18 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? |
| 22180 | Multiple realisability is said to make reduction impossible [Okasha] |
| Full Idea: Philosophers have often invoked multiple realisability to explain why psychology cannot be reduced to physics or chemistry, but in principle the explanation works for any higher-level science. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 3) | |
| A reaction: He gives the example of a 'cell' in biology, which can be implemented in all sorts of ways. Presumably that can be reduced to many sorts of physics, but not just to one sort. The high level contains patterns that vanish at the low level. |
| 16065 | Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman] |
| Full Idea: Some insist that constitution is identity, on the grounds that distinct material objects cannot occupy the same place at the same time. Others argue that constitution is not identity, since the statue and its material differ in important respects. | |
| From: Ryan Wasserman (Material Constitution [2009], Intro) | |
| A reaction: The 'important respects' seem to concern possibilities rather than actualities, which is suspicious. It is misleading to think we are dealing with two things and their relation here. Objects must have constitutions; constitutions make objects. |
| 16067 | Constitution is not identity, because it is an asymmetric dependence relation [Wasserman] |
| Full Idea: For those for whom 'constitution is not identity' (the 'constitution view'), constitution is said to be an asymmetric relation, and also a dependence relation (unlike identity). | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: It seems obvious that constitution is not identity, because there is more to a thing's identity than its mere constitution. But this idea makes it sound as if constitution has nothing to do with identity (chalk and cheese), and that can't be right. |
| 16069 | There are three main objections to seeing constitution as different from identity [Wasserman] |
| Full Idea: The three most common objections to the constitution view are the Impenetrability Objection (two things in one place?), the Extensionality Objection (mereology says wholes are just their parts), and the Grounding Objection (their ground is the same). | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: [summary] He adds a fourth, that if two things can be in one place, why stop at two? [Among defenders of the Constitution View he lists Baker, Fine, Forbes, Koslicki, Kripke, Lowe, Oderberg, N.Salmon, Shoemaker, Simons and Yablo.] |
| 16068 | The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman] |
| Full Idea: We do not calculate the weight of something by summing the weights of all its parts - weigh bricks and the molecules of a wall and you will get the wrong result, since you have weighed some parts more than once. | |
| From: Ryan Wasserman (Material Constitution [2009], 2) | |
| A reaction: In fact the complete inventory of the parts of a thing is irrelevant to almost anything we would like to know about the thing. The parts must be counted at some 'level' of division into parts. An element can belong to many different sets. |
| 16074 | Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman] |
| Full Idea: If the relative identity theorist denies transitivity (to deal with the Ship of Theseus, for example), this would make us suspect that relativised identity relations are not identity relations, since transitivity seems central to identity. | |
| From: Ryan Wasserman (Material Constitution [2009], 6) | |
| A reaction: The problem here, I think, focuses on the meaning of the word 'same'. One change of plank leaves you with the same ship, but that is not transitive. If 'identical' is too pure to give the meaning of 'the same' it's not much use in discussing the world. |
| 22177 | Randomised Control Trials have a treatment and a control group, chosen at random [Okasha] |
| Full Idea: In the Randomised Controlled Trial for a new drug, patients are divided at random into a treatment group who receive the drug, and a control group who do not. Randomisation is important to eliminate confounding factors. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
| A reaction: [compressed] Devised in the 1930s, and a major breakthrough in methodology for that kind of trial. Psychologists use the method all the time. Some theorists say it is the only reliable method. |
| 22172 | Not all sciences are experimental; astronomy relies on careful observation [Okasha] |
| Full Idea: Not all sciences are experimental - astronomers obviously cannot do experiments on the heavens, but have to content themselves with careful observation instead. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 1) | |
| A reaction: Biology too. Psychology tries hard to be experimental, but I doubt whether the main theories emerge from experiments. |
| 22174 | The discoverers of Neptune didn't change their theory because of an anomaly [Okasha] |
| Full Idea: Adams and Leverrier began with Newton's theory of gravity, which made an incorrect prediction about the orbit of Uranus. They explained away the conflicting observations by postulating a new planet, Neptune. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 1) | |
| A reaction: The falsificationists can say that the anomalous observation did not falsify the theory, because they didn't know quite what they were observing. It was not in fact an anomaly for Newtonian theory at all. |
| 22175 | Science mostly aims at confirming theories, rather than falsifying them [Okasha] |
| Full Idea: The goal of science is not solely to refute theories, but also to determine which theories are true (or probably true). When a scientist collects data …they are trying to show that their own theory is true. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
| A reaction: This is the aim of 'accommodation' to a wide set of data, rather than prediction or refutation. |
| 22182 | Theories with unobservables are underdetermined by the evidence [Okasha] |
| Full Idea: According to anti-realists, scientific theories which posit unobservable entities are underdetermined by the empirical data - there will always be a number of competing theories which can account for the data equally well. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 4) | |
| A reaction: The fancy version is Putnam's model theoretic argument, explored by Tim Button. The reply, apparently, is that there are other criteria for theory choice, apart from the data. And we don't have to actually observe everything in a theory. |
| 22185 | Two things can't be incompatible if they are incommensurable [Okasha] |
| Full Idea: If two things are incommensurable they cannot be incompatible. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 5) | |
| A reaction: Kuhn had claimed that two rival theories are incompatible, which forces the paradigm shift. He can't stop the slide off into total relativism. The point is there cannot be a conflict if there cannot even be a comparison. |
| 22176 | Induction is inferences from examined to unexamined instances of a given kind [Okasha] |
| Full Idea: Some philosophers use 'inductive' to just mean not deductive, …but we reserve it for inferences from examined to unexamined instances of a given kind. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
| A reaction: The instances must at least be comparable. Must you know the kind before you start? Surely you can examine a sequence of things, trying to decide whether or not they are of one kind? Is checking the uniformity of a kind induction? |
| 22178 | If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha] |
| Full Idea: If the only objective constraints concern how we should change our credences, but what our initial credences should be is entirely subjective, then individuals with very bizarre opinions about the world will count as perfectly rational. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
| A reaction: The important rationality has to be the assessement of a diverse batch of evidence, for which there can never be any rules or mathematics. |
| 22173 | Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha] |
| Full Idea: Galileo's most enduring contribution lay in mechanics, where he refuted the Aristotelian theory that heavier bodies fall faster than lighter. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
| A reaction: This must the first idea in the theory of mechanics, allowing mathematical treatment and accurate comparisons. |
| 17366 | Virtually all modern views of speciation rest on relational rather than intrinsic features [Okasha] |
| Full Idea: On all modern species concepts (except the phenetic), the property in virtue of which a particular organism belongs to one species rather than another is a relational rather than an intrinsic property of the organism. | |
| From: Samir Okasha (Darwinian Metaphysics: Species and Essentialism [2002], p.201), quoted by Michael Devitt - Resurrecting Biological Essentialism 4 | |
| A reaction: I am in sympathy with Devitt's attack on this view, for the same reason that I take relational explanations of almost anything (such as the mind) to be inadequate. We need to know the intrinsic features that enable the relations. |