22 ideas
| 18996 | A statement S is 'partly true' if it has some wholly true parts [Yablo] |
| Full Idea: A statement S is 'partly true' insofar as it has wholly true parts: wholly true implications whose subject matter is included in that of S. | |
| From: Stephen Yablo (Aboutness [2014], 01.6) | |
| A reaction: He suggests that if we have rival theories, we agree that it is one or the other. And 'we may have pork for dinner, or human flesh' is partly true. |
| 19006 | An 'enthymeme' is an argument with an indispensable unstated assumption [Yablo] |
| Full Idea: An 'enthymeme' is a deductive argument with an unstated assumption that must be true for the premises to lead to the conclusion. | |
| From: Stephen Yablo (Aboutness [2014], 11.1) |
| 17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
| Full Idea: One feature of the Axiom of Choice that troubled many mathematicians was the so-called Banach-Tarski paradox: using the Axiom, a sphere can be decomposed into finitely many parts and those parts reassembled into two spheres the same size as the original. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) | |
| A reaction: (The key is that the parts are non-measurable). To an outsider it is puzzling that the Axiom has been universally accepted, even though it produces such a result. Someone can explain that, I'm sure. |
| 18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
| Full Idea: The principle of Supplementation says that y is properly part of x, only if a z exists that 'makes up the difference' between them. [note: that is, z is disjoint from y and sums with y to form x] | |
| From: Stephen Yablo (Aboutness [2014], 03.2) |
| 17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
| Full Idea: If-thenism denies that mathematics is in the business of discovering truths about abstracta. ...[their opponents] obviously don't regard any starting point, even a consistent one, as equally worthy of investigation. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.3) | |
| A reaction: I have some sympathy with if-thenism, in that you can obviously study the implications of any 'if' you like, but deep down I agree with the critics. |
| 19001 | 'Pegasus doesn't exist' is false without Pegasus, yet the absence of Pegasus is its truthmaker [Yablo] |
| Full Idea: 'Pegasus does not exist' has a paradoxical, self-undermining flavour. On the one hand, the empty name makes it untrue. But now, why is the name empty? Because Pegasus does not exist. 'Pegasus does not exist' is untrue because Pegasus does not exist. | |
| From: Stephen Yablo (Aboutness [2014], 05.7 n20) | |
| A reaction: Beautiful! This is Yablo's reward for continuing to ask 'why?' after everyone else has stopped in bewilderment at the tricky phenomenon. |
| 17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
| Full Idea: At the end of the nineteenth century there was a renewed emphasis on rigor, the central tool of which was axiomatization, along the lines of Hilbert's axioms for geometry and Dedekind's axioms for real numbers. | |
| From: Penelope Maddy (Defending the Axioms [2011], 1.3) |
| 17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
| Full Idea: The fact that two apparently fruitful mathematical themes turn out to coincide makes it all the more likely that they're tracking a genuine strain of mathematical depth. | |
| From: Penelope Maddy (Defending the Axioms [2011], 5.3ii) |
| 17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
| Full Idea: One form of the Continuum Hypothesis is the claim that every infinite set of reals is either countable or of the same size as the full set of reals. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.4 n40) |
| 17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
| Full Idea: Our set-theoretic methods track the underlying contours of mathematical depth. ...What sets are, most fundamentally, is markers for these contours ...they are maximally effective trackers of certain trains of mathematical fruitfulness. | |
| From: Penelope Maddy (Defending the Axioms [2011], 3.4) | |
| A reaction: This seems to make it more like a map of mathematics than the actual essence of mathematics. |
| 19002 | A nominalist can assert statements about mathematical objects, as being partly true [Yablo] |
| Full Idea: If I am a nominalist non-Platonist, I think it is false that 'there are primes over 10', but I want to be able to say it like everyone else. I argue that this because the statement has a part that I do believe, a part that remains interestingly true. | |
| From: Stephen Yablo (Aboutness [2014], 05.8) | |
| A reaction: This is obviously a key motivation for Yablo's book, as it reinforces his fictional view of abstract objects, but aims to capture the phenomena, by investigating what such sentences are 'about'. Admirable. |
| 17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
| Full Idea: Ordinary perceptual cognition is most likely involved in our grasp of elementary arithmetic, but ...this connection to the physical world has long since been idealized away in the infinitary structures of contemporary pure mathematics. | |
| From: Penelope Maddy (Defending the Axioms [2011], 2.3) | |
| A reaction: Despite this, Maddy's quest is for a 'naturalistic' account of mathematics. She ends up defending 'objectivity' (and invoking Tyler Burge), rather than even modest realism. You can't 'idealise away' the counting of objects. I blame Cantor. |
| 18998 | Parthood lacks the restriction of kind which most relations have [Yablo] |
