Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'In Defence of Three-Dimensionalism' and 'Reflections on my Critics'

unexpand these ideas     |    start again     |     specify just one area for these texts


12 ideas

3. Truth / H. Deflationary Truth / 2. Deflationary Truth
'Truth' may only apply within a theory [Kuhn]
     Full Idea: 'Truth' may, like 'proof', be a term with only intra-theoretic applications.
     From: Thomas S. Kuhn (Reflections on my Critics [1970], §5)
     A reaction: I think we can blame Tarski (via Quine, Kuhn's teacher) for this one. I take it to be an utter failure to grasp the meaning of the word 'truth' (and sneakily substituting 'satisfaction' for it). For a start, we have to compare theories on some basis.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
     Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10)
     A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
     Full Idea: Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
     A reaction: See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
     Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01)
We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
     Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori.
     From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02)
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
3-D says things are stretched in space but not in time, and entire at a time but not at a location [Fine,K]
     Full Idea: Three-dimensionalist think a thing is somehow 'stretched out' through its location at a given time though not through the period during which it exists, and it is present in its entirety at a moment when it exists though not at a position of its location.
     From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.1)
     A reaction: This definition is designed to set up Fine's defence of the 3-D view, by showing that various dubious asymmetries show up if you do not respect the distinctions offered by the 3-D view.
Genuine motion, rather than variation of position, requires the 'entire presence' of the object [Fine,K]
     Full Idea: In order to have genuine motion, rather than mere variation in position, it is necessary that the object should be 'entirely present' at each moment of the change. Thus without entire presence, or existence, genuine motion will not be possible.
     From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.6)
     A reaction: See Idea 4786 for a rival view of motion. Of course, who says we have to have Kit Fine's 'genuine' motion, if some sort of ersatz motion still gets you to work in the morning?
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
4-D says things are stretched in space and in time, and not entire at a time or at a location [Fine,K]
     Full Idea: Four-dimensionalists have thought that a material thing is as equally 'stretched out' in time as it is in space, and that there is no special way in which it is entirely present at a moment rather than at a position.
     From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.1)
     A reaction: Compare his definition of 3-D in Idea 12295. The 4-D is contrary to our normal way of thinking. Since I don't think the future exists, I presume that if I am a 4-D object then I have to say that I don't yet exist, and I disapprove of such talk.
You can ask when the wedding was, but not (usually) when the bride was [Fine,K, by Simons]
     Full Idea: Fine says it is acceptable to ask when a wedding was and where it was, and it is acceptable to ask or state where the bride was (at a certain time), but not when she was.
     From: report of Kit Fine (In Defence of Three-Dimensionalism [2006], p.18) by Peter Simons - Modes of Extension: comment on Fine p.18
     A reaction: This is aimed at three-dimensionalists who seem to think that a bride is a prolonged event, just as a wedding is. Fine is, interestingly, invoking ordinary language. When did the wedding start and end? When was the bride's birth and death?
9. Objects / E. Objects over Time / 5. Temporal Parts
Three-dimensionalist can accept temporal parts, as things enduring only for an instant [Fine,K]
     Full Idea: Even if one is a three-dimensionalist, one might affirm the existence of temporal parts, on the grounds that everything merely endures for an instant.
     From: Kit Fine (In Defence of Three-Dimensionalism [2006], p.2)
     A reaction: This seems an important point, as belief in temporal parts is normally equated with four-dimensionalism (see Idea 12296). The idea is that a thing might be 'entirely present' at each instant, only to be replaced by a simulacrum.
14. Science / B. Scientific Theories / 1. Scientific Theory
Kuhn came to accept that all scientists agree on a particular set of values [Kuhn, by Bird]
     Full Idea: Kuhn later came to accept that there are five values to which scientists in all paradigms adhere: accuracy; consistency with accepted theories; broad scope; simplicity; and fruitfulness.
     From: report of Thomas S. Kuhn (Reflections on my Critics [1970]) by Alexander Bird - Philosophy of Science Ch.8
     A reaction: To shake off the relativism for which Kuhn is notorious, we should begin by asking the question WHY scientists favoured these particular values, rather than (say) bizarreness, consistency with Lewis Carroll, or alliteration. (They are epistemic virtues).
14. Science / B. Scientific Theories / 5. Commensurability
In theory change, words shift their natural reference, so the theories are incommensurable [Kuhn]
     Full Idea: In transitions between theories words change their meanings or applicability. Though most of the signs are used before and after a revolution - force, mass, cell - the ways they attach to nature has changed. Successive theories are thus incommensurable.
     From: Thomas S. Kuhn (Reflections on my Critics [1970], §6)
     A reaction: A very nice statement of the view, from the horse's mouth. A great deal of recent philosophy has been implicitly concerned with meeting Kuhn's challenge, by providing an account of reference that doesn't have such problems.