16 ideas
| 15395 | Give up objects necessitating truths, and say their natures cause the truths? [Cameron] |
| Full Idea: We could abandon the view that truthmakers necessitate the truth of that which makes them true, and say that an object makes a truth when its intrinsic nature suffices for that truth. The object would have a different intrinsic nature if the truth failed. | |
| From: Ross P. Cameron (Intrinsic and Extrinsic Properties [2009], 'Truthmakers') | |
| A reaction: [He cites Josh Parsons 1999, 2005 for this] This approach seems closely related to Kit Fine's proposal that necessities arise from the natures of things. It sounds to me as if an object with that intrinsic nature would necessitate that truth. |
| 15394 | Truthmaker requires a commitment to tropes or states of affairs, for contingent truths [Cameron] |
| Full Idea: The most popular view is that an object is a truthmaker if the object couldn't exist and the truth be false. But contingent predications are also held to need truthmakers. Socrates is not necessarily snub-nosed, so a trope or state of affairs is needed. | |
| From: Ross P. Cameron (Intrinsic and Extrinsic Properties [2009], 'Truthmakers') | |
| A reaction: Cameron calls this 'some heavy ontological commitments'. If snub-nosedness is necessitated by the trope of 'being snub-nosed', what is the truthmaker for Socrates having that trope? |
| 10580 | 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. |
| 10579 | 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. |
| 10577 | 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) |
| 10578 | 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) |
| 15401 | Essentialists say intrinsic properties arise from what the thing is, irrespective of surroundings [Cameron] |
| Full Idea: The essentialist approach would be to say that an intrinsic property is one such that it is no part of what it is to instantiate that property that the bearer stands in some relation to its surroundings. | |
| From: Ross P. Cameron (Intrinsic and Extrinsic Properties [2009], 'Analysis') | |
| A reaction: This is offered as an alternative to the David Lewis account in terms of duplicates across possible worlds. You will have gathered by now, if you have spent days poring over my stuff, that I favour the essentialist approach. |
| 15393 | An object's intrinsic properties are had in virtue of how it is, independently [Cameron] |
| Full Idea: Intrinsic properties are those that an object has solely in virtue of how it is, independently of its surroundings. | |
| From: Ross P. Cameron (Intrinsic and Extrinsic Properties [2009], 'Intro') | |
| A reaction: Better not mention quantum mechanics and fields if you want to talk of objects being independent of their surroundings. Am I 'independent' of gravity, or is gravity 'independent' of me? |
| 472 | No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus] |
| Full Idea: No existing things would be clear to anyone, either in themselves or in their relationship to one another, unless there existed Number and its essence. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B11), quoted by John Stobaeus - Anthology 1.03.8 |
| 15396 | Most criteria for identity over time seem to leave two later objects identical to the earlier one [Cameron] |
| Full Idea: Criteria for identity across times have proven hard to give. Whatever criteria we lay down, it seems that there are possible situations in which two later objects bear the relevant relation to one earlier object, though only one of them can be identical. | |
| From: Ross P. Cameron (Intrinsic and Extrinsic Properties [2009], 'Personal') | |
| A reaction: We only have to think of twins, amoebae that fission, and the Ship of Theseus. We seem to end up inventing a dubious criterion in order to break the tie. |
| 1518 | Everything must involve numbers, or it couldn't be thought about or known [Philolaus] |
| Full Idea: Everything which is known has number, because otherwise it is impossible for anything to be the object of thought or knowledge. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B04), quoted by John Stobaeus - Anthology 1.21.7b |
| 1519 | Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus] |
| Full Idea: It would have been impossible for the dissimilar and incompatible sources to have been made into an orderly universe unless harmony had been present in some form or other. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B06), quoted by John Stobaeus - Anthology 1.21.7d |
| 473 | There is no falsehood in harmony and number, only in irrational things [Philolaus] |
| Full Idea: The nature of number and harmony admits of no falsehood; for this is unrelated to them. Falsehood and envy belong to the nature of the Unlimited and the Unintelligent and the Irrational. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B11), quoted by (who?) - where? |
| 469 | Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus] |
| Full Idea: Since it is plain that existing things are neither wholly from the Limiting, nor wholly from the Unlimited, clearly the cosmos and its contents were fitted together from both the Limiting and the Unlimited. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B02), quoted by John Stobaeus - Anthology 1.21.7a |
| 476 | Self-created numbers make the universe stable [Philolaus] |
| Full Idea: Number is the ruling and self-created bond which maintains the everlasting stability of the contents of the universe. | |
| From: Philolaus (On the Cosmos (lost) [c.435 BCE], B23), quoted by (who?) - where? |
| 1787 | Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius] |
| Full Idea: Philolaus was the first person to affirm that the earth moves in a circle. | |
| From: report of Philolaus (On the Cosmos (lost) [c.435 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 08.Ph.3 |