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Single Idea 9142

[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence ]

Full Idea

Fine considers abstraction principles as instances of reconceptualization (rather than implicit definition, or using the Context Principle). This centres not on reference, but on new senses emerging from analysis of a given sense.

Gist of Idea

Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses

Source

report of Kit Fine (The Limits of Abstraction [2002], 035) by R Cook / P Ebert - Notice of Fine's 'Limits of Abstraction' 2

Book Ref

-: 'British Soc for the Philosophy of Science' [-], p.793

A Reaction

Fine develops an argument against this view, because (roughly) the procedure does not end in a unique result. Intuitively, the idea that abstraction is 'reconceptualization' sounds quite promising to me.

The 229 ideas from Kit Fine

12302 Definitions formed an abstract hierarchy for Aristotle, as sets do for us [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]
14265 The components of abstract definitions could play the same role as matter for physical objects [Fine,K]
14266 Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K]
14268 Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K]
9146 After abstraction all numbers seem identical, so only 0 and 1 will exist! [Fine,K]
9148 I think of variables as objects rather than as signs [Fine,K]
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]
9152 If green is abstracted from a thing, it is only seen as a type if it is common to many things [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]
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]
12298 Genuine motion, rather than variation of position, requires the 'entire presence' of the object [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]
16537 Essence as necessary properties produces a profusion of essential properties [Fine,K, by Lowe]
11152 Essences are either taken as real definitions, or as necessary properties [Fine,K]
11151 An object is dependent if its essence prevents it from existing without some other object [Fine,K]
11157 Modern philosophy has largely abandoned real definitions, apart from sortals [Fine,K]
11159 My account shows how the concept works, rather than giving an analysis [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]
11161 Essentially having a property is naturally expressed as 'the property it must have to be what it is' [Fine,K]
11162 Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence [Fine,K]
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]
11165 If Socrates lacks necessary existence, then his nature cannot require his parents' existence [Fine,K]
11168 Metaphysical necessities are true in virtue of the nature of all objects [Fine,K]
11166 The subject of a proposition need not be the source of its necessity [Fine,K]
11167 Metaphysical necessity is a special case of essence, not vice versa [Fine,K]
11169 Conceptual necessities rest on the nature of all concepts [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]
11171 Defining a term and giving the essence of an object don't just resemble - they are the same [Fine,K]
17271 Is there metaphysical explanation (as well as causal), involving a constitutive form of determination? [Fine,K]
17273 Each basic modality has its 'own' explanatory relation [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]
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]
17280 Ground is best understood as a sentence operator, rather than a relation between predicates [Fine,K]
17281 If grounding is a relation it must be between entities of the same type, preferably between facts [Fine,K]
17275 Realist metaphysics concerns what is real; naive metaphysics concerns natures of things [Fine,K]
17277 If mind supervenes on the physical, it may also explain the physical (and not vice versa) [Fine,K]
17279 Even a three-dimensionalist might identify temporal parts, in their thinking [Fine,K]
17282 Truths need not always have their source in what exists [Fine,K]
17283 If the truth-making relation is modal, then modal truths will be grounded in anything [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]
17287 Facts, such as redness and roundness of a ball, can be 'fused' into one fact [Fine,K]
17286 Logical consequence is verification by a possible world within a truth-set [Fine,K]
17291 We explain by identity (what it is), or by truth (how things are) [Fine,K]
17288 We learn grounding from what is grounded, not what does the grounding [Fine,K]
17290 Only metaphysical grounding must be explained by essence [Fine,K]
17289 Every necessary truth is grounded in the nature of something [Fine,K]
9200 Empiricists suspect modal notions: either it happens or it doesn't; it is just regularities. [Fine,K]
9202 Objects, as well as sentences, can have logical form [Fine,K]
9205 The three basic types of necessity are metaphysical, natural and normative [Fine,K]
9206 We must distinguish between the identity or essence of an object, and its necessary features [Fine,K]
9208 Philosophers with a new concept are like children with a new toy [Fine,K]
9209 Metaphysical necessity may be 'whatever the circumstance', or 'regardless of circumstances' [Fine,K]
9207 If sentence content is all worlds where it is true, all necessary truths have the same content! [Fine,K]
9210 Possible objects are abstract; actual concrete objects are possible; so abstract/concrete are compatible [Fine,K]
9211 A non-standard realism, with no privileged standpoint, might challenge its absoluteness or coherence [Fine,K]
9222 The objects and truths of mathematics are imperative procedures for their construction [Fine,K]
