General Index
General Index
aboutness 75, 77, 126, 129–30, 138; see also intentional; intentionality; reference
absolute creationism 50, 54–7, 66–8, 206 and ontological commitment 70 bootstrapping objection 60–3, 64, 68, 206
heavyweight 68–71
problems of scope and freedom in creation 56–8 abstract objects, see objects, abstract
Adams, Robert 112–13
agenētos/genētos 32–4, 37, 39; see also agennētos/gennētos; ginomai; Council of Nicea
agennētos/gennētos 32, 38; see also agenētos/genētos; Council of Nicea ante-Nicene Fathers, see early Church Fathers
anti-Platonism 6–8, 173; see also Platonism
anti-realism 6–9, 11–12, 50, 82–3, 139, 151–2, 157–8
argument from “lightheartedness” 176
theistic 164, 206–8 see also taxonomy of views on abstract objects applicability of mathematics, see mathematical, structure of physical world arealism 50, 51–3; see also taxonomy of views on abstract objects Arianism 32–3
Aristotle 56
aseity 1, 12, 206
and biblical theology, see biblical theology and perfect being theology 41
as corollary of omnipotence 41, 43, 54–5 early Church Fathers on 33–40
as essential attribute 30–1, 53 see also doctrine of aseity Athanasius 32–3
atheism 11, 72 n.1
Athenagoras 35
attributes, see properties, aseity, as essential attribute Augustinian tradition 73
axiomatization 188–97
as fix for naïve set theory 191 axioms 42, 133, 145, 148, 162–3
Peano 149, 162
set theory, see set theory, axioms of
Zermelo-Fraenkel set theory 174 see also statements; mathematical Azzouni, Jody 105–6, 108, 129–30, 134, 139, 152
Balaguer, Mark 45, 49, 52, 145–6, 163
Bar-Hillel, Yehoshua 191, 196
Bauckham, Richard 16, 34
Båve, Arvid 135–9
being, to come into 14–15, 18, 79; see also ginomai
being, uncreated 14, 15
begotten, Christ as, see Christ and Nicene statements on, agennētos/gennētos
Bentham, Jeremy 145
biblical theology 29–31; see also biblical; exegesis; systematic theology; theology Boolos, George 193
bootstrapping objection, see absolute creationism, conceptualism, ontological assay Brentano, Franz 136
Burgess, John 11, 113, 155, 174
Cantor, Georg 191
Carnap, Rudolf 51–3, 158
causal dependence 61–3, 78; see also logical dependence; ontological dependence Christ 24
and Nicene statements on 32; see also agenētos; Council of Nicea as Logos or agent of creation 25
(p.234) Christian Platonism, see Platonism, Christian “Christological monotheism” 18
Church Fathers, see early Church Fathers
classical theism 12, 43, 50, 56, 69, 74, 78, 144, 165, 180, 186–7, 204; see also theism
Cohen, Paul 202
combinatorial approach, see objects, abstract objects, combinatorial approach to communicable attributes, see properties, communicable
conceptualism 51, 55, 72, 206 and bootstrapping objection 78–9
and God’s first-person beliefs, see God, first-person beliefs of problem of thoughts as concrete objects; see also objects; concrete;
as God’s thoughts 84–5, 92–4 see also taxonomy of views on abstract objects; theistic conceptual realism concrete objects, see objects, concrete
concretism 50–1
constructivism 194–5
contingent 6, 30, 34; see also metaphysical contingency
Continuum Hypothesis 174, 202–3
conventionalism 51–3; see also taxonomy of views on abstract objects Council of Nicea 31, 34–5, 39; see also Nicene Creed
counterfactuals 160
counting, see numbers, experience of counting
creatio ex nihilo 26, 37, 173; see also doctrine, of creation creation, the 57–8, 164; see also doctrine, of creation Creator, see God
Davis, Richard 66 n.27, 78
Dedekind, Richard 191
deductivism 184, 190
deflationary theory, see reference, deflationary theory of, truth, deflationary theory of demiurge 36 n.38, 43
discourse:
