46 ideas
| 5333 | Philosophy needs wisdom about who we are, as well as how we ought to be [Flanagan] |
| Full Idea: Any good philosophy will need to offer wisdom about who we are as well as about how we ought to be. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 14) | |
| A reaction: This sop should be accepted gratefully by fans of bioethics, who seem inclined to think that describing 'how we are' is all that needs to be said. Maybe the key wisdom lies in the relationship between the 'is' and the 'ought' of human nature. |
| 5334 | We resist science partly because it can't provide ethical wisdom [Flanagan] |
| Full Idea: The inability of science to provide ethical wisdom is partly responsible for our resistance to the scientific image. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 14) | |
| A reaction: This seems right. A.J. Ayer, for example, declared "I believe in science", and his account of ethics was vacuously nihilistic. A description of the mechanisms of moral life is not the same as ethical wisdom. |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| Full Idea: Intuitionists in mathematics deny excluded middle, because it is symptomatic of faith in the transcendent existence of mathematical objects and/or the truth of mathematical statements. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: There are other problems with excluded middle, such as vagueness, but on the whole I, as a card-carrying 'realist', am committed to the law of excluded middle. |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| Full Idea: It is surely wise to identify the positions in the natural numbers structure with their counterparts in the integer, rational, real and complex number structures. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: The point is that this might be denied, since 3, 3/1, 3.00.., and -3*i^2 are all arrived at by different methods of construction. Natural 3 has a predecessor, but real 3 doesn't. I agree, intuitively, with Shapiro. Russell (1919) disagreed. |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| Full Idea: A sequence a1,a2,... of rational numbers is 'Cauchy' if for each rational number ε>0 there is a natural number N such that for all natural numbers m, n, if m>N and n>N then -ε < am - an < ε. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.2 n4) | |
| A reaction: The sequence is 'Cauchy' if N exists. |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| Full Idea: There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7) | |
| A reaction: He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties. |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| Full Idea: Zermelo said that for each number n, its successor is the singleton of n, so 3 is {{{null}}}, and 1 is not a member of 3. Von Neumann said each number n is the set of numbers less than n, so 3 is {null,{null},{null,{null}}}, and 1 is a member of 3. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.2) | |
| A reaction: See Idea 645 - Zermelo could save Plato from the criticisms of Aristotle! These two accounts are cited by opponents of the set-theoretical account of numbers, because it seems impossible to arbitrate between them. |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| Full Idea: The structuralist vigorously rejects any sort of ontological independence among the natural numbers; the essence of a natural number is its relations to other natural numbers. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: This seems to place the emphasis on ordinals (what order?) rather than on cardinality (how many?). I am strongly inclined to think that this is the correct view, though you can't really have relations if there is nothing to relate. |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| Full Idea: A 'system' is a collection of objects with certain relations among them; a 'pattern' or 'structure' is the abstract form of a system, highlighting the interrelationships and ignoring any features they do not affect how they relate to other objects. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 10.1) | |
| A reaction: Note that 'ignoring' features is a psychological account of abstraction, which (thanks to Frege and Geach) is supposed to be taboo - but which I suspect is actually indispensable in any proper account of thought and concepts. |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| Full Idea: The thesis that principles of arithmetic are derivable from the laws of logic runs against a now common view that logic itself has no ontology. There are no particular logical objects. From this perspective logicism is a non-starter. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 5.1) | |
| A reaction: This criticism strikes me as utterly devastating. There are two routes to go: prove that logic does have an ontology of objects (what would they be?), or - better - deny that arithmetic contains any 'objects'. Or give up logicism. |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| Full Idea: Term Formalism is the view that mathematics is just about characters or symbols - the systems of numerals and other linguistic forms. ...This will cover integers and rational numbers, but what are real numbers supposed to be, if they lack names? | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.1) | |
| A reaction: Real numbers (such as pi and root-2) have infinite decimal expansions, so we can start naming those. We could also start giving names like 'Harry' to other reals, though it might take a while. OK, I give up. |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| Full Idea: Game Formalism likens mathematics to chess, where the 'content' of mathematics is exhausted by the rules of operating with its language. ...This, however, leaves the problem of why the mathematical games are so useful to the sciences. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.1.2) | |
