Combining Texts

All the ideas for 'fragments/reports', 'The philosophical basis of intuitionist logic' and 'Identity, Ostension, and Hypostasis'

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19 ideas

1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
We aren't stuck with our native conceptual scheme; we can gradually change it [Quine]
     Full Idea: We must not leap to the fatalistic conclusion that we are stuck with the conceptual scheme that we grew up in. We can change it bit by bit, plank by plank.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5)
     A reaction: This is an interesting commitment to Strawson's 'revisionary' metaphysics, rather than its duller cousin 'descriptive' metaphysics. Good for Quine. Remember, though, Davidson's 'On the Very Idea of Conceptual Scheme'.
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
     Full Idea: Dummett argues that classical logic depends on the choice of the concept of truth as central to the theory of meaning, while for the intuitionist the concept of assertability occupies this position.
     From: report of Michael Dummett (The philosophical basis of intuitionist logic [1973]) by Philip Kitcher - The Nature of Mathematical Knowledge 06.5
     A reaction: Since I can assert any nonsense I choose, this presumably means 'warranted' assertability, which is tied to the concept of proof in mathematics. You can reason about falsehoods, or about uninterpreted variables. Can you 'assert' 'Fx'?
5. Theory of Logic / G. Quantification / 1. Quantification
Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
     Full Idea: Classical quantification represents an infinite conjunction or disjunction, and the truth-value is determined by the infinite sum or product of the instances ....but this presupposes that all the instances already possess determinate truth-values.
     From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.246)
     A reaction: In the case of the universal quantifier, Dummett is doing no more than citing the classic empiricism objection to induction - that you can't make the universal claim if you don't know all the instances. The claim is still meaningful, though.
7. Existence / B. Change in Existence / 2. Processes
A river is a process, with stages; if we consider it as one thing, we are considering a process [Quine]
     Full Idea: A river is a process through time, and the river stages are its momentary parts. Identification of the river bathed in once with the river bathed in again is just what determines our subject matter to be a river process as opposed to a river stage.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 1)
     A reaction: So if we take a thing which has stages, but instead of talking about the stages we talk about a single thing that endures through them, then we are talking about a process. Sounds very good to me.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
We don't say 'red' is abstract, unlike a river, just because it has discontinuous shape [Quine]
     Full Idea: 'Red' is surely not going to be opposed to 'Cayster' [name of a river], as abstract to concrete, merely because of discontinuity in geometrical shape?
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2)
     A reaction: I've been slow to grasp the truth of this. However, Quine assumes that 'red' is concrete because 'Cayster' is, but it is perfectly arguable that 'Cayster' is an abstraction, despite all that water.
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
General terms don't commit us ontologically, but singular terms with substitution do [Quine]
     Full Idea: The use of general terms does not commit us to admitting a corresponding abstract entity into our ontology, but an abstract singular term, including the law of putting equals for equals, flatly commits us to an abstract entity named by the term.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 4)
     A reaction: Does this mean that in 'for the sake of the children', I have to believe in 'sakes' if I can find a synonym which will substitute for it?
7. Existence / E. Categories / 5. Category Anti-Realism
Discourse generally departmentalizes itself to some degree [Quine]
     Full Idea: Discourse generally departmentalizes itself to some degree.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2)
     A reaction: I pick this out because I think it is important. There is a continually shifting domain in any conversation ('what we are talking about'), and speech cannot be understand if the shifting domain or department has not been grasped.
8. Modes of Existence / E. Nominalism / 4. Concept Nominalism
Understanding 'is square' is knowing when to apply it, not knowing some object [Quine]
     Full Idea: No more need be demanded of 'is square' than that our listener learn when to expect us to apply it to an object and when not; there is no need for the phrase itself to be the name in turn of a separate object of any kind.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 4)
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
'Red' is a single concrete object in space-time; 'red' and 'drop' are parts of a red drop [Quine]
     Full Idea: Why not view 'red' as naming a single concrete object extended in space and time? ..To say a drop is red is to say that the one object, the drop, is a spatio-temporal part of the other, red, as a waterfall is part of a river.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2)
Red is the largest red thing in the universe [Quine]
     Full Idea: Red is the largest red thing in the universe - the scattered total thing whose parts are all the red things.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 3)
9. Objects / F. Identity among Objects / 1. Concept of Identity
To unite a sequence of ostensions to make one object, a prior concept of identity is needed [Quine]
     Full Idea: The concept of identity is central in specifying spatio-temporally broad objects by ostension. Without identity, n acts of ostension merely specify up to n objects. ..But when we affirm identity of object between ostensions, they refer to the same object.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 1)
     A reaction: Quine says that there is an induction involved. On the whole, Quine seems to give a better account of identity than Geach or Wiggins can offer.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
We should just identify any items which are indiscernible within a given discourse [Quine]
     Full Idea: We might propound the maxim of the 'identification of indiscernibles': Objects indistinguishable from one another within the terms of a given discourse should be construed as identical for that discourse.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 2)
     A reaction: This increasingly strikes me as the correct way to discuss such things. Identity is largely contextual, and two things can be viewed as type-identical for practical purposes (e.g. teaspoons), but distinguished if it is necessary.
18. Thought / D. Concepts / 5. Concepts and Language / b. Concepts are linguistic
Concepts are language [Quine]
     Full Idea: Concepts are language.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5)
     A reaction: Hm. This seems to mean that animals and pre-linguistic children have no concepts. I just don't believe that.
18. Thought / E. Abstraction / 1. Abstract Thought
Apply '-ness' or 'class of' to abstract general terms, to get second-level abstract singular terms [Quine]
     Full Idea: Applying the operator '-ness' or 'class of' to abstract general terms, we get second-level abstract singular terms.
     From: Willard Quine (Identity, Ostension, and Hypostasis [1950], 5)
     A reaction: This is the derivation of abstract concepts by naming classes, rather than by deriving equivalence classes. Any theory which doesn't allow multi-level abstraction is self-evidently hopeless. Quine says Frege and Russell get numbers this way.
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
     Full Idea: An ability to state the condition for the truth of a sentence is, in effect, no more than an ability to express the content of the sentence in other words.
     From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.224)
     A reaction: Alternatively, if you give something other than a paraphrase of the sentence as its meaning (such as a proof of its truth), then you seem to have departed from your target sentence. Can we reduce and eliminate our sentences in this way?
If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
     Full Idea: If a sentence is effectively undecidable, the condition which must obtain for it to be true is not one which we are capable of recognising whenever it obtains, or of getting ourselves in a position to do so.
     From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.225)
     A reaction: The instances of 'undecidable' sentences are most clearly seen in mathematics, such as the Continuum Hypothesis or Goldbach's Conjecture, or anything involving vast infinite cardinals. But do you need precise truth-conditions for meaning?
19. Language / A. Nature of Meaning / 6. Meaning as Use
Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]
     Full Idea: If use constitutes meaning, it might seem that use is beyond criticism. ....But such an attitude can, ultimately, be supported onlly by the adoption of a holistic view of language.
     From: Michael Dummett (The philosophical basis of intuitionist logic [1973], p.218)
     A reaction: Dummett goes on to say that the rejection of the holistic view of mathematical meaning leads to his preference for intuitionistic logic.
25. Social Practice / E. Policies / 5. Education / b. Education principles
Learned men gain more in one day than others do in a lifetime [Posidonius]
     Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes.
     From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078
     A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book.
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]
     Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness.
     From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42
     A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them.