372 ideas
14255 | We understand things through their dependency relations [Fine,K] |
9208 | Philosophers with a new concept are like children with a new toy [Fine,K] |
14250 | Metaphysics deals with the existence of things and with the nature of things [Fine,K] |
15053 | If metaphysics can't be settled, it hardly matters whether it makes sense [Fine,K] |
17275 | Realist metaphysics concerns what is real; naive metaphysics concerns natures of things [Fine,K] |
15054 | 'Quietist' says abandon metaphysics because answers are unattainable (as in Kant's noumenon) [Fine,K] |
11159 | My account shows how the concept works, rather than giving an analysis [Fine,K] |
9766 | Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K] |
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
10237 | Coherence is a primitive, intuitive notion, not reduced to something formal [Shapiro] |
10528 | Definitions concern how we should speak, not how things are [Fine,K] |
10143 | 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K] |
9143 | Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert] |
12302 | Definitions formed an abstract hierarchy for Aristotle, as sets do for us [Fine,K] |
11157 | Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K] |
14259 | Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K] |
14266 | Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K] |
11171 | Defining a term and giving the essence of an object don't just resemble - they are the same [Fine,K] |
11178 | The essence or definition of an essence involves either a class of properties or a class of propositions [Fine,K] |
10204 | An 'implicit definition' gives a direct description of the relations of an entity [Shapiro] |
17282 | Truths need not always have their source in what exists [Fine,K] |
15063 | Some sentences depend for their truth on worldly circumstances, and others do not [Fine,K] |
17283 | If the truth-making relation is modal, then modal truths will be grounded in anything [Fine,K] |
13634 | Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro] |
13643 | Aristotelian logic is complete [Shapiro] |
10206 | Modal operators are usually treated as quantifiers [Shapiro] |
9560 | S5 provides the correct logic for necessity in the broadly logical sense [Fine,K] |
14263 | Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value [Fine,K] |
13651 | A set is 'transitive' if contains every member of each of its members [Shapiro] |
13647 | Choice is essential for proving downward Löwenheim-Skolem [Shapiro] |
10208 | Axiom of Choice: some function has a value for every set in a given set [Shapiro] |
10252 | The Axiom of Choice seems to license an infinite amount of choosing [Shapiro] |
10301 | The axiom of choice is controversial, but it could be replaced [Shapiro] |
13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
13654 | It is central to the iterative conception that membership is well-founded, with no infinite descending chains [Shapiro] |
13640 | Russell's paradox shows that there are classes which are not iterative sets [Shapiro] |
13666 | Iterative sets are not Boolean; the complement of an iterative set is not an iterative sets [Shapiro] |
13653 | 'Well-ordering' of a set is an irreflexive, transitive, and binary relation with a least element [Shapiro] |
10207 | Anti-realists reject set theory [Shapiro] |
13331 | Part and whole contribute asymmetrically to one another, so must differ [Fine,K] |
10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
13627 | There is no 'correct' logic for natural languages [Shapiro] |
13642 | Logic is the ideal for learning new propositions on the basis of others [Shapiro] |
13668 | Bernays (1918) formulated and proved the completeness of propositional logic [Shapiro] |
13669 | Can one develop set theory first, then derive numbers, or are numbers more basic? [Shapiro] |
13667 | Skolem and Gödel championed first-order, and Zermelo, Hilbert, and Bernays championed higher-order [Shapiro] |
13662 | First-order logic was an afterthought in the development of modern logic [Shapiro] |
13624 | The 'triumph' of first-order logic may be related to logicism and the Hilbert programme, which failed [Shapiro] |
13660 | Maybe compactness, semantic effectiveness, and the Löwenheim-Skolem properties are desirable [Shapiro] |
13673 | The notion of finitude is actually built into first-order languages [Shapiro] |
10588 | First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro] |
23548 | Indeterminacy is in conflict with classical logic [Fine,K] |
15944 | Second-order logic is better than set theory, since it only adds relations and operations, and nothing else [Shapiro, by Lavine] |
13629 | Broad standard semantics, or Henkin semantics with a subclass, or many-sorted first-order semantics? [Shapiro] |
13650 | Henkin semantics has separate variables ranging over the relations and over the functions [Shapiro] |
10298 | Some say that second-order logic is mathematics, not logic [Shapiro] |
13645 | In standard semantics for second-order logic, a single domain fixes the ranges for the variables [Shapiro] |
13649 | Completeness, Compactness and Löwenheim-Skolem fail in second-order standard semantics [Shapiro] |
10299 | If the aim of logic is to codify inferences, second-order logic is useless [Shapiro] |
10300 | Logical consequence can be defined in terms of the logical terminology [Shapiro] |