| A reaction: This thought pushes us towards structuralism. It could still be a game, but one we learned from observing nature, which plays its own games. Chess is, after all, modelled on warfare. |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| Full Idea: The Deductivist version of formalism (sometimes called 'if-thenism') says that the practice of mathematics consists of determining logical consequences of otherwise uninterpreted axioms. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 6.2) | |
| A reaction: [Hilbert is the source] More plausible than Term or Game Formalism (qv). It still leaves the question of why it seems applicable to nature, and why those particular axioms might be chosen. In some sense, though, it is obviously right. |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| Full Idea: Critics commonly complain that the intuitionist restrictions cripple the mathematician. On the other hand, intuitionist mathematics allows for many potentially important distinctions not available in classical mathematics, and is often more subtle. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 7.1) | |
| A reaction: The main way in which it cripples is its restriction on talk of infinity ('Cantor's heaven'), which was resented by Hilbert. Since high-level infinities are interesting, it would be odd if we were not allowed to discuss them. |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| Full Idea: I classify conceptualists according to what they say about properties or concepts. If someone classified properties as existing independent of language I would classify her as a realist in ontology of mathematics. Or they may be idealists or nominalists. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 2.2.1) | |
| A reaction: In other words, Shapiro wants to eliminate 'conceptualist' as a useful label in philosophy of mathematics. He's probably right. All thought involves concepts, but that doesn't produce a conceptualist theory of, say, football. |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| Full Idea: A definition of a mathematical entity is 'impredicative' if it refers to a collection that contains the defined entity. The definition of 'least upper bound' is impredicative as it refers to upper bounds and characterizes a member of this set. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.2) | |
| A reaction: The big question is whether mathematics can live with impredicative definitions, or whether they threaten to be viciously circular, and undermine the whole enterprise. |
| 12756 | Substance is a force for acting and being acted upon [Leibniz] |
| Full Idea: The very substance in things consists of a force for acting and being acted upon. | |
| From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §08) | |
| A reaction: Garber places this text just before the spiritual notion of monads took a grip on Leibniz. He seems to have thought that only some non-physical entity, with appetite and perception, could generate force. Wrong. |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| Full Idea: Rationalism is a long-standing school that can be characterized as an attempt to extend the perceived methodology of mathematics to all of knowledge. | |
| From: Stewart Shapiro (Thinking About Mathematics [2000], 1.1) | |
| A reaction: Sometimes called 'Descartes's Dream', or the 'Enlightenment Project', the dream of proving everything. Within maths, Hilbert's Programme aimed for the same certainty. Idea 22 is the motto for the opposition to this approach. |
| 5340 | Explanation does not entail prediction [Flanagan] |
| Full Idea: Explanation does not entail prediction. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 73n) | |
| A reaction: Presumably the inverse of this is also true, as we might be able to predict through pure induction, without knowing why something happened. We predict that smoking is likely to cause cancer. Complex things might be explicable but unpredictable. |
| 12755 | Final causes can help with explanations in physics [Leibniz] |
| Full Idea: Final causes not only advance virtue and piety in ethics and natural theology, but also help us to find and lay bare hidden truths in physics itself. | |
| From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §04) | |
| A reaction: This rearguard action against the attack on teleology is certainly aimed at Spinoza. The notion of purpose still seems to have a role to play in evolutionary biology, but probably not in physics. |
| 5346 | In the 17th century a collisionlike view of causation made mental causation implausible [Flanagan] |
| Full Idea: In the seventeenth century the dominant idea that causation is collisionlike made mental causation almost impossible to envision. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.136) | |
| A reaction: Interesting. This makes Descartes' interaction theory look rather bold, and Leibniz's and Malebranche's rejection of it understandable. Personally I still think of causation as collisionlike, except that the collisions are of very very tiny objects. |
| 5341 | Only you can have your subjective experiences because only you are hooked up to your nervous system [Flanagan] |
| Full Idea: It is easy to explain why certain brain events are uniquely experienced by you subjectively: only you are properly hooked up to your own nervous system to have your own experiences. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 87) | |
| A reaction: This is in reply to Nagel's oft quoted claim that mind can only be understood as "what it is like to be" that mind. I agree with Flanagan, and it is nice illustration of how philosophers can confuse themselves with high-sounding questions. |
| 5351 | We only have a sense of our self as continuous, not as exactly the same [Flanagan] |
| Full Idea: We only have a sense of our self as continuous, but not as exactly the same. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.178) | |
