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Single Idea 10567
[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence
]
Full Idea
Instead of viewing the abstracts (or sums) as being generated from objects, via the concepts from which they are defined, we can take them to be generated from conditions. The number of the universe ∞ is the number of self-identical objects.
Gist of Idea
We can create objects from conditions, rather than from concepts
Source
Kit Fine (Replies on 'Limits of Abstraction' [2005], 1)
Book Ref
-: 'Philosophical Studies' [-], p.373
A Reaction
The point is that no particular object is now required to make the abstraction.
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]
|
12296
|
4-D says things are stretched in space and in time, and not entire at a time or at a location
[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]
|
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]
|
11163
|
The nature of singleton Socrates has him as a member, but not vice versa
[Fine,K]
|
11162
|
Socrates is necessarily distinct from the Eiffel Tower, but that is not part of his essence
[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]
|
11167
|
Metaphysical necessity is a special case of essence, not vice versa
[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]
|
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]
|
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]
|
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]
|
17275
|
Realist metaphysics concerns what is real; naive metaphysics concerns natures of things
[Fine,K]
|
17279
|
Even a three-dimensionalist might identify temporal parts, in their thinking
[Fine,K]
|
17277
|
If mind supervenes on the physical, it may also explain the physical (and not vice versa)
[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]
|
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]
|
17291
|
We explain by identity (what it is), or by truth (how things are)
[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]
|
15065
|
What it is is fixed prior to existence or the object's worldly features
[Fine,K]
|
15064
|
Proper necessary truths hold whatever the circumstances; transcendent truths regardless of circumstances
[Fine,K]
|
15067
|
A-theorists tend to reject the tensed/tenseless distinction
[Fine,K]
|
15066
|
B-theorists say tensed sentences have an unfilled argument-place for a time
[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]
|
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]
|
10568
|
Logicists say mathematics can be derived from definitions, and can be known that way
[Fine,K]
|
10571
|
Concern for rigour can get in the way of understanding phenomena
[Fine,K]
|
10575
|
Why should a Dedekind cut correspond to a number?
[Fine,K]
|
10570
|
Assigning an entity to each predicate in semantics is largely a technical convenience
[Fine,K]
|
10573
|
Dedekind cuts lead to the bizarre idea that there are many different number 1's
[Fine,K]
|
10574
|
Unless we know whether 0 is identical with the null set, we create confusions
[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]
|
11174
|
A logical truth is true in virtue of the nature of the logical concepts
[Fine,K]
|
11175
|
Logical concepts rest on certain inferences, not on facts about implications
[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]
|
13332
|
Hierarchical set membership models objects better than the subset or aggregate relations do
[Fine,K]
|
13333
|
The matter is a relatively unstructured version of the object, like a set without membership structure
[Fine,K]
|
23542
|
Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause
[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]
|
23539
|
Classical semantics has referents for names, extensions for predicates, and T or F for sentences
[Fine,K]
|
23541
|
Supervaluation can give no answer to 'who is the last bald man'
[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]
|
23548
|
Indeterminacy is in conflict with classical logic
[Fine,K]
|
23546
|
Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen
[Fine,K]
|
23547
|
It seems absurd that there is no identity of any kind between two objects which involve survival
[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]
|
9766
|
Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics
[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]
|