17286 | Logical consequence is verification by a possible world within a truth-set [Fine,K] |
10259 | The two standard explanations of consequence are semantic (in models) and deductive [Shapiro] |
13626 | Semantic consequence is ineffective in second-order logic [Shapiro] |
13637 | If a logic is incomplete, its semantic consequence relation is not effective [Shapiro] |
10257 | Intuitionism only sanctions modus ponens if all three components are proved [Shapiro] |
10253 | Either logic determines objects, or objects determine logic, or they are separate [Shapiro] |
9775 | Excluded Middle, and classical logic, may fail for vague predicates [Fine,K] |
10251 | The law of excluded middle might be seen as a principle of omniscience [Shapiro] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
12220 | Is it the sentence-token or the sentence-type that has a logical form? [Fine,K] |
13632 | Finding the logical form of a sentence is difficult, and there are no criteria of correctness [Shapiro] |
11175 | Logical concepts rest on certain inferences, not on facts about implications [Fine,K] |
10212 | Classical connectives differ from their ordinary language counterparts; '∧' is timeless, unlike 'and' [Shapiro] |
15592 | The usual Tarskian interpretation of variables is to specify their range of values [Fine,K] |
15593 | Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K] |
9148 | I think of variables as objects rather than as signs [Fine,K] |
15590 | It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K] |
15591 | In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K] |
15595 | The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K] |
15594 | 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K] |
10209 | A function is just an arbitrary correspondence between collections [Shapiro] |
14620 | Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms [Fine,K] |
15599 | Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K] |
11176 | The property of Property Abstraction says any suitable condition must imply a property [Fine,K] |
13674 | We might reduce ontology by using truth of sentences and terms, instead of using objects satisfying models [Shapiro] |
12222 | Substitutional quantification is referential quantification over expressions [Fine,K] |
10290 | Second-order variables also range over properties, sets, relations or functions [Shapiro] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
10268 | Maybe plural quantifiers should be understood in terms of classes or sets [Shapiro] |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
23539 | Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K] |
11174 | A logical truth is true in virtue of the nature of the logical concepts [Fine,K] |
9771 | Logic holding between indefinite sentences is the core of all language [Fine,K] |
13633 | 'Satisfaction' is a function from models, assignments, and formulas to {true,false} [Shapiro] |
10235 | A sentence is 'satisfiable' if it has a model [Shapiro] |
10239 | The central notion of model theory is the relation of 'satisfaction' [Shapiro] |
13644 | Semantics for models uses set-theory [Shapiro] |
10240 | Model theory deals with relations, reference and extensions [Shapiro] |
13670 | Categoricity can't be reached in a first-order language [Shapiro] |
13636 | An axiomatization is 'categorical' if its models are isomorphic, so there is really only one interpretation [Shapiro] |
10214 | Theory ontology is never complete, but is only determined 'up to isomorphism' [Shapiro] |
10238 | The set-theoretical hierarchy contains as many isomorphism types as possible [Shapiro] |
13648 | The Löwenheim-Skolem theorems show an explosion of infinite models, so 1st-order is useless for infinity [Shapiro] |
13675 | Substitutional semantics only has countably many terms, so Upward Löwenheim-Skolem trivially fails [Shapiro] |
10292 | Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro] |
10590 | Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro] |
10296 | The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro] |
13658 | Downward Löwenheim-Skolem: each satisfiable countable set always has countable models [Shapiro] |
13659 | Upward Löwenheim-Skolem: each infinite model has infinite models of all sizes [Shapiro] |
10297 | The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro] |
10234 | Any theory with an infinite model has a model of every infinite cardinality [Shapiro] |
13635 | 'Weakly sound' if every theorem is a logical truth; 'sound' if every deduction is a semantic consequence [Shapiro] |
13628 | We can live well without completeness in logic [Shapiro] |
13630 | Non-compactness is a strength of second-order logic, enabling characterisation of infinite structures [Shapiro] |
13646 | Compactness is derived from soundness and completeness [Shapiro] |
13661 | A language is 'semantically effective' if its logical truths are recursively enumerable [Shapiro] |
10201 | Virtually all of mathematics can be modeled in set theory [Shapiro] |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
13641 | Complex numbers can be defined as reals, which are defined as rationals, then integers, then naturals [Shapiro] |
8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
13676 | Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro] |
13677 | Natural numbers are the finite ordinals, and integers are equivalence classes of pairs of finite ordinals [Shapiro] |