figurative and literal, see figuralism mathematical, see statements, mathematical metaphysically heavyweight, see Ontologese modal, see statements, modal
possible worlds, see statements, modal divine aseity, see aseity
divine conceptualism, see conceptualism divine omnipotence, see omnipotence divine omniscience, see omniscience divine simplicity, see simplicity
divine sovereignty, see sovereignty doctrine:
of aseity 3, 17, 81, 208
of creation 3, 57
of independence and eternality of matter 35
domain of quantification, see quantification; quantifiers Dummett, Michael 9, 11, 131
Dunn, James D. G. 26
early Church Fathers 31–40
and divine conceptualism 72, 207 and use of quantifiers, see quantifiers views on numbers 34, 38
views on properties 34–5, 37, 40
eternal and eternity 2, 3, 17; see also eternality; objects, abstract; temporal vs timeless eternality 6, 34, 57
exegesis, biblical 17, 33; see also biblical theology exemplification 43, 67–8, 80
existential metaphors 168
existential quantification, see quantification, existential “exists” 49, 105–6, 112–13, 115–16, 120
stipulated as heavyweight, see quantifiers, stipulated as heavyweight 208
existentially loaded quantifier, see ontological commitment, existentially loaded quantifier extensional contexts 47–8, 74 n.8
external questions, see linguistic frameworks
fictionalism 51, 144–7, 153
and linguistic frameworks 158–60
and neo-Quinean criterion 148–51, 186, 208 (p.235) and obviousness of arithmetic 147–51, 156 and utility of mathematics 153–7, 161, 163
as self-defeating 158–60, 162, 164 see also taxonomy of views on abstract objects fictionally true 159–60; see also truth
Field, Hartry 8, 145–6, 161
figuralism 51, 144, 145, 165, 167 arguments and replies 174–8 explanatory benefits 173
figurative discourse and Platonic object discourse 169
figurative discourse vs literal discourse 167, 176–9 see also taxonomy of views on abstract objects; anti-realism first-order logic, see logic, first-order
formalism 190 n.17; see also taxonomy of views on abstract objects Forms, Platonic 2
as ideas in the mind of God 36, 38 n.41 see also Platonism Fraenkel, Abraham 191, 196, 197
free logic, see logic, free; taxonomy of views on abstract objects Frege, Gottlob 7, 72, 191, 192
ginomai 14; see also being, to come into; agenētos/genētos
God 1–6, 11, 177–8
and “late creation”, see “late creation” as beginningless 35
as cause of everything other than Himself 4, 33, 41, 82
concept of 1, 31
from Stoic philosophers 24–6
as creator 2, 4, 11–12, 14, 16, 24–5, 30, 35, 57–8, 164
of His own properties, see absolute creationism, bootstrapping objection first-person beliefs of 85–7
the Father as source and goal of all things 24, 26 goodness of 8 n.6, 19, 35
as greatest conceivable being 31 nature of 43, 43 n.47, 55, 57, 64
objects existing “inside” vs “outside” Himself 80–3 ontological argument for, see ontological argument self-existence of 1, 3, 9, 12; see also self-existence
as sole ultimate reality 2, 12, 13–43, 206
as sole uncreated being 14, 16, 16 n.4, 18, 23–4, 26, 31–4, 40 the Son as creator 26; see also Logos; Christ
thoughts as abstract objects 80–1, 92–4; see also conceptualism as transcendent 34
will of 57, 58
Word of 14–15, 17, 18, 39–40; see also Logos see also perfect being theology Gould, Paul 66 n.27, 78
great-making property, see properties, great-making Hale, Bob 10
heavyweight, see metaphysically heavyweight; Platonism, heavyweight; absolute creationism Hilbert, David 192
Hippolytus 33, 38–9
Horsley, Richard 25
Husserl, Edmund 136
ideal objects, see objects, abstract
identity statements, see logic, free, logic, standard
immaterial vs material objects, see objects, immaterial vs material incommunicable attributes, see properties, incommunicable Indispensability Arguments, see Platonism, arguments for
