27 ideas
| 13430 | Infinity: there is an infinity of distinguishable individuals [Ramsey] |
| Full Idea: The Axiom of Infinity means that there are an infinity of distinguishable individuals, which is an empirical proposition. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §5) | |
| A reaction: The Axiom sounds absurd, as a part of a logical system, but Ramsey ends up defending it. Logical tautologies, which seem to be obviously true, are rendered absurd if they don't refer to any objects, and some of them refer to infinities of objects. |
| 13428 | Reducibility: to every non-elementary function there is an equivalent elementary function [Ramsey] |
| Full Idea: The Axiom of Reducibility asserted that to every non-elementary function there is an equivalent elementary function [note: two functions are equivalent when the same arguments render them both true or both false]. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §2) | |
| A reaction: Ramsey in the business of showing that this axiom from Russell and Whitehead is not needed. He says that the axiom seems to be needed for induction and for Dedekind cuts. Since the cuts rest on it, and it is weak, Ramsey says it must go. |
| 13427 | Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey] |
| Full Idea: In 'a = b' either 'a' and 'b' are names of the same thing, in which case the proposition says nothing, or of different things, in which case it is absurd. In neither case is it an assertion of a fact; it only asserts when a or b are descriptions. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1) | |
| A reaction: This is essentially Frege's problem with Hesperus and Phosphorus. How can identities be informative? So 2+2=4 is extensionally vacuous, but informative because they are different descriptions. |
| 13334 | Contradictions are either purely logical or mathematical, or they involved thought and language [Ramsey] |
| Full Idea: Group A consists of contradictions which would occur in a logical or mathematical system, involving terms such as class or number. Group B contradictions are not purely logical, and contain some reference to thought, language or symbolism. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], p.171), quoted by Graham Priest - The Structure of Paradoxes of Self-Reference 1 | |
| A reaction: This has become the orthodox division of all paradoxes, but the division is challenged by Priest (Idea 13373). He suggests that we now realise (post-Tarski?) that language is more involved in logic and mathematics than we thought. |
| 13426 | Formalists neglect content, but the logicists have focused on generalizations, and neglected form [Ramsey] |
| Full Idea: The formalists neglected the content altogether and made mathematics meaningless, but the logicians neglected the form and made mathematics consist of any true generalisations; only by taking account of both sides can we obtain an adequate theory. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1) | |
| A reaction: He says mathematics is 'tautological generalizations'. It is a criticism of modern structuralism that it overemphasises form, and fails to pay attention to the meaning of the concepts which stand at the 'nodes' of the structure. |
| 13425 | Formalism is hopeless, because it focuses on propositions and ignores concepts [Ramsey] |
| Full Idea: The hopelessly inadequate formalist theory is, to some extent, the result of considering only the propositions of mathematics and neglecting the analysis of its concepts. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], §1) | |
| A reaction: You'll have to read Ramsey to see how this thought pans out, but it at least gives a pointer to how to go about addressing the question. |
| 11897 | A principle of individuation may pinpoint identity and distinctness, now and over time [Mackie,P] |
| Full Idea: One view of a principle of individuation is what is called a 'criterion of identity', determining answers to questions about identity and distinctness at a time and over time - a principle of distinction and persistence. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 8.2) | |
| A reaction: Since the term 'Prime Minister' might do this job, presumably there could be a de dicto as well as a de re version of individuation. The distinctness consists of chairing cabinet meetings, rather than being of a particular sex. |
| 11898 | Individuation may include counterfactual possibilities, as well as identity and persistence [Mackie,P] |
| Full Idea: A second view of the principle of individuation includes criteria of distinction and persistence, but also determines the counterfactual possibilities for a thing. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 8.5) | |
| A reaction: It would be a pretty comprehensive individuation which defined all the counterfactual truths about a thing, as well as its actual truths. This is where powers come in. We need to know a thing's powers, but not how they cash out counterfactually. |
| 11883 | A haecceity is the essential, simple, unanalysable property of being-this-thing [Mackie,P] |
| Full Idea: Socrates can be assigned a haecceity: an essential property of 'being Socrates' which (unlike the property of 'being identical with Socrates') may be regarded as what 'makes' its possessor Socrates in a non-trivial sense, but is simple and unanalysable. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.2) | |
