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Single Idea 15130
[filed under theme 4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
]
Full Idea
Barcan's axiom says if there can be something that has a certain property, then there is something that can have that property. It and its converse are not obviously correct or incorrect. They claim that it is non-contingent what individuals there are.
Gist of Idea
If a property is possible, there is something which can have it
Source
Timothy Williamson (Laudatio: Prof Ruth Barcan Marcus [2011], p.1)
A Reaction
Williamson defends the two Barcan formulas, but the more I understand them the less plausible they sound to me.
The
96 ideas
from Timothy Williamson
6858
|
Formal logic struck me as exactly the language I wanted to think in
[Williamson]
|
6859
|
Analytic philosophy has much higher standards of thinking than continental philosophy
[Williamson]
|
6860
|
How can one discriminate yellow from red, but not the colours in between?
[Williamson]
|
6861
|
What sort of logic is needed for vague concepts, and what sort of concept of truth?
[Williamson]
|
6862
|
Fuzzy logic uses a continuum of truth, but it implies contradictions
[Williamson]
|
6863
|
Close to conceptual boundaries judgement is too unreliable to give knowledge
[Williamson]
|
19512
|
Don't analyse knowledge; use knowledge to analyse other concepts in epistemology
[Williamson, by DeRose]
|
4760
|
Belief aims at knowledge (rather than truth), and mere believing is a kind of botched knowing
[Williamson]
|
19526
|
Surely I am acquainted with physical objects, not with appearances?
[Williamson]
|
19527
|
We don't acquire evidence and then derive some knowledge, because evidence IS knowledge
[Williamson]
|
19528
|
Knowledge is prior to believing, just as doing is prior to trying to do
[Williamson]
|
19529
|
Belief explains justification, and knowledge explains belief, so knowledge explains justification
[Williamson]
|
19530
|
A neutral state of experience, between error and knowledge, is not basic; the successful state is basic
[Williamson]
|
19531
|
Internalism about mind is an obsolete view, and knowledge-first epistemology develops externalism
[Williamson]
|
19534
|
How does inferentialism distinguish the patterns of inference that are essential to meaning?
[Williamson]
|
19535
|
Internalist inferentialism has trouble explaining how meaning and reference relate
[Williamson]
|
19533
|
Inferentialist semantics relies on internal inference relations, not on external references
[Williamson]
|
19532
|
Truth-conditional referential semantics is externalist, referring to worldly items
[Williamson]
|
19536
|
Knowledge-first says your total evidence IS your knowledge
[Williamson]
|
15130
|
If a property is possible, there is something which can have it
[Williamson]
|
14531
|
Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals
[Williamson, by Hale/Hoffmann,A]
|
14625
|
Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation
[Williamson]
|
14623
|
Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B)
[Williamson]
|
14624
|
Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B)
[Williamson]
|
14626
|
In S5 matters of possibility and necessity are non-contingent
[Williamson]
|
14628
|
Imagination is important, in evaluating possibility and necessity, via counterfactuals
[Williamson]
|
18925
|
If talking donkeys are possible, something exists which could be a talking donkey
[Williamson, by Cameron]
|
19216
|
Propositions (such as 'that dog is barking') only exist if their items exist
[Williamson]
|
16536
|
Williamson can't base metaphysical necessity on the psychology of causal counterfactuals
[Lowe on Williamson]
|
9592
|
Intuition is neither powerful nor vacuous, but reveals linguistic or conceptual competence
[Williamson]
|
9593
|
Progress in philosophy is incremental, not an immature seeking after drama
[Williamson]
|
9594
|
Correspondence to the facts is a bad account of analytic truth
[Williamson]
|
9595
|
You might know that the word 'gob' meant 'mouth', but not be competent to use it
[Williamson]
|
9596
|
We scorn imagination as a test of possibility, forgetting its role in counterfactuals
[Williamson]
|
9597
|
There are 'armchair' truths which are not a priori, because experience was involved
[Williamson]
|
9598
|
Modal thinking isn't a special intuition; it is part of ordinary counterfactual thinking
[Williamson]
|
9599
|
There cannot be vague objects, so there may be no such thing as a mountain
[Williamson]
|
9600
|
If languages are intertranslatable, and cognition is innate, then cultures are all similar
[Williamson]
|
9601
|
The realist/anti-realist debate is notoriously obscure and fruitless
[Williamson]
|
9602
|
Common sense and classical logic are often simultaneously abandoned in debates on vagueness
[Williamson]
|
20181
|
When analytic philosophers run out of arguments, they present intuitions as their evidence
[Williamson]
|
9183
|
Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist
[Williamson]
|
9184
|
We can't presume that all interesting concepts can be analysed
[Williamson]
|
15131
|
If metaphysical possibility is not a contingent matter, then S5 seems to suit it best
[Williamson]
|
15133
|
A thing can't be the only necessary existent, because its singleton set would be as well
[Williamson]
|
15134
|
The truthmaker principle requires some specific named thing to make the difference
[Williamson]
|
15135
|
If the domain of propositional quantification is constant, the Barcan formulas hold
[Williamson]
|
15138
|
Not all quantification is objectual or substitutional
[Williamson]
|
15136
|
Substitutional quantification is metaphysical neutral, and equivalent to a disjunction of instances
[Williamson]
|
15137
|
If 'fact' is a noun, can we name the fact that dogs bark 'Mary'?