9223 My Proceduralism has one simple rule, and four complex rules [Fine,K]
9224 Proceduralism offers a version of logicism with no axioms, or objects, or ontological commitment [Fine,K]
9142 Fine considers abstraction as reconceptualization, to produce new senses by analysing given senses [Fine,K, by Cook/Ebert]
9143 Implicit definitions must be satisfiable, creative definitions introduce things, contextual definitions build on things [Fine,K, by Cook/Ebert]
9144 Fine's 'procedural postulationism' uses creative definitions, but avoids abstract ontology [Fine,K, by Cook/Ebert]
10135 We can abstract from concepts (e.g. to number) and from objects (e.g. to direction) [Fine,K]
10137 Abstractionism can be regarded as an alternative to set theory [Fine,K]
10136 Points in Euclidean space are abstract objects, but not introduced by abstraction [Fine,K]
10138 An object is the abstract of a concept with respect to a relation on concepts [Fine,K]
10141 Many different kinds of mathematical objects can be regarded as forms of abstraction [Fine,K]
10143 'Creative definitions' do not presuppose the existence of the objects defined [Fine,K]
10144 Postulationism says avoid abstract objects by giving procedures that produce truth [Fine,K]
10145 Abstracts cannot be identified with sets [Fine,K]
9560 S5 provides the correct logic for necessity in the broadly logical sense [Fine,K]
15063 Some sentences depend for their truth on worldly circumstances, and others do not [Fine,K]
15064 Proper necessary truths hold whatever the circumstances; transcendent truths regardless of circumstances [Fine,K]
15065 What it is is fixed prior to existence or the object's worldly features [Fine,K]
15066 B-theorists say tensed sentences have an unfilled argument-place for a time [Fine,K]
15067 A-theorists tend to reject the tensed/tenseless distinction [Fine,K]
15068 The actual world is a totality of facts, so we also think of possible worlds as totalities [Fine,K]
15069 Possible worlds may be more limited, to how things might actually turn out [Fine,K]
15070 It is the nature of Socrates to be a man, so necessarily he is a man [Fine,K]
15071 Tensed and tenseless sentences state two sorts of fact, which belong to two different 'realms' of reality [Fine,K]
15072 Bottom level facts are subject to time and world, middle to world but not time, and top to neither [Fine,K]
15074 We would understand identity between objects, even if their existence was impossible [Fine,K]
15073 Self-identity should have two components, its existence, and its neutral identity with itself [Fine,K]
15076 Essential features of an object have no relation to how things actually are [Fine,K]
15075 Modal features are not part of entities, because they are accounted for by the entity [Fine,K]
15078 There are levels of existence, as well as reality; objects exist at the lowest level in which they can function [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]
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]
14252 We should understand identity in terms of the propositions it renders true [Fine,K]
14251 A natural modal account of dependence says x depends on y if y must exist when x does [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]
14250 Metaphysics deals with the existence of things and with the nature of things [Fine,K]
14255 We understand things through their dependency relations [Fine,K]
14254 Dependency is the real counterpart of one term defining another [Fine,K]
14257 An object depends on another if the second cannot be eliminated from the first's definition [Fine,K]
14256 How do we distinguish basic from derived esssences? [Fine,K]
14260 An object only essentially has a property if that property follows from every definition of the object [Fine,K]
14258 Maybe some things have essential relationships as well as essential properties [Fine,K]
14261 There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K]
14259 Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K]
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
10528 Definitions concern how we should speak, not how things are [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]
9213 The actual world is a possible world, so we can't define possible worlds as 'what might have been' [Fine,K]
9212 Possible states of affairs are not propositions; a proposition can't be a state of affairs! [Fine,K]
16755 The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau]
12211 It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K]
12209 The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K]
12212 Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K]
12214 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K]
12213 Ontological claims are often universal, and not a matter of existential quantification [Fine,K]
12215 The existence of numbers is not a matter of identities, but of constituents of the world [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]
12217 For ontology we need, not internal or external views, but a view from outside reality [Fine,K]
15007 If you make 'grounding' fundamental, you have to mention some non-fundamental notions [Sider on 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]
15048 In metaphysics, reality is regarded as either 'factual', or as 'fundamental' [Fine,K]
15006 Something is grounded when it holds, and is explained, and necessitated by something else [Fine,K, by Sider]
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]
15054 'Quietist' says abandon metaphysics because answers are unattainable (as in Kant's noumenon) [Fine,K]
15053 If metaphysics can't be settled, it hardly matters whether it makes sense [Fine,K]
15056 The notion of reduction (unlike that of 'ground') implies the unreality of what is reduced [Fine,K]
