Combining Texts

All the ideas for 'fragments/reports', 'On Note L to Bayle's 'Rorarius'' and 'Intro to 'The Reason's Proper Study''

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12 ideas

5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright]
     Full Idea: If we stipulate that 'x is heterological' iff it does not apply to itself, we speedily arrive at the contradiction that 'heterological' is itself heterological just in case it is not.
     From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2)
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright]
     Full Idea: The incompletability of formal arithmetic reveals, not arithmetical truths which are not truths of logic, but that logical truth likewise defies complete deductive characterization. ...Gödel's result has no specific bearing on the logicist project.
     From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §2 n5)
     A reaction: This is the key defence against the claim that Gödel's First Theorem demolished logicism.
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
If structures are relative, this undermines truth-value and objectivity [Hale/Wright]
     Full Idea: The relativization of ontology to theory in structuralism can't avoid carrying with it a relativization of truth-value, which would compromise the objectivity which structuralists wish to claim for mathematics.
     From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26)
     A reaction: This is the attraction of structures which grow out of the physical world, where truth-value is presumably not in dispute.
The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright]
     Full Idea: It is not clear how the view that natural numbers are purely intra-structural 'objects' can be squared with the widespread use of numerals outside purely arithmetical contexts.
     From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2 n26)
     A reaction: I don't understand this objection. If they refer to quantity, they are implicitly cardinal. If they name things in a sequence they are implicitly ordinal. All users of numbers have a grasp of the basic structure.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright]
     Full Idea: The neo-Fregean takes a more optimistic view than Frege of the prospects for the kind of contextual explanation of the fundamental concepts of arithmetic and analysis (cardinals and reals), which he rejected in 'Grundlagen' 60-68.
     From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], §1)
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
Objects just are what singular terms refer to [Hale/Wright]
     Full Idea: Objects, as distinct from entities of other types (properties, relations or, more generally, functions of different types and levels), just are what (actual or possible) singular terms refer to.
     From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.1)
     A reaction: I find this view very bizarre and hard to cope with. It seems either to preposterously accept the implications of the way we speak into our ontology ('sakes'?), or preposterously bend the word 'object' away from its normal meaning.
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
The soul doesn't understand many of its own actions, if perceptions are confused and desires buried [Leibniz]
     Full Idea: The soul does many things without knowing how it does them - when it does them by means of confused perceptions and unconscious inclinations or appetites.
     From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [L])
     A reaction: This increasingly strikes me as a wonderful and important insight for its time. He's really paid attention to his own mind, and given up the simplistic view that derives from Descartes. Are birds conscious? Yes or no! Silly.
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
We should say that body is mechanism and soul is immaterial, asserting their independence [Leibniz]
     Full Idea: I think we should keep both sides: we should be more Democritean and make all actions of bodies mechanical and independent of souls, and we should also be more than Platonic and hold that all actions of souls are immaterial and independent of mechanism.
     From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [C])
     A reaction: This is about as dualist as it is possible to get. It certainly looks as if many of Leibniz's doctrines are rebellions against Spinoza (in this case his 'dual aspect monism'). I take Leibniz to be utterly but heroically wrong.
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright]
     Full Idea: The new kind of abstract objects are not creations of the human mind. ...The existence of such objects depends upon whether or not the relevant equivalence relation holds among the entities of the presupposed kind.
     From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2)
     A reaction: It seems odd that we no longer have any choice about what abstract objects we use, and that we can't evade them if the objects exist, and can't have them if the objects don't exist - and presumably destruction of the objects kills the concept?
19. Language / E. Analyticity / 2. Analytic Truths
Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright]
     Full Idea: There are many statements which are plausibly viewed as conceptual truths (such as 'what is yellow is extended') which do not qualify as analytic under Frege's definition (as provable using only logical laws and definitions).
     From: B Hale / C Wright (Intro to 'The Reason's Proper Study' [2001], 3.2)
     A reaction: Presumably this is because the early assumptions of Frege were mathematical and logical, and he was trying to get away from Kant. That yellow is extended is a truth for non-linguistic beings.
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
     Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
     From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
Minds unconsciously count vibration beats in music, and enjoy it when they coincide [Leibniz]
     Full Idea: In music, the soul counts the beats of the vibrating object which makes the sound, and when these beats regularly coincide at short intervals, it finds them pleasing. Thus it counts without knowing it.
     From: Gottfried Leibniz (On Note L to Bayle's 'Rorarius' [1705], [L])
     A reaction: Only a mathematician would see music this way! He is defending his account of the unconscious mind. The proposal that we unconsciously count sounds highly implausible. He needs to recognise the patterns that ground mathematics.