Inman, Ross 122 n.59 instrumentalism 154–7
intelligible realm 20, 20 n.12, 21, 23, 25, 35, 38, 39; see also kosmos noētos; sensible realm
intensional contexts 47–8, 74 n.8, 114, 118 intentional statements, see statements, intentional
(p.236) intentionality 74, 92, 137, 139
derivative vs intrinsic 75–6, 134 see also reference internal questions, see linguistic frameworks intuitionism 203
intuitive warrant 190, 191, 192, 202–3
“iterative concept of set” 194, 195
Jewish merism 26
Jewish monotheism 18, 30
John (biblical author) 13, 15, 17, 18
Logos doctrine of 13–19, 27, 38–9
John’s prologue 13–23, 38–9
use of quantifiers in, see quantifiers uses of ‘being’ and ‘becoming’ 23–4 Judaism
first-century 16–17
Hellenistic 18, 24, 25, 38, 39
kosmos noētos 21, 25–6; see also intelligible realm Kripke, Saul 110–11
Kunen, Kenneth 198
Lambert, Karel 140, 141 “late creation”:
and abstract objects 29 and angels 29
and souls 29
models of 28–9
Leftow, Brian 2, 27–8, 30, 55, 82
Leng, Mary 148–51, 163, 183–6
Leonhardt-Balzer, Jutta 18–19, 20 n.10 Lewis, C. S. 177 n.17
Lewis, David 119, 122–3
lightweight, see metaphysically lightweight; Platonism, lightweight linguistic frameworks 51–2
and external questions 51, 159
and internal questions 51–2, 158–9; see also fictionalism see also metalanguage logic:
existence assumptions of 140, 141
first-order 49, 119
semantics for 107–10
free 51, 126, 127, 137, 153
and dual domain semantics 128 identity statements in 141–2
positive 142, 166, 208 see also taxonomy of views on abstract objects standard 140 n.34
identity statements in 141–2 logical dependence 61–2
logicism 190
Logos 25–6
as Wisdom personified 36–7 role causally prior to creation 20
role in creation 18–21 see also Christ; God, the Son as creator; God, Word of Logos Christology 38–40
Maddy, Penelope 52, 153, 199
manifestation condition 154–6, 188 Marcus, Ruth Barcan 108 mathematical:
depth 189
discourse, see statements, mathematical fictional interpretation of, see set theory
“maximizing principles”, see Platonism, “maximizing principles” objects, see objects, mathematical
philosophy of, see philosophy of mathematics structure of physical world 163–4
Maudlin, Tim 163
McCann, Hugh 56
Meinong, Alexius 104, 126–7, 136–7
Menzel, Christopher 54
mereological nihilism 9 n.7, 12 n.17, 30
mereological sums 122–4
mereological universalism 122
metalanguage 108–10, 159; see also linguistic frameworks meta-ontology 49
and neo-Quinean theses 97–8, 100, 104
metaphysical contingency 5
metaphysically heavyweight 49, 120
metaphysically lightweight 112–13, 208
metaphysical necessity 5, 5 n.4, 30, 31, 35, 53; see also necessity; properties, essential; necessitism
Methodius 33, 37, 41
Middle Platonism, see Platonism, Middle Moltmann, Friederike 68
(p.237) Moo, Douglas 24, 26
Moreland, J. P. 63, 90–1
Morris, Thomas 31, 54
naturalism, explanatory resources of 164 necessitism 119, 121
necessity 3, 6, 30, 39, 57; see also metaphysical necessity; properties, essential
neo-Meinongianism 51, 104, 115–16, 125–7
compared to neutralism 127 see also taxonomy of views on neo-Platonic emanationism 58
neutralism 51, 104–7, 110–12, 137, 142–3, 165, 207
as collapsing into fictionalism 151–2
compared to neo-Meinongian and neo-Quinean theses 127, 129–30, 141 replies to 112–13, 115–16, 139 see also taxonomy of views on abstract objects Nicene Creed 31–2, see also Council of Nicea
Nicene Fathers, see early Church Fathers Nicomachus of Gerasa 21
Nietzsche, Friedrich 11
Nolt, John 127–8
nominalism 7, 7 n.5, 8, 158
hermeneutic vs revolutionary, see figuralism, arguments & replies vs anti-Platonism and anti-realism 7