10213 | Real numbers are thought of as either Cauchy sequences or Dedekind cuts [Shapiro] |
18243 | Understanding the real-number structure is knowing usage of the axiomatic language of analysis [Shapiro] |
18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
18245 | Cuts are made by the smallest upper or largest lower number, some of them not rational [Shapiro] |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
13652 | The 'continuum' is the cardinality of the powerset of a denumerably infinite set [Shapiro] |
10236 | There is no grounding for mathematics that is more secure than mathematics [Shapiro] |
8764 | Categories are the best foundation for mathematics [Shapiro] |
10256 | For intuitionists, proof is inherently informal [Shapiro] |
13657 | First-order arithmetic can't even represent basic number theory [Shapiro] |
10202 | Natural numbers just need an initial object, successors, and an induction principle [Shapiro] |
10294 | Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro] |
10205 | Mathematics originally concerned the continuous (geometry) and the discrete (arithmetic) [Shapiro] |
12215 | The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K] |
10529 | If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K] |
10530 | Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K] |
8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
13656 | Some sets of natural numbers are definable in set-theory but not in arithmetic [Shapiro] |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
10222 | Mathematical foundations may not be sets; categories are a popular rival [Shapiro] |
10218 | Baseball positions and chess pieces depend entirely on context [Shapiro] |
10224 | The even numbers have the natural-number structure, with 6 playing the role of 3 [Shapiro] |
10228 | Could infinite structures be apprehended by pattern recognition? [Shapiro] |
10230 | The 4-pattern is the structure common to all collections of four objects [Shapiro] |
10249 | The main mathematical structures are algebraic, ordered, and topological [Shapiro] |
10273 | Some structures are exemplified by both abstract and concrete [Shapiro] |
10276 | Mathematical structures are defined by axioms, or in set theory [Shapiro] |
8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
10270 | The main versions of structuralism are all definitionally equivalent [Shapiro] |
10221 | Is there is no more to structures than the systems that exemplify them? [Shapiro] |
10248 | Number statements are generalizations about number sequences, and are bound variables [Shapiro] |
10220 | Because one structure exemplifies several systems, a structure is a one-over-many [Shapiro] |
10223 | There is no 'structure of all structures', just as there is no set of all sets [Shapiro] |
8703 | Shapiro's structuralism says model theory (comparing structures) is the essence of mathematics [Shapiro, by Friend] |
10274 | Does someone using small numbers really need to know the infinite structure of arithmetic? [Shapiro] |
10200 | We distinguish realism 'in ontology' (for objects), and 'in truth-value' (for being either true or false) [Shapiro] |
10210 | If mathematical objects are accepted, then a number of standard principles will follow [Shapiro] |
10215 | Platonists claim we can state the essence of a number without reference to the others [Shapiro] |
10233 | Platonism must accept that the Peano Axioms could all be false [Shapiro] |
12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K] |
10244 | Intuition is an outright hindrance to five-dimensional geometry [Shapiro] |
12209 | The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K] |
10280 | A stone is a position in some pattern, and can be viewed as an object, or as a location [Shapiro] |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
9224 | Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K] |
13664 | Logicism is distinctive in seeking a universal language, and denying that logic is a series of abstractions [Shapiro] |
13625 | Mathematics and logic have no border, and logic must involve mathematics and its ontology [Shapiro] |
8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
9222 | The objects and truths of mathematics are imperative procedures for their construction [Fine,K] |
10254 | Can the ideal constructor also destroy objects? [Shapiro] |
9223 | My Proceduralism has one simple rule, and four complex rules [Fine,K] |
10255 | Presumably nothing can block a possible dynamic operation? [Shapiro] |
8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
13663 | Some reject formal properties if they are not defined, or defined impredicatively [Shapiro] |
8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
12214 | 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K] |
10279 | Can we discover whether a deck is fifty-two cards, or a person is time-slices or molecules? [Shapiro] |
15078 | There are levels of existence, as well as reality; objects exist at the lowest level in which they can function [Fine,K] |
14253 | An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K] |
10145 | Abstracts cannot be identified with sets [Fine,K] |
10136 | Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K] |
10144 | Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K] |
12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K] |
