Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'Philosophy of Logics' and 'Vagueness: a global approach'

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16 ideas

3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Logical truth seems much less likely to 'correspond to the facts' than factual truth does [Haack]
     Full Idea: It is surely less plausible to suppose that logical truth consists in correspondence to the facts than that 'factual' truth does.
     From: Susan Haack (Philosophy of Logics [1978], 7.6)
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
The same sentence could be true in one language and meaningless in another, so truth is language-relative [Haack]
     Full Idea: The definition of truth will have to be, Tarski argues, relative to a language, for one and the same sentence may be true in one language, and false or meaningless in another.
     From: Susan Haack (Philosophy of Logics [1978], 7.5)
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Indeterminacy is in conflict with classical logic [Fine,K]
     Full Idea: I now believe that the existence of indeterminacy is in conflict with classical logic.
     From: Kit Fine (Vagueness: a global approach [2020], 3)
     A reaction: I think that prior to this Fine had defended classical logic. Presumably the difficulty is over Bivalence. Nietzsche spotted this problem, despite not being a logician. Logic has to simplify the world. Hence philosophy is quite different from logic.
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K]
     Full Idea: A precise language is often assigned a classical semantics, in which the semantic value of a name is its referent, the semantic value of a predicate is its extension (the objects of which it is true), and the value of a sentence is True or False.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: Helpful to have this clear statement of how predicates are treated. This extensionalism in logic causes trouble when it creeps into philosophy, and people say that 'red' just means all the red things. No it doesn't.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
     Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10)
     A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
     Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
     A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
     Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01)
We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
     Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02)
7. Existence / D. Theories of Reality / 10. Vagueness / a. Problem of vagueness
Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K]
     Full Idea: Vagueness concerns 'local' indeterminacy, such as whether one man in the lineup is bald, and 'global' indeterminacy, applying to a range of cases, as when it is indeterminate how 'bald' applies to the lineup. But how do these relate?
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: This puts the focus either on objects or on predicates which are vague.
Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K]
     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.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     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.
Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K]
     Full Idea: Standard notions of vagueness all accept borderline cases, and presuppose a higher standpoint from which a judgement of being borderline F, rather than simply being F or being not F, can be made.
     From: Kit Fine (Vagueness: a global approach [2020], 3)
     A reaction: He says that the concept of borderline cases is an impediment to understanding vagueness. Proposing a third group when you are struggling to separate two other groups doesn't seem helpful, come to think of it. Limbo cases.
7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause [Fine,K]
     Full Idea: We can see Epistemicism [vagueness as ignorance] as a common and misguided tendency to identify a cause with its symptoms. We are unsure how to characterise vagueness, and identify it with the resulting ignorance, instead of explaining it.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: Love it. This echoes my repeated plea in these reactions to stop identifying features of reality with the functions which embody them or the patterns they create. We need to explain them, and must dig deeper.
7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
Supervaluation can give no answer to 'who is the last bald man' [Fine,K]
     Full Idea: Under supervaluation there should always be someone who is the last bald man in the sequence, but there is always an acceptable way to make some other man the last bald man.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: Fine seems to take this as a conclusive refutation of the supervaluation approach. Fine says (p.41) that supervaluation says there is a precisification for every instance.
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
We do not have an intelligible concept of a borderline case [Fine,K]
     Full Idea: We simply have no intelligible notion of local indeterminacy or of a borderline case.
     From: Kit Fine (Vagueness: a global approach [2020], 2)
     A reaction: He mentions cases which are near a borderline, and cases which are hard to decide, but denies that these are intrinsically borderline. If there are borderline cases between red and orange, what are the outer boundaries of the border?
16. Persons / D. Continuity of the Self / 2. Mental Continuity / b. Self as mental continuity
It seems absurd that there is no identity of any kind between two objects which involve survival [Fine,K]
     Full Idea: Pace Parfit and others, it boggles the mind that survival could be independent of any relation of identity between the currently existing object and the objects that subsequently exist.
     From: Kit Fine (Vagueness: a global approach [2020], 3)
     A reaction: Yes. If the self or mind just consists of a diachronic trail of memories such that the two ends of the trail have no connection at all, that isn't the kind of survival that any of us want. I want to live my life, not a life.
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
We identify laws with regularities because we mistakenly identify causes with their symptoms [Fine,K]
     Full Idea: There is a common tendency to identify a cause with its symptoms. Hence we are not sure how to characterise a law, and so we identify it with the regularities to which it gives rise.
     From: Kit Fine (Vagueness: a global approach [2020], 1)
     A reaction: A lovely clear identification of my pet hate, which is superficial accounts of things, which claim to be the last word, but actually explain nothing.