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Single Idea 23540
[filed under theme 7. Existence / D. Theories of Reality / 10. Vagueness / a. Problem of vagueness
]
Full Idea
If 'P is red' and 'P is orange' are indefinite, then 'P is red and P is orange' seems false, because red and orange are exclusive. But if two conjoined indefinite sentences are false, that makes 'P is red and P is red' false, when it should be indefinite.
Gist of Idea
Conjoining two indefinites by related sentences seems to produce a contradiction
Source
Kit Fine (Vagueness: a global approach [2020], 1)
Book Ref
Fine,Kit: 'Vagueness: a global approach' [OUP 2020], p.10
A Reaction
[compressed] This is the problem of 'penumbral connection', where two indefinite values are still logically related, by excluding one another. Presumably 'P is red and P is of indefinite shape' can be true? Doubtful about this argument.
The
229 ideas
from Kit Fine
12302
|
Definitions formed an abstract hierarchy for Aristotle, as sets do for us
[Fine,K]
|
14265
|
The components of abstract definitions could play the same role as matter for physical objects
[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]
|
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]
|
16537
|
Essence as necessary properties produces a profusion of essential properties
[Fine,K, by Lowe]
|
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]
|
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]
|
11158
|
Essentialist claims can be formulated more clearly with quantified modal logic
[Fine,K]
|
11160
|
Simple modal essentialism refers to necessary properties of an 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]
|
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]
|
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]
|
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]
|
17279
|
Even a three-dimensionalist might identify temporal parts, in their thinking
[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]
|
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]
|
9209
|
Metaphysical necessity may be 'whatever the circumstance', or 'regardless of circumstances'
[Fine,K]
|
9208
|
Philosophers with a new concept are like children with a new toy
[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]
|
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]
|
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]
|
14252
|
We should understand identity in terms of the propositions it renders true
[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]
|
14256
|
How do we distinguish basic from derived esssences?
[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]
|
14261
|
There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions
[Fine,K]
|
14258
|
Maybe some things have essential relationships as well as essential properties
[Fine,K]
|
14260
|
An object only essentially has a property if that property follows from every definition of the object
[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]
|
9212
|
Possible states of affairs are not propositions; a proposition can't be a state of affairs!
[Fine,K]
|
9213
|
The actual world is a possible world, so we can't define possible worlds as 'what might have been'
[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]
|
15047
|
What is real can only be settled in terms of 'ground'
[Fine,K]
|
15046
|
Reality is a primitive metaphysical concept, which cannot be understood in other terms
[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]
|
15057
|
Ultimate explanations are in 'grounds', which account for other truths, which hold in virtue of the grounding
[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]
|
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]
|
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]
|
10562
|
We can combine ZF sets with abstracts as urelements
[Fine,K]
|
10561
|
Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object
[Fine,K]
|
10560
|
Set-theoretic imperialists think sets can represent every mathematical object
[Fine,K]
|
10563
|
A generative conception of abstracts proposes stages, based on concepts of previous objects
[Fine,K]
|
10567
|
We can create objects from conditions, rather than from concepts
[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]
|
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]
|
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]
|
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]
|
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]
|
23541
|
Supervaluation can give no answer to 'who is the last bald man'
[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]
|
23547
|
It seems absurd that there is no identity of any kind between two objects which involve survival
[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]
|
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]
|