12216 | Real objects are those which figure in the facts that constitute reality [Fine,K] |
12218 | Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K] |
15007 | If you make 'grounding' fundamental, you have to mention some non-fundamental notions [Sider on Fine,K] |
15006 | Something is grounded when it holds, and is explained, and necessitated by something else [Fine,K, by Sider] |
14262 | Formal grounding needs transitivity of grounding, no self-grounding, and the existence of both parties [Fine,K] |
17272 | 2+2=4 is necessary if it is snowing, but not true in virtue of the fact that it is snowing [Fine,K] |
17276 | If you say one thing causes another, that leaves open that the 'other' has its own distinct reality [Fine,K] |
17284 | An immediate ground is the next lower level, which gives the concept of a hierarchy [Fine,K] |
17285 | 'Strict' ground moves down the explanations, but 'weak' ground can move sideways [Fine,K] |
17288 | We learn grounding from what is grounded, not what does the grounding [Fine,K] |
15055 | Grounding relations are best expressed as relations between sentences [Fine,K] |
17281 | If grounding is a relation it must be between entities of the same type, preferably between facts [Fine,K] |
17280 | Ground is best understood as a sentence operator, rather than a relation between predicates [Fine,K] |
17290 | Only metaphysical grounding must be explained by essence [Fine,K] |
14268 | Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K] |
17274 | Philosophical explanation is largely by ground (just as cause is used in science) [Fine,K] |
17278 | We can only explain how a reduction is possible if we accept the concept of ground [Fine,K] |
15050 | Reduction might be producing a sentence which gets closer to the logical form [Fine,K] |
15051 | Reduction might be semantic, where a reduced sentence is understood through its reduction [Fine,K] |
15052 | Reduction is modal, if the reductions necessarily entail the truth of the target sentence [Fine,K] |
15056 | The notion of reduction (unlike that of 'ground') implies the unreality of what is reduced [Fine,K] |
14261 | There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K] |
11151 | An object is dependent if its essence prevents it from existing without some other object [Fine,K] |
14251 | A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K] |
14257 | An object depends on another if the second cannot be eliminated from the first's definition [Fine,K] |
14254 | Dependency is the real counterpart of one term defining another [Fine,K] |
9210 | Possible objects are abstract; actual concrete objects are possible; so abstract/concrete are compatible [Fine,K] |
10227 | The abstract/concrete boundary now seems blurred, and would need a defence [Shapiro] |
10226 | Mathematicians regard arithmetic as concrete, and group theory as abstract [Shapiro] |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
12217 | For ontology we need, not internal or external views, but a view from outside reality [Fine,K] |
15060 | Why should what is explanatorily basic be therefore more real? [Fine,K] |
15048 | In metaphysics, reality is regarded as either 'factual', or as 'fundamental' [Fine,K] |
15072 | Bottom level facts are subject to time and world, middle to world but not time, and top to neither [Fine,K] |
9211 | A non-standard realism, with no privileged standpoint, might challenge its absoluteness or coherence [Fine,K] |
15046 | Reality is a primitive metaphysical concept, which cannot be understood in other terms [Fine,K] |
15047 | What is real can only be settled in terms of 'ground' [Fine,K] |
10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
17287 | Facts, such as redness and roundness of a ball, can be 'fused' into one fact [Fine,K] |
15071 | Tensed and tenseless sentences state two sorts of fact, which belong to two different 'realms' of reality [Fine,K] |
23540 | Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K] |
23546 | Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K] |
23544 | Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K] |
23542 | Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause [Fine,K] |
9768 | Vagueness is semantic, a deficiency of meaning [Fine,K] |
9776 | A thing might be vaguely vague, giving us higher-order vagueness [Fine,K] |
9767 | A vague sentence is only true for all ways of making it completely precise [Fine,K] |
9770 | Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K] |
9772 | Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K] |
9773 | With the super-truth approach, the classical connectives continue to work [Fine,K] |
9774 | Borderline cases must be under our control, as capable of greater precision [Fine,K] |
23541 | Supervaluation can give no answer to 'who is the last bald man' [Fine,K] |
12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
14217 | The 'standard' view of relations is that they hold of several objects in a given order [Fine,K] |
14216 | The 'positionalist' view of relations says the number of places is fixed, but not the order [Fine,K] |
14218 | A block on top of another contains one relation, not both 'on top of' and 'beneath' [Fine,K] |
14219 | Language imposes a direction on a road which is not really part of the road [Fine,K] |
14220 | Explain biased relations as orderings of the unbiased, or the unbiased as permutation classes of the biased? [Fine,K] |
