Combining Texts

All the ideas for 'Mind and Its Place in Nature', 'Logicism in the 21st Century' and 'Things and Their Parts'

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14 ideas

4. Formal Logic / G. Formal Mereology / 1. Mereology

13331	Part and whole contribute asymmetrically to one another, so must differ [Fine,K]
	Full Idea: The whole identity of a part is relevant to whether it is a part, but the identity of the whole makes a part a part. The whole part belongs to the whole as a part. The standard account in terms of time-slices fails to respect this part/whole asymmetry.
	From: Kit Fine (Things and Their Parts [1999], §2)
	A reaction: Hard to follow, but I think the asymmetry is that the wholeness of the part contributes to the wholeness of the whole, while the wholeness of the whole contributes to the parthood of the part. Wholeness does different jobs in different directions. OK?

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle

8784	Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
	Full Idea: The result of joining Hume's Principle to second-order logic is a consistent system which is a foundation for arithmetic, in the sense that all the fundamental laws of arithmetic are derivable within it as theorems. This seems a vindication of logicism.
	From: B Hale / C Wright (Logicism in the 21st Century [2007], 1)
	A reaction: The controversial part seems to be second-order logic, which Quine (for example) vigorously challenged. The contention against most attempts to improve Frege's logicism is that they thereby cease to be properly logical.

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem

8787	The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
	Full Idea: The Julius Caesar problem is the problem of supplying a criterion of application for 'number', and thereby setting it up as the concept of a genuine sort of object. (Why is Julius Caesar not a number?)
	From: B Hale / C Wright (Logicism in the 21st Century [2007], 3)
	A reaction: One response would be to deny that numbers are objects. Another would be to derive numbers from their application in counting objects, rather than the other way round. I suspect that the problem only real bothers platonists. Serves them right.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

8788	Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
	Full Idea: It is only if logic is metaphysically and epistemologically privileged that a reduction of mathematical theories to logical ones can be philosophically any more noteworthy than a reduction of any mathematical theory to any other.
	From: B Hale / C Wright (Logicism in the 21st Century [2007], 8)
	A reaction: It would be hard to demonstrate this privileged position, though intuitively there is nothing more basic in human rationality. That may be a fact about us, but it doesn't make logic basic to nature, which is where proper reduction should be heading.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism

8783	Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
	Full Idea: Two modern approaches to logicism are the quantificational approach of David Bostock, and the abstraction-free approach of Neil Tennant.
	From: B Hale / C Wright (Logicism in the 21st Century [2007], 1 n2)
	A reaction: Hale and Wright mention these as alternatives to their own view. I merely catalogue them for further examination. My immediate reaction is that Bostock sounds hopeless and Tennant sounds interesting.

9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual

13332	Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K]
	Full Idea: It is the hierarchical conception of sets and their members, rather than the linear conception of set and subset or of aggregate and component, that provides us with the better model for the structure of part-whole in its application to material things.
	From: Kit Fine (Things and Their Parts [1999], §5)
	A reaction: His idea is to give some sort of internal structure. He says of {a,b,c,d} that we can create subsets {a,b} and {c,d} from that. But {{a,b},{c,d}} has given member sets, and he is looking for 'natural' divisions between the members.

9. Objects / C. Structure of Objects / 3. Matter of an Object

13333	The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K]
	Full Idea: The wood is, as it were, a relatively unstructured version of the tree, just as the set {a,b,c,d} is an unstructured counterpart of the set {{a,b},{c,d}}.
	From: Kit Fine (Things and Their Parts [1999], §5)
	A reaction: He is trying to give a modern logicians' account of the Aristotelian concept of 'form' (as applied to matter). It is part of the modern project that objects must be connected to the formalism of mereology or set theory. If it works, are we thereby wiser?

9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects

13326	A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K]
	Full Idea: First, a thing can be a part in a way that is relative to a time, for example, that a newly installed carburettor is now part of my car, whereas earlier it was not. (This will be called a 'temporary' part).
	From: Kit Fine (Things and Their Parts [1999], Intro)
	A reaction: [Cf Idea 13327 for the 'second' concept of part] I'm immediately uneasy. Being a part seems to be a univocal concept. He seems to be distinguishing parts which are necessary for identity from those which aren't. Fine likes to define by example.

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]
	Full Idea: Second, an object can be a part of another in a way that is not relative to time ('timeless'). It is not appropriate to ask when it is a part. Thus pants and jacket are parts of the suit, atoms of a water molecule, and two pints part of a quart of milk.
	From: Kit Fine (Things and Their Parts [1999], Intro)
	A reaction: [cf Idea 13326 for the other concept of 'part'] Again I am uneasy that 'part' could have two meanings. A Life Member is a member in the same way that a normal paid up member is a member.

9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts

13329	An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K]
	Full Idea: In the 'aggregative' understanding of a sum, it is spread out in time, so that exists whenever any of its components exists (just as it is located at any time wherever any of its components are located).
	From: Kit Fine (Things and Their Parts [1999], §1)
	A reaction: This works particularly well for something like an ancient forest, which steadily changes its trees. On that view, though, the ship which has had all of its planks replaced will be the identical single sum of planks all the way through. Fine agrees.

13330	An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K]
	Full Idea: In the 'compound' notion of sum, the mereological sum is spread out only in space, not also in time. For it to exist at a time, all of its components must exist at the time.
	From: Kit Fine (Things and Their Parts [1999], §1)
	A reaction: It is hard to think of anything to which this applies, apart from for a classical mereologist. Named parts perhaps, like Tom, Dick and Harry. Most things preserve sum identity despite replacement of parts by identical components.

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

13328	Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K]
	Full Idea: I develop a version of hylomorphism, in which the theory of 'rigid embodiment' provides an account of the timeless relation of part, and the theory of 'variable embodiment' is an account of the temporary relation. We must accept two new kinds of whole.
	From: Kit Fine (Things and Their Parts [1999], Intro)
	A reaction: [see Idea 13326 and Idea 13327 for the two concepts of 'part'] This is easier to take than the two meanings for 'part'. Since Aristotle, everyone has worried about true wholes (atoms, persons?) and looser wholes (houses).

12. Knowledge Sources / B. Perception / 6. Inference in Perception

7628	Broad rejects the inferential component of the representative theory [Broad, by Maund]
	Full Idea: Broad, one of the most important modern defenders of the representative theory of perception, explicitly rejects the inferential component of the theory.
	From: report of C.D. Broad (Mind and Its Place in Nature [1925]) by Barry Maund - Perception Ch.1
	A reaction: Since the supposed inferences happen much too quickly to be conscious, it is hard to see how we could distinguish an inference from an interpretation mechanism. Personally I interpret things long before the question of truth arises.

18. Thought / E. Abstraction / 7. Abstracta by Equivalence

8786	One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright]
	Full Idea: An example of a first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines; a higher-order example (which refers to first-order predicates) defines 'equinumeral' in terms of one-to-one correlation (Hume's Principle).
	From: B Hale / C Wright (Logicism in the 21st Century [2007], 1)
	A reaction: [compressed] This is the way modern logicians now treat abstraction, but abstraction principles include the elusive concept of 'equivalence' of entities, which may be no more than that the same adjective ('parallel') can be applied to them.