| Full Idea: Most relations obtain only between certain kinds of thing. To learn that x is a part of y, however, tells you nothing about x and y taken individually. | |
| From: Stephen Yablo (Aboutness [2014], 03.2) | |
| A reaction: Too sweeping. To be a part of crowd you have to be a person. To be part of the sea you have to be wet. It might depend on whether composition is unrestricted. |
| 19004 | Gettier says you don't know if you are confused about how it is true [Yablo] |
| Full Idea: We know from Gettier that if you are right to regard Q as true, but you are sufficiently confused about HOW it is true - about how things stand with respect to its subject matter - then you don't know that Q. | |
| From: Stephen Yablo (Aboutness [2014], 07.4) | |
| A reaction: I'm inclined to approach Gettier by focusing on the propositions being expressed, where his cases tend to focus on the literal wording of the sentences. What did the utterer mean by the sentences - not what did they appear to say. |
| 19007 | A theory need not be true to be good; it should just be true about its physical aspects [Yablo] |
| Full Idea: A physical theory need not be true to be good, Field has argued, and I agree. All we ask of it truth-wise is that its physical implications should be true, or, in my version, that it should be true about the physical. | |
| From: Stephen Yablo (Aboutness [2014], 12.5) | |
| A reaction: Yablo is, of course, writing a book here about the concept of 'about'. This seems persuasive. The internal terminology of the theory isn't committed to anything - it is only at its physical periphery (Quine) that the ontology matters. |
| 18993 | If sentences point to different evidence, they must have different subject-matter [Yablo] |
| Full Idea: 'All crows are black' cannot say quite the same as 'All non-black things are non-crows', for the two are confirmed by different evidence. Subject matter looks to be the distinguishing feature. One is about crows, the other not. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: You might reply that they are confirmed by the same evidence (but only in its unobtainable totality). The point, I think, is that the sentences invite you to start your search in different places. |
| 19003 | Most people say nonblack nonravens do confirm 'all ravens are black', but only a tiny bit [Yablo] |
| Full Idea: The standard response to the raven paradox is to say that a nonblack nonraven does confirm that all ravens are black. But it confirms it just the teeniest little bit - not as much as a black raven does. | |
| From: Stephen Yablo (Aboutness [2014], 06.5) | |
| A reaction: It depends on the proportion between the relevant items. How do you confirm 'all the large animals in this zoo are mammals'? Check for size every animal which is obviously not a mammal? |
| 18992 | Sentence-meaning is the truth-conditions - plus factors responsible for them [Yablo] |
| Full Idea: A sentence's meaning is to do with its truth-value in various possible scenarios, AND the factors responsible for that truth-value. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: The thesis of his book, which I welcome. I'm increasingly struck by the way in which much modern philosophy settles for a theory being complete, when actually further explanation is possible. Exhibit A is functional explanations. Why that function? |
| 18994 | The content of an assertion can be quite different from compositional content [Yablo] |
| Full Idea: Assertive content - what a sentence is heard as saying - can be at quite a distance from compositional content. | |
| From: Stephen Yablo (Aboutness [2014], Intro) | |
| A reaction: This is the obvious reason why semantics cannot be entirely compositional, since there is nearly always a contextual component which then has to be added. In the case of irony, the compositional content is entirely reversed. |
| 18997 | Truth-conditions as subject-matter has problems of relevance, short cut, and reversal [Yablo] |
| Full Idea: If the subject-matter of S is how it is true, we get three unfortunate results: S has truth-value in worlds where its subject-matter draws a blank; learning what S is about tells you its truth-value; negating S changes what it's about. | |
| From: Stephen Yablo (Aboutness [2014], 02.8) | |
| A reaction: Together these make fairly devastating objections to the truth-conditions (in possible worlds) theory of meaning. The first-objection concerns when S is false |
| 19005 | Not-A is too strong to just erase an improper assertion, because it actually reverses A [Yablo] |
| Full Idea: The idea that negation is, or can be, a cancellation device raises an interesting question. What does one do to wipe the slate clean after an improper assertion? Not-A is too strong; it reverses our stand on A rather than nullifying it. | |
| From: Stephen Yablo (Aboutness [2014], 09.8) | |
| A reaction: [He is discussing a remark of Strawson 1952] It seems that 'not' has two meanings or uses: a weak use of 'nullifying' an assertion, and a strong use of 'reversing' an assertion. One could do both: 'that's not right; in fact, it's just the opposite'. |
| 22237 | The Greeks had a single word meaning both 'beautiful' and 'good' [Pormann] |
| Full Idea: The later Greeks coined the term 'kalokagathia' for the fact of being both beautiful [kalos] and good [agathos], thus linking moral and physical health. | |
| From: Peter E. Pormann (Medical Conceptions of Health pre-Renaissance [2019], p.44) | |
| A reaction: In their literature good people are often handsome, and bad people ugly. Socrates was famous for being an exception. |