Combining Texts

All the ideas for 'Things and Their Parts', 'Does moral phil rest on a mistake?' and 'On Second-Order Logic'

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20 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?

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic

14249	Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
	Full Idea: Boolos's conception of plural logic is as a reinterpretation of second-order logic.
	From: report of George Boolos (On Second-Order Logic [1975]) by Oliver,A/Smiley,T - What are Sets and What are they For? n5
	A reaction: Oliver and Smiley don't accept this view, and champion plural reference differently (as, I think, some kind of metalinguistic device?).

10830	Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
	Full Idea: The metatheory of second-order logic is hopelessly set-theoretic, and the notion of second-order validity possesses many if not all of the epistemic debilities of the notion of set-theoretic truth.
	From: George Boolos (On Second-Order Logic [1975], p.45)
	A reaction: Epistemic problems arise when a logic is incomplete, because some of the so-called truths cannot be proved, and hence may be unreachable. This idea indicates Boolos's motivation for developing a theory of plural quantification.

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic

10829	A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
	Full Idea: One may be of the opinion that no sentence ought to be considered as a truth of logic if, no matter how it is interpreted, it asserts that there are sets of certain sorts.
	From: George Boolos (On Second-Order Logic [1975], p.44)
	A reaction: My intuition is that in no way should any proper logic assert the existence of anything at all. Presumably interpretations can assert the existence of numbers or sets, but we should be able to identify something which is 'pure' logic. Natural deduction?

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

10832	'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
	Full Idea: One may say that '∀x x=x' means 'everything is identical to itself', but one must realise that one's answer has a determinate sense only if the reference (range) of 'everything' is fixed.
	From: George Boolos (On Second-Order Logic [1975], p.46)
	A reaction: This is the problem now discussed in the recent book 'Absolute Generality', of whether one can quantify without specifying a fixed or limited domain.

5. Theory of Logic / K. Features of Logics / 4. Completeness

10834	Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
	Full Idea: A weak completeness theorem shows that a sentence is provable whenever it is valid; a strong theorem, that a sentence is provable from a set of sentences whenever it is a logical consequence of the set.
	From: George Boolos (On Second-Order Logic [1975], p.52)
	A reaction: So the weak version says |- φ → |= φ, and the strong versions says Γ |- φ → Γ |= φ. Presumably it is stronger if it can specify the source of the inference.

5. Theory of Logic / K. Features of Logics / 6. Compactness

13841	Why should compactness be definitive of logic? [Boolos, by Hacking]
	Full Idea: Boolos asks why on earth compactness, whatever its virtues, should be definitive of logic itself.
	From: report of George Boolos (On Second-Order Logic [1975]) by Ian Hacking - What is Logic? §13

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order

10833	Many concepts can only be expressed by second-order logic [Boolos]
	Full Idea: The notions of infinity and countability can be characterized by second-order sentences, though not by first-order sentences (as compactness and Skolem-Löwenheim theorems show), .. as well as well-ordering, progression, ancestral and identity.
	From: George Boolos (On Second-Order Logic [1975], p.48)

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).

22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics

9261	The 'Ethics' is disappointing, because it fails to try to justify our duties [Prichard]
	Full Idea: Reading the 'Ethics' is so disappointing, because Aristotle does not try to convince us that we really ought to do what our non-reflective consciousness has hitherto believed we ought to do.
	From: H.A. Prichard (Does moral phil rest on a mistake? [1912])
	A reaction: Aristotle didn't speak the language of 'duty' (see Idea 2172), but he could work it into his account if Prichard asked nicely. I take the truly virtuous person to be, above all, a wonderful citizen. Duties are contractual; good deeds flow from virtue.

23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism

9262	The mistake is to think we can prove what can only be seen directly in moral thinking [Prichard]
	Full Idea: Moral Philosophy rests on the mistake of supposing the possibility of proving what can only be apprehended directly by an act of moral thinking.
	From: H.A. Prichard (Does moral phil rest on a mistake? [1912])
	A reaction: This is a beginning of the rebellion against the Enlightenment Project in ethics, which is why Prichard has become popular. At bottom he is offering intuition ('direct moral thinking'), which is a frustratingly thin concept.

23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique

9260	Virtues won't generate an obligation, so it isn't a basis for morality [Prichard]
	Full Idea: It is untrue to urge that, since courage is a virtue, we ought to act courageously. We feel an obligation to act, but not from a certain desire. The action is done from obligation, so isn't an act of courage. ..In fact, virtue is no basis for morality.
	From: H.A. Prichard (Does moral phil rest on a mistake? [1912])
	A reaction: One of the few interesting and direct attacks on virtue theory, before its modern revival. Prichard urges a perception of what is valuable (or good) as the basis for obligation and right action. He is right that values come first, in virtue and elsewhere.

23. Ethics / D. Deontological Ethics / 2. Duty

9259	We feel obligations to overcome our own failings, and these are not relations to other people [Prichard]
	Full Idea: The relation involved in an obligation need not be a relation to another at all. Thus we should admit that there is an obligation to overcome our natural timidity or greediness, and this involves no relations to others.
	From: H.A. Prichard (Does moral phil rest on a mistake? [1912])
	A reaction: An interesting un-Aristotelian and individualistic view of virtue. Why would we want to rid ourselves of timidity or greediness? Either it is self-interested, or we wish to be better citizens. See Richard Taylor on duty.

23. Ethics / E. Utilitarianism / 1. Utilitarianism

9258	If pain were instrinsically wrong, it would be immoral to inflict it on ourselves [Prichard]
	Full Idea: If the badness of pain were the reason why we ought not to inflict pain on another, it would equally be a reason why we ought not to inflict pain on ourselves; yet, though we would call such behaviour foolish, we wouldn't think it wrong.
	From: H.A. Prichard (Does moral phil rest on a mistake? [1912], n4)
	A reaction: A very nice point. Note that it will equally well apply to 'benefit' or 'preferences', or any other ideal which utilitarians set out to maximise. It may not be bad to hurt yourself, but it might still be bad to harm yourself.