13638 | Properties are often seen as intensional; equiangular and equilateral are different, despite identity of objects [Shapiro] |
10591 | Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro] |
16755 | The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau] |
10272 | The notion of 'object' is at least partially structural and mathematical [Shapiro] |
9202 | Objects, as well as sentences, can have logical form [Fine,K] |
15075 | Modal features are not part of entities, because they are accounted for by the entity [Fine,K] |
14252 | We should understand identity in terms of the propositions it renders true [Fine,K] |
13332 | Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K] |
9769 | Vagueness can be in predicates, names or quantifiers [Fine,K] |
10275 | A blurry border is still a border [Shapiro] |
23545 | We do not have an intelligible concept of a borderline case [Fine,K] |
13333 | The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K] |
14267 | There is no distinctive idea of constitution, because you can't say constitution begins and ends [Fine,K] |
14264 | Is there a plausible Aristotelian notion of constitution, applicable to both physical and non-physical? [Fine,K] |
13326 | A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K] |
13327 | A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K] |
13329 | An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K] |
13330 | An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K] |
13328 | Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K] |
11177 | Can the essence of an object circularly involve itself, or involve another object? [Fine,K] |
14256 | How do we distinguish basic from derived esssences? [Fine,K] |
11152 | Essences are either taken as real definitions, or as necessary properties [Fine,K] |
14258 | Maybe some things have essential relationships as well as essential properties [Fine,K] |
11173 | Being a man is a consequence of his essence, not constitutive of it [Fine,K] |
11179 | If there are alternative definitions, then we have three possibilities for essence [Fine,K] |
14260 | An object only essentially has a property if that property follows from every definition of the object [Fine,K] |
11161 | Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K] |
15065 | What it is is fixed prior to existence or the object's worldly features [Fine,K] |
11160 | Simple modal essentialism refers to necessary properties of an object [Fine,K] |
11158 | Essentialist claims can be formulated more clearly with quantified modal logic [Fine,K] |
11167 | Metaphysical necessity is a special case of essence, not vice versa [Fine,K] |
16537 | Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe] |
11163 | The nature of singleton Socrates has him as a member, but not vice versa [Fine,K] |
11164 | It is not part of the essence of Socrates that a huge array of necessary truths should hold [Fine,K] |
9206 | We must distinguish between the identity or essence of an object, and its necessary features [Fine,K] |
10935 | An essential property of something must be bound up with what it is to be that thing [Fine,K, by Rami] |
10936 | Essential properties are part of an object's 'definition' [Fine,K, by Rami] |
15076 | Essential features of an object have no relation to how things actually are [Fine,K] |
12295 | 3-D says things are stretched in space but not in time, and entire at a time but not at a location [Fine,K] |
12298 | Genuine motion, rather than variation of position, requires the 'entire presence' of the object [Fine,K] |
12296 | 4-D says things are stretched in space and in time, and not entire at a time or at a location [Fine,K] |
18882 | You can ask when the wedding was, but not (usually) when the bride was [Fine,K, by Simons] |
12297 | Three-dimensionalist can accept temporal parts, as things enduring only for an instant [Fine,K] |
17279 | Even a three-dimensionalist might identify temporal parts, in their thinking [Fine,K] |
11165 | If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K] |
15603 | I can only represent individuals as the same if I do not already represent them as the same [Fine,K] |
15073 | Self-identity should have two components, its existence, and its neutral identity with itself [Fine,K] |
15604 | If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K] |
15074 | We would understand identity between objects, even if their existence was impossible [Fine,K] |
9205 | The three basic types of necessity are metaphysical, natural and normative [Fine,K] |
9209 | Metaphysical necessity may be 'whatever the circumstance', or 'regardless of circumstances' [Fine,K] |
10258 | Logical modalities may be acceptable, because they are reducible to satisfaction in models [Shapiro] |
15064 | Proper necessary truths hold whatever the circumstances; transcendent truths regardless of circumstances [Fine,K] |
9200 | Empiricists suspect modal notions: either it happens or it doesn't; it is just regularities. [Fine,K] |
9212 | Possible states of affairs are not propositions; a proposition can't be a state of affairs! [Fine,K] |
11166 | The subject of a proposition need not be the source of its necessity [Fine,K] |
9216 | Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K] |
17273 | Each basic modality has its 'own' explanatory relation [Fine,K] |