[Williamson]
|
15139
|
Converse Barcan: could something fail to meet a condition, if everything meets that condition?
[Williamson]
|
15141
|
Truthmaker is incompatible with modal semantics of varying domains
[Williamson]
|
15140
|
The converse Barcan formula will not allow contingent truths to have truthmakers
[Williamson]
|
15142
|
Our ability to count objects across possibilities favours the Barcan formulas
[Williamson]
|
18492
|
Not all quantification is either objectual or substitutional
[Williamson]
|
21589
|
When bivalence is rejected because of vagueness, we lose classical logic
[Williamson]
|
21591
|
Vagueness is epistemic. Statements are true or false, but we often don't know which
[Williamson]
|
21590
|
Asking when someone is 'clearly' old is higher-order vagueness
[Williamson]
|
21592
|
Supervaluation keeps classical logic, but changes the truth in classical semantics
[Williamson]
|
21596
|
Vagueness undermines the stable references needed by logic
[Williamson]
|
21599
|
A sorites stops when it collides with an opposite sorites
[Williamson]
|
21600
|
'Blue' is not a family resemblance, because all the blues resemble in some respect
[Williamson]
|
21601
|
A vague term can refer to very precise elements
[Williamson]
|
21602
|
Many-valued logics don't solve vagueness; its presence at the meta-level is ignored
[Williamson]
|
21603
|
You can't give a precise description of a language which is intrinsically vague
[Williamson]
|
21604
|
Supervaluation assigns truth when all the facts are respected
[Williamson]
|
21607
|
Supervaluation has excluded middle but not bivalence; 'A or not-A' is true, even when A is undecided
[Williamson]
|
21606
|
'Bivalence' is the meta-linguistic principle that 'A' in the object language is true or false
[Williamson]
|
21605
|
Excluded Middle is 'A or not A' in the object language
[Williamson]
|
21611
|
Formal semantics defines validity as truth preserved in every model
[Williamson]
|
21612
|
Or-elimination is 'Argument by Cases'; it shows how to derive C from 'A or B'
[Williamson]
|
21608
|
Truth-functionality for compound statements fails in supervaluation
[Williamson]
|
21609
|
Supervaluationism defines 'supertruth', but neglects it when defining 'valid'
[Williamson]
|
21610
|
Supervaluation adds a 'definitely' operator to classical logic
[Williamson]
|
21613
|
Supervaluationism cannot eliminate higher-order vagueness
[Williamson]
|
21614
|
The 'nihilist' view of vagueness says that 'heap' is not a legitimate concept
[Williamson]
|
21615
|
References to the 'greatest prime number' have no reference, but are meaningful
[Williamson]
|
18038
|
The 't' and 'f' of formal semantics has no philosophical interest, and may not refer to true and false
[Williamson]
|
21617
|
We can say propositions are bivalent, but vague utterances don't express a proposition
[Williamson]
|
21616
|
Truth and falsity apply to suppositions as well as to assertions
[Williamson]
|
21618
|
If the vague 'TW is thin' says nothing, what does 'TW is thin if his perfect twin is thin' say?
[Williamson]
|
21619
|
If a heap has a real boundary, omniscient speakers would agree where it is
[Williamson]
|
21620
|
The epistemic view says that the essence of vagueness is ignorance
[Williamson]
|
21621
|
We can't infer metaphysical necessities to be a priori knowable - or indeed knowable in any way
[Williamson]
|
21622
|
If there is a true borderline of which we are ignorant, this drives a wedge between meaning and use
[Williamson]
|
21623
|
True and false are not symmetrical; false is more complex, involving negation
[Williamson]
|
21624
|
It is known that there is a cognitive loss in identifying propositions with possible worlds
[Williamson]
|
21625
|
The vagueness of 'heap' can remain even when the context is fixed
[Williamson]
|
9120
|
Vagueness in a concept is its indiscriminability from other possible concepts
[Williamson]
|
21626
|
Knowing you know (KK) is usually denied if the knowledge concept is missing, or not considered
[Williamson]
|
21627
|
We have inexact knowledge when we include margins of error
[Williamson]
|
21630
|
If fuzzy edges are fine, then why not fuzzy temporal, modal or mereological boundaries?
[Williamson]
|
21629
|
Equally fuzzy objects can be identical, so fuzziness doesn't entail vagueness
[Williamson]
|
21632
|
A river is not just event; it needs actual and counterfactual boundaries
[Williamson]
|
21633
|
Nominalists suspect that properties etc are our projections, and could have been different
[Williamson]
|
21631
|
To know, believe, hope or fear, one must grasp the thought, but not when you fail to do them
[Williamson]
|