non-existent objects, see objects, non-existent
numbers 34, 38, 42, 51–2, 57, 87–8, 92, 95, 130, 137, 149–50, 158
experience of counting 150–1 natural 42
transfinite 42 objects:
abstract 3–10, 12, 15–18, 21, 23, 26–7, 29, 32, 34, 40–1, 43
combinatorial approach to 174, 207, 208
examples of 3–5, 18
as fictional entities 144; see also object, mathematical as mind-dependent 8, 20–4, 36, 79
as mind-independent 15, 27, 72
as referents 49–50
role in a physical theory 16
taxonomy of views on, see taxonomy of views on abstract objects temporal vs timeless 29 n.30, 57
abstract-concrete distinction 3–6, 16 n.3
and social (or institutional) facts 131–2, 133 n.19, 207; see also socially constructed reality; Searle, John concrete 3–9, 16 n.3, 18
and immaterial objects 20 n.12 as creations of God 23, 26–7
as God’s thoughts 80–1, 84; see also conceptualism as more substantial than abstract objects 35, 37 material vs immaterial 4, 20
mathematical 2–3, 7–8, 11, 27, 41, 50, 158
as useful fictions 145, 157, 184–5, 190; see also fictionalism; pretence theory
incompleteness of 201
non-existent 104, 126, 129, 136, 137, 139, 182; see also neo-Meinongianism
semantic 10, 12
spatiotemporal vs non-spatiotemporal 4, 5, 76, 91, 119; see also linguistic frameworks
omnipotence 1, 30, 41, 65; see also sovereignty
omniscience 86, 109
One over the Many, problem of 44 Ontologese 152–3, 152–3 n.22, 165, 207, 208
ontological argument 192
ontological assay 63, 64, 66–7, 68, 79, 206
ontological commitment 9, 12, 40, 165–6 and beliefs of scientific community 155, 179 and counterfactuals 160
and existentially loaded quantifier 104–5, 116, 117–18, 119–21, 124, 126–7, 141, 143; see also quantifiers, particular and meta-ontological claims 49
and set theory 199
(p.238) and truths of elementary arithmetic 148–51; see also statements, mathematical criterion of 46, 48, 69–70, 96–7, 114, 118
existential quantification as device of 48, 50, 51, 104, 107–10, 118, 119, 159, 207
neo-Quinean theses on 97–8, 116–17, 118, 121, 142 n.38, 167, 186; see also meta-ontology
as person-relative 106
singular terms as devices of 46–8, 50, 51, 125, 127, 140–3, 159, 207; see also heavyweight; lightweight
ontological dependence 57, 58
ontological pluralism 52 ontology:
inflated 83
relational vs constituent 69 see also meta-ontology Oppy, Graham 85–6
Origen 35–6
Paul (biblical author) 13, 24–7 paradox 158; see also fictionalism paraphrasability 120, 169
paraphrases 10 n.13, 87–8, 97–8, 101–3, 160
Parsons, Charles 195
particular quantifier, see quantifiers, particular; see also Routley, Richard particulars 3, 4, 5, 7
perfect being theology 31, 41 Philo of Alexandria 18
and Aristotle’s four causes 19–20 and provenance of John’s views 23
and provenance of Paul’s expressions 25–6 on creation 164
Logos doctrine of 18–21 view of ideal objects 23 n.16
philosophy of mathematics 7, 44–5, 53–4, 72 n.1
Plantinga, Alvin 54–5, 73, 91, 92
Plato 2, 3, 3 n.3, 20, 34
Platonic Forms, see Platonic realm, Forms, Platonic Platonic Ideas, see Platonic realm
Platonic realm 20–1, 145–6, 178
Platonism 2, 6–7, 8–12, 35, 41, 151, 203
and anti-Platonism vs realism and anti-realism 7–8
and Axiom Schema of Unrestricted Comprehension 191 and uses of term “Platonism” 8–12
arguments against, see taxonomy of views on abstract objects arguments for:
Indispensability Arguments 45–6, 49–53, 69, 70 n.37, 74, 96, 125, 144, 186, 207 see alsotaxonomy of views on abstract objects
Christian 14, 15, 18, 26, 32, 43
classical 3, 18
contemporary 3, 5, 9, 12, 40
heavyweight 8–9, 12, 16, 43, 151–2; see also heavyweight
lightweight 9–10, 12, 69; see also lightweight
“maximizing principles” 199–200
Middle 18–19, 21