14530 | The role of semantic necessity in semantics is like metaphysical necessity in metaphysics [Fine,K, by Hale/Hoffmann,A] |
17289 | Every necessary truth is grounded in the nature of something [Fine,K] |
11169 | Conceptual necessities rest on the nature of all concepts [Fine,K] |
11162 | Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K] |
11168 | Metaphysical necessities are true in virtue of the nature of all objects [Fine,K] |
15070 | It is the nature of Socrates to be a man, so necessarily he is a man [Fine,K] |
10266 | Why does the 'myth' of possible worlds produce correct modal logic? [Shapiro] |
9213 | The actual world is a possible world, so we can't define possible worlds as 'what might have been' [Fine,K] |
15069 | Possible worlds may be more limited, to how things might actually turn out [Fine,K] |
15068 | The actual world is a totality of facts, so we also think of possible worlds as totalities [Fine,K] |
15061 | Although colour depends on us, we can describe the world that way if it picks out fundamentals [Fine,K] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
9214 | Unsupported testimony may still be believable [Fine,K] |
17291 | We explain by identity (what it is), or by truth (how things are) [Fine,K] |
17271 | Is there metaphysical explanation (as well as causal), involving a constitutive form of determination? [Fine,K] |
15059 | Grounding is an explanation of truth, and needs all the virtues of good explanations [Fine,K] |
15057 | Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding [Fine,K] |
10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
9152 | If green is abstracted from a thing, it is only seen as a type if it is common to many things [Fine,K] |
23547 | It seems absurd that there is no identity of any kind between two objects which involve survival [Fine,K] |
17277 | If mind supervenes on the physical, it may also explain the physical (and not vice versa) [Fine,K] |
15602 | Mental files are devices for keeping track of basic coordination of objects [Fine,K] |
15588 | You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K] |
9144 | Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert] |
9149 | To obtain the number 2 by abstraction, we only want to abstract the distinctness of a pair of objects [Fine,K] |
9150 | We should define abstraction in general, with number abstraction taken as a special case [Fine,K] |
10141 | Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K] |
10229 | Simple types can be apprehended through their tokens, via abstraction [Shapiro] |
9626 | A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro] |
10217 | We can apprehend structures by focusing on or ignoring features of patterns [Shapiro] |
9554 | We can focus on relations between objects (like baseballers), ignoring their other features [Shapiro] |
10135 | We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K] |
9142 | Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert] |
10137 | Abstractionism can be regarded as an alternative to set theory [Fine,K] |
10138 | An object is the abstract of a concept with respect to a relation on concepts [Fine,K] |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
10527 | An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K] |
10231 | Abstract objects might come by abstraction over an equivalence class of base entities [Shapiro] |
9146 | After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K] |
15596 | The standard aim of semantics is to assign a semantic value to each expression [Fine,K] |
15587 | That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K] |
15589 | The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K] |
15598 | We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K] |
15600 | Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K] |
15601 | Fregeans approach the world through sense, Referentialists through reference [Fine,K] |
14618 | Semantics is either an assignment of semantic values, or a theory of truth [Fine,K] |
14621 | Semantics is a body of semantic requirements, not semantic truths or assigned values [Fine,K] |
14622 | Referential semantics (unlike Fregeanism) allows objects themselves in to semantic requirements [Fine,K] |
9207 | If sentence content is all worlds where it is true, all necessary truths have the same content! [Fine,K] |
15605 | I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K] |
15058 | A proposition ingredient is 'essential' if changing it would change the truth-value [Fine,K] |
11170 | Analytic truth may only be true in virtue of the meanings of certain terms [Fine,K] |
11172 | The meaning of 'bachelor' is irrelevant to the meaning of 'unmarried man' [Fine,K] |
14619 | The Quinean doubt: are semantics and facts separate, and do analytic sentences have no factual part? [Fine,K] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
14265 | The components of abstract definitions could play the same role as matter for physical objects [Fine,K] |
23543 | We identify laws with regularities because we mistakenly identify causes with their symptoms [Fine,K] |
9215 | Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K] |
15067 | A-theorists tend to reject the tensed/tenseless distinction [Fine,K] |
15077 | It is said that in the A-theory, all existents and objects must be tensed, as well as the sentences [Fine,K] |
15066 | B-theorists say tensed sentences have an unfilled argument-place for a time [Fine,K] |