| A reaction: I don't accept that there is any such property as 'being Socrates' (or even 'being identical with Socrates'), except as empty locutions or logical devices. A haecceity seems to be the 'ultimate subject of predication', with no predicates of its own. |
| 11889 | Essentialism must avoid both reduplication of essences, and multiple occupancy by essences [Mackie,P] |
| Full Idea: The argument for unshareable properties (the Reduplication Argument) suggests the danger of reduplication of Berkeley; the argument for incompatible properties (Multiple Occupancy) says Berkeley and Hume could be in the same possible object. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.8) | |
| A reaction: These are her arguments in favour of essential properties being necessarily incompatible between objects. Whatever the answer, it must allow essences for indistinguishables like electrons. 'Incompatible' points towards a haecceity. |
| 11877 | An individual essence is the properties the object could not exist without [Mackie,P] |
| Full Idea: By essentialism about individuals I simply mean the view that individual things have essential properties, where an essential property of an object is a property that the object could not have existed without. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 1.1) | |
| A reaction: This presumably means I could exist without a large part of my reason and consciousness, but could not exist without one of my heart valves. This seems to miss the real point of essence. I couldn't exist without oxygen - not one of my properties. |
| 11882 | No other object can possibly have the same individual essence as some object [Mackie,P] |
| Full Idea: Individual essences are essential properties that are unique to them alone. ...If a set of properties is an individual essence of A, then A has the properties essentially, and no other actual or possible object actually or possibly has them. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.1/2) | |
| A reaction: I'm unconvinced about this. Tigers have an essence, but individual tigers have individual essences over and above their tigerish qualities, yet the perfect identity of two tigers still seems to be possible. |
| 11886 | There are problems both with individual essences and without them [Mackie,P] |
| Full Idea: If all objects had individual essences, there would be no numerical difference without an essential difference. But if there aren't individual essences, there could be two things sharing all essential properties, differing only in accidental properties. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.5) | |
| A reaction: Depends how you define individual essence. Why can't two electrons have the same individual essence. To postulate a 'kind essence' which bestows the properties on each electron is to get things the wrong way round. |
| 11909 | Unlike Hesperus=Phosophorus, water=H2O needs further premisses before it is necessary [Mackie,P] |
| Full Idea: There is a disanalogy between 'necessarily water=H2O' and 'necessarily Hesperus=Phosphorus'. The second just needs the necessity of identity, but the first needs 'x is a water sample' and 'x is an H2O' sample to coincide in all possible worlds. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 10.1.) | |
| A reaction: This comment is mainly aimed at Kripke, who bases his essentialism on identities, rather than at Putnam. |
| 11899 | Why are any sortals essential, and why are only some of them essential? [Mackie,P] |
| Full Idea: Accounts of sortal essentialism do not give a satisfactory explanation of why any sortals should be essential sortals, or a satisfactory account of why some sortals should be essential while others are not. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 8.6) | |
| A reaction: A theory is not wrong, just because it cannot give a 'satisfactory explanation' of every aspect of the subject. We might, though, ask why the theory isn't doing well in this area. |
| 11906 | The Kripke and Putnam view of kinds makes them explanatorily basic, but has modal implications [Mackie,P] |
| Full Idea: Kripke and Putnam chose for their typical essence of kinds, sets of properties that could be thought of as explanatorily basic. ..But the modal implications of their views go well beyond this. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 10.1) | |
| A reaction: Cf. Idea 11905. The modal implications are that the explanatory essence is also necessary to the identity of the thing under discussion, such as H2O. So do basic explanations carry across into all possible worlds? |
| 11894 | Origin is not a necessity, it is just 'tenacious'; we keep it fixed in counterfactual discussions [Mackie,P] |
| Full Idea: I suggest 'tenacity of origin' rather than 'necessity of origin'. ..The most that we need is that Caesar's having something similar to his actual origin in certain respects (e.g. his actual parents) is normally kept fixed in counterfactual speculation. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 6.9) | |
| A reaction: I find necessity or essentially of origin very unconvincing, so I rather like this. Origin is just a particularly stable way to establish our reference to something. An elusive spy may have little more than date and place of birth to fix them. |
