorems of mathematics:

statements deducible from the axioms of a mathematical theory

theoretical entity:

an unobservable object which may or may not exist but is posited by a scientific theory for its value in modelling physical phenomena

transcendent:

beyond space and time, or beyond the physical universe

transitive:

a relation > is transitive just in case if A > B, and B > C, then A > C

truth value:

the property of being true/false

universal (n.):

a property; it is what particular objects have in common that explains their resemblance to one another; e.g. a British pillar box and a fire engine both share the universal redness

Universal Instantiation:

a logical rule permitting us to infer from ‘Everything is F’ that ‘a is F’

universal quantifier:

a logical operator which makes a statement a universally quantified statement. Ordinary language expressions like ‘all’, ‘every’, ‘any’, and so forth, are informal quantifiers; in formal or symbolic logic, the operator ‘∀’ is a formal quantifier symbolizing such informal expressions. The symbol for the formal quantifier is often omitted for simplicity’s sake. (p.218) For example, instead of (∀x) (Fx → Gx), one might write (x) (Fx → Gx), to be read ‘For any x, if x is F, then x is G’

universally quantified statement:

an assertion about all the members of a class, usually indicated by words like ?all?, ?every?, ?any?, and so forth

univocal:

having a single meaning; not equivocal

value:

in logic, the thing that replaces the variable in a sentence like (∃x) (x is an F); e.g. in ‘a is F’, the thing a stands for is the value of x

variable:

in first-order logic, the universal and existential quantifiers ‘∀’ and ‘∃’ are said to bind or have within their scope variables (like x, y, z) which may be replaced by certain constants (like a, b, c) to make statements about certain individuals in the domain of objects. E.g. in (∀x) (Fx → Gx), xis a variable which

may be replaced by the constant a to make the statement Fa → Ga

verificationism:

the view that meaningful sentences must be, in principle, capable of being verified empirically

voluntarism:

any view that privileges God’s free will over His nature

Wisdom literature:

ancient Jewish literature which especially emphasized the role of God’s wisdom in creation

YHWH:

abbreviation for the Hebrew name of God Yahweh, or the LORD

Zermelo-Fraenkel set theory:

standard set theory whose axioms were laid by Ernst Zermelo and Abraham Fraenkel

ZFC: