Combining Texts

All the ideas for 'The Gettier Problem', 'Things and Their Parts' and 'Carnap and Logical Truth'

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18 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 / 1. Overview of Logic

13010	In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine]
	Full Idea: Quine ends up with the logic that is maximally justified by experience, ...but a large number of the core principles of logic will have to be used to select the logic that is maximally justified by experience.
	From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Paul Boghossian - Knowledge of Logic p.233
	A reaction: In order to grasp some core principles of logic, you will probably need a certain amount of experience. I take logic to be an abstracted feature of reality (unless it is extended by pure fictions). Some basic logic may be hard wired in us.

5. Theory of Logic / A. Overview of Logic / 6. Classical Logic

9002	Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine]
	Full Idea: Elementary logic, as commonly systematized nowadays, comprises truth-function theory (involving 'or', 'and', 'not' etc.), quantifiers (and their variables), and identity theory ('='). In addition, set theory requires classes among values of variables.
	From: Willard Quine (Carnap and Logical Truth [1954], II)
	A reaction: Quine is famous for trying to squeeze properties out of the picture, which would then block higher-order logics (which quantify over properties). Quine's list gives a nice programme for a student of the philosophy of logic to understand.

5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence

13681	Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider]
	Full Idea: Quine's view of logical consequence is that it is when there is no way of uniformly substituting nonlogical expressions in the premises and consequences so that the premises all remain true but the consequence now becomes false.
	From: report of Willard Quine (Carnap and Logical Truth [1954], p.103) by Theodore Sider - Logic for Philosophy 1.5
	A reaction: One might just say that the consequence holds if you insert consistent variables for the nonlogical terms, which looks like Aristotle's view of the matter.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

13829	If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine]
	Full Idea: Quine said a logical truth is a truth in which only logical constants occur essentially, ...but then a fruitful definition of 'logical constant' is called for.
	From: comment on Willard Quine (Carnap and Logical Truth [1954]) by Ian Hacking - What is Logic? §02

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes

9003	Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine]
	Full Idea: Unlike elementary logic, the truths of set theory are not obvious. Set theory was straining at the leash of intuition ever since Cantor discovered higher infinites; and with the added impetus of the paradoxes of set theory the leash snapped.
	From: Willard Quine (Carnap and Logical Truth [1954], II)
	A reaction: This problem seems to have forced Quine into platonism about sets, because he felt they were essential for mathematics and science, but couldn't be constructed with precision. So they must be real, but we don't quite understand them.

6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique

9004	If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine]
	Full Idea: We might say that set theory is not really logic, but a branch of mathematics. This would deprive 'includes' of the status of a logical word. Frege's derivation of arithmetic would then cease to count as a derivation from logic: for he used set theory.
	From: Willard Quine (Carnap and Logical Truth [1954], II)
	A reaction: Quine has been making the point that higher infinities and the paradoxes undermine the status of set theory as logic, but he decides to continue thinking of set theory as logic. Critics of logicism frequently ask whether the reduction is to logic.

8. Modes of Existence / E. Nominalism / 1. Nominalism / b. Nominalism about universals

9006	Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine]
	Full Idea: One's hypothesis as to there being universals is at bottom just as arbitrary or pragmatic a matter as one's adoption of a new brand of set theory or even a new system of bookkeeping.
	From: Willard Quine (Carnap and Logical Truth [1954], x)
	A reaction: This spells out clearly the strongly pragmatist vein in Quine's thinking.

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).

10. Modality / A. Necessity / 6. Logical Necessity

9001	Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine]
	Full Idea: When Kant's arithmetical examples of a priori synthetic judgements were sweepingly disqualified by Frege's reduction of arithmetic to logic, attention moved to the less tendentious and logically prior question 'How is logical certainty possible?'
	From: Willard Quine (Carnap and Logical Truth [1954], I)
	A reaction: A nice summary of the story so far, from someone who should know. This still leaves the question open of whether any synthetic truths can be derived from the logical certainties which are available.

12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention

9005	Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine]
	Full Idea: In trying to make sense of the role of convention in a priori knowledge, the very distinction between a priori and empirical begins to waver and dissolve.
	From: Willard Quine (Carnap and Logical Truth [1954], VI)
	A reaction: This is the next stage in the argument after Wittgenstein presents the apriori as nothing more than what arises from truth tables. The rationalists react by taking us back to the original 'natural light of reason' view. Then we go round again...

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / b. Gettier problem

19699	A Gettier case is a belief which is true, and its fallible justification involves some luck [Hetherington]
	Full Idea: A Gettier case contains a belief which is true and well justified without being knowledge. Its justificatory support is also fallible, ...and there is considerable luck in how the belief combnes being true with being justified.
	From: Stephen Hetherington (The Gettier Problem [2011], 5)
	A reaction: This makes luck the key factor. 'Luck' is a rather vague concept, and so the sort of luck involved must first be spelled out. Or the varieties of luck that can produce this outcome.