and interpretation of Genesis 1, 20 as reflected in John’s Prologue 23
as reflected in Paul’s letters 24 see also anti-Platonism; ontological commitment; taxonomy of views on abstract objects positive free logic, see logic, free, positive
possible worlds 3, 18, 30–1, 74
Potter, Michael 190, 198
“prepositional metaphysics” 19, 24
prescribed imagining 182, 190; see also pretence theory presentism 117–18, 119–20
Prestige, George 34
pretence theory 51, 93–4, 144, 165, 181, 196, 203–5
and make-believe 182, 187, 190–1
vs fictionalism 187
vs figuralism 204
set theory as ideal candidate for 200, 201 principle of universal comprehension 191, 197
principle of unrestricted mereological composition, see mereological sums principles of generation 182–4, 202
problem of the One over the Many, see One over the Many, problem of
(p.239) properties 1, 3–5, 7–9, 10 n.13, 29 n.30, 30–1, 34–5, 37, 40–1, 43, 59, 89–92, 206
and independent existence 34–5 communicable 1
created and uncreated 66
early Church Fathers’ views, see early Church Fathers, views on properties essential 61
great-making 31, 41
incommunicable 1
propositions 3–5, 7, 8, 18, 74, 76 aboutness of, see aboutness; intentionality as objects of God’s beliefs 84–5 psychologism 72
Pythagoras 34, 38 qualities, see properties quantification:
and objectual semantics for, see logic, first-order, semantics for
and substitutional semantics for, see logic, first-order, semantics for domain of 14, 15, 16, 26–7, 32–3, 40, 48, 107; see also quantifiers existential:
as metaphysically heavyweight 49, 99, 151
vs universal 48–9
ontically irrelevant 105, 106
ontically neutral 106, 107; see also “exist” quantifiers 17
existentially loaded, see ontological commitment, existentially loaded quantifier objectual, see quantifiers, referential, logic, first-order, semantics for
particular 105
referential 110–11
stipulated as heavyweight 109, 110, 151, 152 as used by Church Fathers 32–3
as used in John’s Prologue 15–16
as used in Paul’s letters 26–7 see also quantification quantifier-variable idiom 97, 100
quarantine (of a theory’s implications) 154–5
Quine, W. V. O. 16, 45–6, 125, 208; see also meta-ontology; ontological commitment
realism 6–8, 11, 50, 80, 152, 196, 199
as impediment to mathematics 200 non-Platonic 72, 74
theistic 164, 207 see also anti-realism; arealism
reference 125–6
Azzouni’s theory of 129–30, 134
deflationary theory of 135–9, 207 and empty singular terms 132 nature of 133–9
as a property 137
as a relation 130, 137 see also aboutness; see also intentionality referentialism 126
resemblance 44–5; see also One over the Many, problem of; universals Rosen, Gideon 155, 161–2, 174
Routley, Richard 104, 105, 114, 125–6
Runia, David 20
scientific use of fictions 184–5; see also objects, abstract; objects, mathematical Searle, John 131–4, 138 n.30, 139 n.32; see also social (or institutional) facts self-existence, see God, self-existence of
Sellars, Wilfrid 109
semantic ascent 162, 207
sensible realm 20–1, 35, 38, 39; see also intelligible realm
sets 3, 5, 8, 21, 42, 190, 193
and being well founded 198 as logical fictions 197
set-theoretical hierarchy 42, 195, 198
set theory 92–3, 162, 173–4, 200, 208
axioms 189, 192, 202
Axiom Schema of Restricted Comprehension 189, 191 of Choice 189, 196, 198
of Constructibility 189, 198–9, 202
of Determinacy 189, 199
of Extensionality 189, 193–4
of Foundation 189, 194–5, 198
of Infinity 189, 190–1, 192
(p.240) as candidate for pretence theoretic approach 188, 196; see also set theory, reasons for fictional interpretation of naïve 191, 192
other set theories 197–8
reasons for fictional interpretation of 188–203 axiomatization, see axiomatization
creative freedom afforded by 197, 203
