24 ideas
| 9208 | Philosophers with a new concept are like children with a new toy [Fine,K] |
| Full Idea: Philosophers with a new concept are like children with a new toy; their world shrinks to one in which it takes centre stage. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p.10) | |
| A reaction: A wonderfully accurate observation, I'm afraid. You can trace the entire history of the subject as a wave of obsessions with exciting new ideas. Fine is referring to a posteriori necessities and possible worlds. |
| 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. |
| 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. |
| 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. |
| 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. |
| 9210 | Possible objects are abstract; actual concrete objects are possible; so abstract/concrete are compatible [Fine,K] |
| Full Idea: If it is in the nature of a possible object to be abstract, this is presumably a property it has in any possible circumstance in which it is actual. If it is actual it is also concrete. So the property of being abstract and concrete are not incompatible. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p.14) | |
| A reaction: A rather startling and powerful idea. What of the definition of an abstract object as one which is not in space-time, and lacks causal powers? Could it be that abstraction is a projection of our minds, onto concepts or objects? |
| 9211 | A non-standard realism, with no privileged standpoint, might challenge its absoluteness or coherence [Fine,K] |
| Full Idea: By challenging the assumption that reality is 'absolute' (not relative to a standpoint), or that reality is 'coherent' (it is of a piece, from one standpoint), one accepts worldly facts without a privilege standpoint. I call this 'non-standard' realism. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p.15) | |
| A reaction: Fine's essay 'Tense and Reality' explores his proposal. I'm not drawn to either of his challenges. I have always taken as articles of faith that there could be a God's Eye view of all of reality, and that everything coheres, independent of our view. |
| 9202 | Objects, as well as sentences, can have logical form [Fine,K] |
| Full Idea: We normally think of logical form as exclusively an attribute of sentences; however, the notion may also be taken to have application to objects. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p. 3) | |
| A reaction: A striking proposal which seems intuitively right. If one said that objects have 'powers', one might subsume abstract and physical objects under a single account. |
| 9206 | We must distinguish between the identity or essence of an object, and its necessary features [Fine,K] |
| Full Idea: The failure to distinguish between the identity or essence of an object and its necessary features is an instance of what we may call 'modal mania'. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p. 9) | |
| A reaction: He blames Kripke's work for modal mania, a reaction to Quine's 'contempt' for modal notions. I don't actually understand Fine's remark (yet), but it strikes me as incredibly important! Explanations by email, please. |
| 9205 | The three basic types of necessity are metaphysical, natural and normative [Fine,K] |
| Full Idea: There are three basic forms of necessity - the metaphysical (sourced in the identity of objects); natural necessity (in the 'fabric' of the universe); and normative necessity (in the realm of norms and values). | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p. 7) | |
| A reaction: Earlier he has allowed, as less 'basic', logical necessity (in logical forms), and analytic necessity (in meaning). Fine insists that the three kinds should be kept separate (so no metaphysical necessities about nature). I resent this. |
| 9209 | Metaphysical necessity may be 'whatever the circumstance', or 'regardless of circumstances' [Fine,K] |
| Full Idea: There are two fundamental ways in which a property may be metaphysically necessary: it may be a worldly necessity, true whatever the circumstances; or it may be a transcendent necessity, true regardless of the circumstances. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p.10) | |
| A reaction: [See Fine's 'Necessity and Non-Existence' for further details] The distinction seems to be that the first sort needs some circumstances (e.g. a physical world?), whereas the second sort doesn't (logical relations?). He also applies it to existence. |
| 9200 | Empiricists suspect modal notions: either it happens or it doesn't; it is just regularities. [Fine,K] |
| Full Idea: Empiricists have always been suspicious of modal notions: the world is an on-or-off matter - either something happens or it does not. ..Empiricists, in so far as they have been able to make sense of modality, have tended to see it as a form of regularity. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p. 1) | |
| A reaction: Fine is discussing the two extreme views of Quine and Lewis. It is one thing to have views about what is possible, and another to include possibilities 'in your ontology'. Our imagination competes with our extrapolations from actuality. |
| 6230 | If the soul were a tabula rasa, with no innate ideas, there could be no moral goodness or justice [Cudworth] |