| 11887 | Transworld identity without individual essences leads to 'bare identities' [Mackie,P] |
| Full Idea: Transworld identity without individual essences leads to 'bare identities'. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.7) | |
| A reaction: [She gives an argument for this, based on Forbes] I certainly favour the notion of individual essences over the notion of bare identities. We must distinguish identity in reality from identity in concept. Identities are points in conceptual space. |
| 11890 | De re modality without bare identities or individual essence needs counterparts [Mackie,P] |
| Full Idea: Anyone who wishes to avoid both bare identities and individual essences, without abandoning de re modality entirely, must adopt counterpart theory. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 4.1) | |
| A reaction: This at least means that Lewis's proposal has an important place in the discussion, forcing us to think more clearly about the identities involved when we talk of possibilities. Mackie herself votes for bare indentities. |
| 11892 | Things may only be counterparts under some particular relation [Mackie,P] |
| Full Idea: A may be a counterpart of B according to one counterpart relation (similarity of origin, say), but not according to another (similarity of later history). | |
| From: Penelope Mackie (How Things Might Have Been [2006], 5.3) | |
| A reaction: Hm. Would two very diverse things have to be counterparts because they were kept in the same cupboard in different worlds? Can the counterpart relationship diverge or converge over time? Yes, I presume. |
| 11893 | Possibilities for Caesar must be based on some phase of the real Caesar [Mackie,P] |
| Full Idea: I take the 'overlap requirement' for Julius Caesar to be that, when considering how he might have been different, you have to take him as he actually was at some time in his existence, and consider possibilities consistent with that. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 6.5) | |
| A reaction: This is quite a large claim (larger than Mackie thinks?), as it seems equally applicable to properties, states of affairs and propositions, as well as to individuals. Possibility that has no contact at all with actuality is beyond our comprehension. |
| 11884 | The theory of 'haecceitism' does not need commitment to individual haecceities [Mackie,P] |
| Full Idea: The theory that things have 'haecceities' must be sharply distinguished from the theory referred to as 'haecceitism', which says there may be differences in transworld identities that do not supervene on qualitative differences. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 2.2 n7) | |
| A reaction: She says later [p,43 n] that it is possible to be a haecceitist without believing in individual haecceities, if (say) the transworld identities had no basis at all. Note that if 'thisness' is 'haecceity', then 'whatness' is 'quiddity'. |
| 22328 | I just confront the evidence, and let it act on me [Ramsey] |
| Full Idea: I can but put the evidence before me, and let it act on my mind. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], p.202), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 70 'Deg' | |
| A reaction: Potter calls this observation 'downbeat', but I am an enthusiastic fan. It is roughly my view of both concept formation and of knowledge. You soak up the world, and respond appropriately. The trick is in the selection of evidence to confront. |
| 22325 | A belief is knowledge if it is true, certain and obtained by a reliable process [Ramsey] |
| Full Idea: I have always said that a belief was knowledge if it was 1) true, ii) certain, iii) obtained by a reliable process. | |
| From: Frank P. Ramsey (The Foundations of Mathematics [1925], p.258), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 66 'Rel' | |
| A reaction: Not sure why it has to be 'certain' as well as 'true'. It seems that 'true' is objective, and 'certain' subjective. I think I know lots of things of which I am not fully certain. Reliabilism long preceded Alvin Goldman. |
| 11905 | Locke's kind essences are explanatory, without being necessary to the kind [Mackie,P] |
| Full Idea: One might speak of 'Lockean real essences' of a natural kind, a set of properties that is basic in the explanation of the other properties of the kind, without commitment to the essence belonging to the kind in all possible worlds. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 10.1) | |
| A reaction: I think this may be the most promising account. The essence of a tiger explains what tigers are like, but tigers may evolve into domestic pets. Questions of individuation and of explaining seem to be quite separate. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 11907 | Maybe the identity of kinds is necessary, but instances being of that kind is not [Mackie,P] |
| Full Idea: One could be an essentialist about natural kinds (of tigers, or water) while holding that every actual instance or sample of a natural kind is only accidentally an instance or a sample of that kind. | |
| From: Penelope Mackie (How Things Might Have Been [2006], 10.2) | |
| A reaction: You wonder, then, in what the necessity of the kind consists, if it is not rooted in the instances, and presumably it could only result from a stipulative definition, and hence be conventional. |