incompleteness, see objects, mathematical, incompleteness of Zermelo-Fraenkel 174, 198
Sider, Theodore 10 n.13, 118, 152
simple sentences 46
simplicity 61–2, 64–6
singular terms, see ontological commitment, singular terms as devices of empty, see reference
socially constructed reality, see objects, and social (or institutional) facts; Searle, John “sole ultimate reality”, see God, as sole ultimate reality
Sophia (personification of divine wisdom), see Logos sovereignty:
and theistic activism 55, 59, 71
comparison to aseity debate in contemporary philosophy 54–5 in Jewish monotheism 16 see also omnipotence
spatiotemporal vs non-spatiotemporal objects, see objects, spatiotemporal vs non-spatiotemporal
special composition question, see statements, mereological; mereological nihilism; mereological sums; mereological universalism
statements:
existentially quantified 45–6, 49–50
as false but useful 98, 153–6, 161–2
intentional 113–17
mathematical 45–6, 50, 51, 96, 173
axioms as truths 145, 148–9, 162, 174, 188 obvious truth of 148–51
truth of as indispensable in science 145–7, 153–6; see also Indispensability Arguments
mereological 121–4
modal 119–20
tensed 117–18
universally quantified 14, 15, 32, 49, 100, 108, 190 see also simple sentences static being vs temporal becoming, see Platonic realm
Steiner, Mark 16, 163
substances 37
systematic theology 31, 41; see also biblical theology; exegesis, biblical; theology Tatian 35, 39
taxonomy of views on abstract objects: absolute creationism, see absolute creationism anti-realism, see anti-realism
arealism, see arealism conceptualism, see conceptualism concretism, see concretism conventionalism, see concretism fictionalism, see fictionalism figuralism, see figuralism formalism, see formalism
free logic, see logic, free
neo-Meinongianism, see neo-Meinongianism neutralism, see neutralism
Platonism, see Platonism
pretence theory, see pretence theory psychologism 72
temporal becoming 15, 57
tensed statements, see statements, tensed
terms, singular, see ontological commitment, singular terms as devices of tense 4
as used in biblical creation accounts 27–9, 29 n.31 theism 14, 16, 43, 59, 79, 117, 163–4 n.38
and tenable theories of abstract objects 165
explanatory resources vs naturalism 164 see also classical theism theistic activism, see sovereignty, theistic activism
theistic conceptual realism 73, 78 and violation of aseity 81
(p.241) theology 59, 61; see also biblical theology; exegesis; systematic theology theory of reference, see reference
“there is” and “there are”, see “exists”
Timaeus 2 n.2, 43, 164
transcendence 34; see also God, as transcendent truth 52, 97
deflationary theory of 161–2, 207
as entailing existence, see ontological commitment, logic, existence assumptions of logical 174
quasi- 118
trivial 141–2
truth conditions 109
truth value 4, 47, 49, 75, 143, 158; see also fictionally true
uncreatability 6
universals 3, 7
problem of 44; see also One over the Many, problem of see also properties “unreasonable effectiveness of mathematics” 163
unrestricted domain of quantification, see quantification, domain of Vaihinger, Hans 145
Van Inwagen, Peter 9, 10 n.13, 69–71, 97–8, 112, 115 verisimilitude, see truth, quasi-
vicious circularity; see also bootstrapping objection 62 voluntarism 58
von Neumann, John 22, 202–3
Walton, Kendall 182–3
Walton’s theory of fiction 182–3, 204
Welty, Greg 58, 73–7, 78, 80–1
Wigner, Eugene 163
Williamson, Timothy 119
will of God, see God, will of; voluntarism
Wisdom (personification of divine wisdom), see Logos Wolfson, Harry Austryn 34
Word of God, see God, Word of; Logos Yablo, Stephen 167, 172, 179, 204
Yahweh 17, 24 YHWH, see Yahweh