| Full Idea: The soul is not a mere rasa tabula, a naked and passive thing, with no innate furniture of its own, nor any thing in it, but what was impressed upon it without; for then there could not possibly be any such thing as moral good and evil, just and unjust. | |
| From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Bk IV Ch 6.4) | |
| A reaction: He goes on to quote Hobbes saying there is no good in objects themselves. I don't see why we must have an innate moral capacity, provided that we have a capacity to make judgements. |
| 6228 | Senses cannot judge one another, so what judges senses cannot be a sense, but must be superior [Cudworth] |
| Full Idea: The sight cannot judge of sounds, nor the hearing of light and colours; wherefore that which judges of all the senses and their several objects, cannot be itself any sense, but something of a superior nature. | |
| From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.VI.1) | |
| A reaction: How nice to find a seventeenth century English writer rebelling against empiricism! |
| 6229 | Sense is fixed in the material form, and so can't grasp abstract universals [Cudworth] |
| Full Idea: Sense which lies flat and grovelling in the individuals, and is stupidly fixed in the material form, is not able to rise up or ascend to an abstract universal notion. | |
| From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.III.III.2) | |
| A reaction: This still strikes me as being one of the biggest problems with reductive physicalism, that a lump of meat in your head can grasp abstractions (whatever they are) and universal concepts. Personally I am a physicalist, but it is weird. |
| 9207 | If sentence content is all worlds where it is true, all necessary truths have the same content! [Fine,K] |
| Full Idea: The content of a sentence is often identified with the set of possible worlds in which it is true, where the worlds are metaphysically possible. But this has the awkward consequence that all metaphysically necessary truths will have the same content. | |
| From: Kit Fine (Intro to 'Modality and Tense' [2005], p.10) | |
| A reaction: I've never understood how the content of a sentence could be a vast set of worlds, so I am delighted to see this proposal be torpedoed. That doesn't mean that truth conditions across possible worlds is not a promising notion. |
| 6227 | Keeping promises and contracts is an obligation of natural justice [Cudworth] |
| Full Idea: To keep faith and perform covenants is that which natural justice obligeth to absolutely. | |
| From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.4) | |
| A reaction: A nice example of an absolute moral intuition, but one which can clearly be challenged. Covenants (contracts) wouldn't work unless everyone showed intense commitment to keeping them, even beyond the grave, and we all benefit from good contracts. |
| 6225 | Obligation to obey all positive laws is older than all laws [Cudworth] |
| Full Idea: Obligation to obey all positive laws is older than all laws. | |
| From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.3) | |
| A reaction: Clearly villains can pass wicked laws, so there can't be an obligation to obey all laws (even if they are 'positive', which seems to beg the question). Nevertheless this is a good reason why laws cannot be the grounding of morality. |
| 6224 | An omnipotent will cannot make two things equal or alike if they aren't [Cudworth] |
| Full Idea: Omnipotent will cannot make things like or equal one to another, without the natures of likeness and equality. | |
| From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.I) | |
| A reaction: This is one of the many classic 'paradoxes of omnipotence'. The best strategy is to define omnipotence as 'being able to do everything which it is possible to do'. Anything beyond that is inviting paradoxical disaster. |
| 6223 | If the will and pleasure of God controls justice, then anything wicked or unjust would become good if God commanded it [Cudworth] |
| Full Idea: If the arbitrary will and pleasure of God is the first and only rule of good and justice, it follows that nothing can be so grossly wicked or unjust but if it were commanded by this omnipotent Deity, it must forthwith become holy, just and righteous. | |
| From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.I.I.5) | |
| A reaction: This is the strong (Platonic) answer to the Euthyphro Question (Idea 336). One answer is that God would not command in such a way - but why not? We may say that God and goodness merge into one, but we are interested in ultimate authority. |
| 6226 | The requirement that God must be obeyed must precede any authority of God's commands [Cudworth] |
| Full Idea: If it were not morally good and just in its own nature before any positive command of God, that God should be obeyed by his creatures, the bare will of God himself could not beget any obligation upon anyone. | |
| From: Ralph Cudworth (On Eternal and Immutable Morality [1688], Ch.II.3) | |
| A reaction: This strikes me as a self-evident truth, and a big problem for anyone who wants to make God the source of morality. You don't have to accept anyone's authority just because they are powerful or clever (though they do bestow a certain natural authority!). |