23 ideas
| 18085 | Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy] |
| Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely. |
| 18084 | When successive variable values approach a fixed value, that is its 'limit' [Cauchy] |
| Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others. | |
| From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4 | |
| A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction? |
| 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... |
| 19558 | Our own intuitions about whether we know tend to vacillate [Cohen,S] |
| Full Idea: One robust feature of our intuitions about whether we know things is that they tend to vacillate. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 1) | |
| A reaction: This strikes me as important. If we were tacit invariantists (Idea 19557) we should be able to ask ourselves whether we 'really and truly' know various things, but we can't decide. I know lots about Nietzsche in a pub, and very little in a university. |
| 19561 | We shouldn't jump too quickly to a contextualist account of claims to know [Cohen,S] |
| Full Idea: Maybe contextualists are too quick to appeal to our conflicting intuitions regarding knowledge. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 1) | |
| A reaction: An important point (from Earl Conee). I thoroughly approve of contextualism, but the whole status of whether a witness or a teacher knows what they are talking about is in danger of collapsing into relativism. This is what peer review is all about. |
| 19563 | The context sensitivity of knowledge derives from its justification [Cohen,S] |
| Full Idea: On my own view, the context sensivity of knowledge is inherited from one of its components, i.e. justification. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 1) | |
| A reaction: That sounds right, and it reinforces the idea that 'justification' is a more important epistemological concept than 'knowledge'. 'Am I justified in believing p?' Answer: 'it depends how well you have researched it'. |
| 19560 | Contextualism is good because it allows knowledge, but bad because 'knowing' is less valued [Cohen,S] |
| Full Idea: Contextualism is a 'good news, bad news' theory. The good news is that we have lots of knowledge and many surfaces are 'flat'; the bad news is that knowledge and flatness are not all they were cracked up to be. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 3) | |
| A reaction: That is exactly my position. I lost all interest in whether someone precisely 'knows' or 'does not know' something a long time ago (even in scientific or forensic contexts). In the case of flatness the case is even more obvious. |
| 12893 | Contextualism says sceptical arguments are true, relative to their strict context [Cohen,S] |
| Full Idea: Contextualism explains the appeal of sceptical arguments by allowing that the claims of the sceptic are true, relative to the very strict context in which they are made. | |
| From: Stewart Cohen (Contextualism Defended [2005], p.57) | |
| A reaction: This strikes me a right. I've always thought that global scepticism must be conceded if we are being very strict indeed about justification, but also that it is ridiculous to be that strict. So the epistemological question is 'How strict should we be?' |
| 12896 | Knowledge is context-sensitive, because justification is [Cohen,S] |
| Full Idea: The context-sensitivity of knowledge is inherited from one of its components, i.e. justification. | |
| From: Stewart Cohen (Contextualism Defended [2005], p.68) | |
| A reaction: I think this is exactly right - that there is nothing relative or contextual about what is actually true, or what someone believes, but knowleddge is wholly relative because it rests on shifting standards of justification. |
| 12894 | There aren't invariant high standards for knowledge, because even those can be raised [Cohen,S] |
| Full Idea: The problem for invariantism is that competent speakers, under sceptical pressure, tend to deny that we know even the most conspicuous facts of perception, the clearest memories etc. | |
| From: Stewart Cohen (Contextualism Defended [2005], p.58) | |
| A reaction: This is aimed at Idea 12892. This seems to me a strong response to the rather weak invariantist case (that there is 'really and truly' only one invariant standard for knowledge). Full strength scepticism about everything demolishes all knowledge. |
| 19559 | Contextualists slightly concede scepticism, but only in extremely strict contexts [Cohen,S] |
| Full Idea: Contextualism concedes that there is some truth to skepticism, but contains the damage by holding that skeptical claims are true only relative to atypically strict contexts. | |
| From: Stewart Cohen (Contextualism Defended (and reply) [2005], 1) | |
| A reaction: My attitude to scepticism is that everything we ever affirm should have a footnote saying '...but you never know...', and it should then be ignored. In the strictest context everything is doubted simultaneously (including language), and that is paralysis. |