15055 Grounding relations are best expressed as relations between sentences [Fine,K]
15057 Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding [Fine,K]
15058 A proposition ingredient is 'essential' if changing it would change the truth-value [Fine,K]
15059 Grounding is an explanation of truth, and needs all the virtues of good explanations [Fine,K]
15061 Although colour depends on us, we can describe the world that way if it picks out fundamentals [Fine,K]
15060 Why should what is explanatorily basic be therefore more real? [Fine,K]
12220 Is it the sentence-token or the sentence-type that has a logical form? [Fine,K]
12222 Substitutional quantification is referential quantification over expressions [Fine,K]
10569 If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K]
10560 Set-theoretic imperialists think sets can represent every mathematical object [Fine,K]
10565 There is no stage at which we can take all the sets to have been generated [Fine,K]
10564 We might combine the axioms of set theory with the axioms of mereology [Fine,K]
10563 A generative conception of abstracts proposes stages, based on concepts of previous objects [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]
10571 Concern for rigour can get in the way of understanding phenomena [Fine,K]
10573 Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K]
10575 Why should a Dedekind cut correspond to a number? [Fine,K]
10574 Unless we know whether 0 is identical with the null set, we create confusions [Fine,K]
10570 Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K]
10568 Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K]
14530 The role of semantic necessity in semantics is like metaphysical necessity in metaphysics [Fine,K, by Hale/Hoffmann,A]
14618 Semantics is either an assignment of semantic values, or a theory of truth [Fine,K]
14619 The Quinean doubt: are semantics and facts separate, and do analytic sentences have no factual part? [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]
14620 Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms [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]
15588 You cannot determine the full content from a thought's intrinsic character, as relations are involved [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]
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]
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]
15596 The standard aim of semantics is to assign a semantic value to each expression [Fine,K]
15598 We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K]
15599 Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [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]
15602 Mental files are devices for keeping track of basic coordination of objects [Fine,K]
15604 If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K]
15603 I can only represent individuals as the same if I do not already represent them as the same [Fine,K]
15605 I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K]
11175 Logical concepts rest on certain inferences, not on facts about implications [Fine,K]
11174 A logical truth is true in virtue of the nature of the logical concepts [Fine,K]
11173 Being a man is a consequence of his essence, not constitutive of it [Fine,K]
11176 The property of Property Abstraction says any suitable condition must imply a property [Fine,K]
11177 Can the essence of an object circularly involve itself, or involve another object? [Fine,K]
11179 If there are alternative definitions, then we have three possibilities for essence [Fine,K]
11178 The essence or definition of an essence involves either a class of properties or a class of propositions [Fine,K]
14262 Formal grounding needs transitivity of grounding, no self-grounding, and the existence of both parties [Fine,K]
14263 Strong Kleene disjunction just needs one true disjunct; Weak needs the other to have some value [Fine,K]
13328 Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [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]
13331 Part and whole contribute asymmetrically to one another, so must differ [Fine,K]
13333 The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K]
13332 Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K]
23541 Supervaluation can give no answer to 'who is the last bald man' [Fine,K]
23544 Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K]
23540 Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K]
23542 Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause [Fine,K]
23539 Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K]
23543 We identify laws with regularities because we mistakenly identify causes with their symptoms [Fine,K]
23545 We do not have an intelligible concept of a borderline case [Fine,K]
23546 Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K]
23548 Indeterminacy is in conflict with classical logic [Fine,K]
23547 It seems absurd that there is no identity of any kind between two objects which involve survival [Fine,K]
9766 Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K]
9768 Vagueness is semantic, a deficiency of meaning [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]
9769 Vagueness can be in predicates, names or quantifiers [Fine,K]
9772 Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K]
9771 Logic holding between indefinite sentences is the core of all language [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]
9775 Excluded Middle, and classical logic, may fail for vague predicates [Fine,K]
9776 A thing might be vaguely vague, giving us higher-order vagueness [Fine,K]
9214 Unsupported testimony may still be believable [Fine,K]
9216 Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K]
9215 Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K]