17 ideas
9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections. | |
From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I | |
A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue. |
12132 | Indiscernibility is a necessary and sufficient condition for identity [Brody] |
Full Idea: Enduring objects should be taken as fundamental in an ontology, and for all such objects indiscernibility is both a necessary and sufficient condition for identity. | |
From: Baruch Brody (Identity and Essence [1980], 3) | |
A reaction: Brody offers a substantial defence, but I don't find it plausible. Apart from Black's well known twin spheres example (Idea 10195), discernibility is relative to the powers of the observer. Two similar people in the mist aren't thereby identical. |
15834 | Brody bases sortal essentialism on properties required throughout something's existence [Brody, by Mackie,P] |
Full Idea: Brody bases sortal essentialism on the notion of a property that an individual must possess throughout its existence if it possesses it at any time in its existence. | |
From: report of Baruch Brody (Identity and Essence [1980]) by Penelope Mackie - How Things Might Have Been 7.1 | |
A reaction: Brody tends to treat categories as properties, which I dislike. How do you assess 'must' here? A person may possess a mole throughout life without it being essential. |
12140 | Modern emphasis is on properties had essentially; traditional emphasis is on sort-defining properties [Brody] |
Full Idea: The modern emphasis has been on the connection between essential properties and the properties that an object must have essentially. But traditionally there is also the connection between essential properties and the sort of thing that it is. | |
From: Baruch Brody (Identity and Essence [1980], 5.6) | |
A reaction: These are the modal essence and the definitional essence. My view is that he has missed out a crucial third (Aristotelian) view, which is that essences are explanatory. This third view can subsume the other two. |
11895 | A sortal essence is a property which once possessed always possessed [Brody, by Mackie,P] |
Full Idea: Brody bases sortal essentialism on the notion of a property that an individual must possess throughout its existence if it possesses it at any time in its existence. ...'Once an F, always an F'. ...Being a parrot is not a temporary occupation. | |
From: report of Baruch Brody (Identity and Essence [1980]) by Penelope Mackie - How Things Might Have Been 7.1 | |
A reaction: Hm. Would being less than fifty metres tall qualify as a sortal essence, for a giraffe or a uranium rod? If there is one thing an essential property should be, it is important. How do we assess importance? By explanatory power! Watch this space. |
12141 | Maybe essential properties are those which determine a natural kind? [Brody] |
Full Idea: We can advance the thesis that all essential properties either determine a natural kind or are part of an essential property that does determine a natural kind. | |
From: Baruch Brody (Identity and Essence [1980]) | |
A reaction: A useful clear statement of the view. I am opposed to it, because I take it to be of the essence of Socrates that he is philosophical, but humans are not essentially philosophical, and philosophers are unlikely to be a natural kind. |
12137 | De re essentialism standardly says all possible objects identical with a have a's essential properties [Brody] |
Full Idea: To say that an object a has a property P essentially is to say that it has P, and in all of certain worlds (all possible, all in which something identical with it exists, ...) the object identical with it has P. This is the standard de re interpretation. | |
From: Baruch Brody (Identity and Essence [1980], 5.4) | |
A reaction: This view always has to be qualified by excluding trivially necessary properties, but that exclusion shows clearly that the notion of essential is more concerned with non-triviality than it is with necessity. |
12142 | Essentially, a has P, always had P, must have had P, and has never had a future without P [Brody] |
Full Idea: 'a has property P essentially' means 'a has P, a always had P, there is no possible past in which P exists without P, and there is no moment of time at which a has had P and at which there is a possible future in which a exists without P' | |
From: Baruch Brody (Identity and Essence [1980], 6) | |
A reaction: This is Brody's own final account of essentialism. This is a carefully qualified form of the view that essential properties are, on the whole, the necessary properties, which view I take to be fundamentally mistaken. |
12143 | An object having a property essentially is equivalent to its having it necessarily [Brody] |
Full Idea: An object having a property essentially is equivalent to its having it necessarily. | |
From: Baruch Brody (Identity and Essence [1980], 6.1) | |
A reaction: This strikes me as blatantly false. Personally I am toying with the very unorthodox view that essential properties are not at all necessary, and that something can retain its identity while changing its essential character. A philosopher with Alzheimers. |
12144 | Essentialism is justified if the essential properties of things explain their other properties [Brody] |
Full Idea: The reasonableness of the essentialist hypothesis will be proportional to the extent that we can, as a result, use a's possession of P to explain a's other properties, ...and there is an inability to explain otherwise why a has P. | |
From: Baruch Brody (Identity and Essence [1980], 6.3) | |
A reaction: Brody as a rather liberal notion of properties. I would hope that we can do rather more than explain a's non-essential properties. If the non-essential properties were entailed by the essential ones, would they not then also be essential? |
12139 | Mereological essentialism says that every part that ensures the existence is essential [Brody] |
Full Idea: Mereological essentialism (whose leading advocate is Chisholm) says that for every x and y, if x is ever part of y, then y is necessarily such that x is part of y at any time that y exists. | |
From: Baruch Brody (Identity and Essence [1980], 5.6) | |
A reaction: This sounds implausible, especially given the transitivity of parthood. Not only are the planks that constitute Theseus's Ship now essential to it, but all the parts of the planks, every last chip, are as well. |
12135 | Interrupted objects have two first moments of existence, which could be two beginnings [Brody] |
Full Idea: If 'beginning of existence' meant 'first moment of existence after a period of nonexistence', then objects with interrupted existence have two beginnings of existence. | |
From: Baruch Brody (Identity and Essence [1980], 4.1) | |
A reaction: One might still maintain that the first beginning was essential to the object, since that is the event that defined it - and that would clarify the reason why we are supposed to think the origins are essential. I say the origin explains it. |
12130 | a and b share all properties; so they share being-identical-with-a; so a = b [Brody] |
Full Idea: Suppose that a and b have all of their properties in common. a certainly has the property of-being-identical-with-a. So, by supposition, does b. Then a = b. | |
From: Baruch Brody (Identity and Essence [1980], 1.2) | |
A reaction: Brody defends this argument, and seems to think that it proves the identity of indiscernibles. As far as I can see it totally begs the question, since we can only assume that both have the property of being-identical-with-a if we have assumed a = b. |
12138 | Identity across possible worlds is prior to rigid designation [Brody] |
Full Idea: Identity across possible worlds is prior to rigid designation. | |
From: Baruch Brody (Identity and Essence [1980], 5.4) | |
A reaction: An interesting view. We might stipulate that any possible Aristotle is 'our Aristotle', but you would still need criteria for deciding which possible Aristotle's would qualify. Long-frozen Aristotles, stupid Aristotles, alien Aristotle's, deformed... |
13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
Full Idea: In a single day there lies open to men of learning more than there ever does to the unenlightened in the longest of lifetimes. | |
From: Posidonius (fragments/reports [c.95 BCE]), quoted by Seneca the Younger - Letters from a Stoic 078 | |
A reaction: These remarks endorsing the infinite superiority of the educated to the uneducated seem to have been popular in late antiquity. It tends to be the religions which discourage great learning, especially in their emphasis on a single book. |
20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
Full Idea: Posidonius defined time thus: it is an interval of motion, or the measure of speed and slowness. | |
From: report of Posidonius (fragments/reports [c.95 BCE]) by John Stobaeus - Anthology 1.08.42 | |
A reaction: Hm. Can we define motion or speed without alluding to time? Looks like we have to define them as a conjoined pair, which means we cannot fully understand either of them. |