| A reaction: Russell said this too, and it seems to me to be right. Personal identity is far too imprecise for me to assert that I remember my ten-year-old self as being identical to me now. Only physical objects like teddy bears can pass that test. |
| 5353 | The self is an abstraction which magnifies important aspects of autobiography [Flanagan] |
| Full Idea: The self is an abstraction from the story of a person's life that isolates and magnifies the experiences, traits and aspirations that are assigned importance. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.240) | |
| A reaction: Personally I am inclined to see personal identity as the central controller of brain activity, the aspect of the biological machine which keeps all the mental events focused on what matters, which is health, safety and happiness. |
| 5354 | We are not born with a self; we develop a self through living [Flanagan] |
| Full Idea: It is a bad mistake to think we are born with a self; the self develops, and acquiring it requires living in the world. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.260) | |
| A reaction: I think this is wrong. He is mistaking a complex cultural concept of the self as the subject for autobiography etc. for the basic biological self which even small animals must have if their brains are to serve any useful purpose in their lives. |
| 5349 | For Buddhists a fixed self is a morally dangerous illusion [Flanagan] |
| Full Idea: According to Buddhism, the idea of a permanent, constant self is an illusion, and a morally dangerous one. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.161) | |
| A reaction: We are familiar with the idea that it might be an illusion, but I am unconvinced by 'morally dangerous'. If you drop both free will and personal identity, I can't see any sort of focus for moral life left, but I am willing to be convinced. |
| 5338 | Normal free will claims control of what I do, but a stronger view claims control of thought and feeling [Flanagan] |
| Full Idea: The standard view of free will is that I have something like complete control over what I do. A stronger view (not widely held) is that I also have complete control over what I think and what I feel. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 60n) | |
| A reaction: To claim free control of feelings looks optimistic, but it does look as if we can decide to think about something, such as a philosophical problem. Deciding what to say comes somewhere between thought and action. |
| 5344 | Free will is held to give us a whole list of desirable capacities for living [Flanagan] |
| Full Idea: Free will is said to give us self-control, self-expression, individuality, reasons-sensitivity, rational deliberation, rational accountability, moral accountability, the capacity to do otherwise, unpredictability, and political freedom. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.104) | |
| A reaction: Nice list. His obvious challenge is to either say we can live happily without some of these things, or else show how we can have them without 'free will'. Personally I agree with Flanagan that we meet the challenge. |
| 5332 | People believe they have free will that circumvents natural law, but only an incorporeal mind could do this [Flanagan] |
| Full Idea: Most people believe we have free will, and that this consists in the ability to circumvent natural law. The trouble is that the only device ever philosophically invented that can do this sort of job is an incorporeal soul or mind. | |
| From: Owen Flanagan (The Problem of the Soul [2002], Pref) | |
| A reaction: I think this is exactly right. We currently have a western world full of people who have rejected dualism, but still cling on to free will, because they think morality depends on it. I think morality depends on personal identity, but not on free will. |
| 5345 | We only think of ourselves as having free will because we first thought of God that way [Flanagan] |
| Full Idea: It is unimaginable to me that, despite the feeling that we control what we do, such a strong conception of ourselves as unmoved movers would have been added to our self-image unless we had first conceived of God along these lines. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.107) | |
| A reaction: I think this is right, though there are signs in fifth century Greece of contradictory evidence. The 'unmoved mover' seems unformulated before Plato's 'Laws' (idea 1423), but there is an implied belief in free will a hundred years earlier. |
| 12760 | Something rather like souls (though not intelligent) could be found everywhere [Leibniz] |
| Full Idea: Nor is there any reason why souls or things analogous to souls should not be everywhere, even if dominant and consequently intelligent souls, like human souls, cannot be everywhere. | |
| From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §12) | |
| A reaction: He is always flirting with panpsychism, though he doesn't seem to offer any account of how these little baby souls can be built up to create one intelligent soul, the latter being indivisible. 'Souls' are very different from things 'analous to souls'! |
| 5343 | People largely came to believe in dualism because it made human agents free [Flanagan] |
| Full Idea: I would say that that my consciousness doesn't seem either physical or non-physical, ..but the belief that the mind is non-physical partly took hold because that fits well with thinking of human agents as free. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.102) | |
| A reaction: I think this is right. I personally think there is no such thing as free will, and that belief in it has been the single greatest delusion amongst philosophers (and others) for the last two thousand years. Dualism has now gone, and free will is next. |
| 5347 | Behaviourism notoriously has nothing to say about mental causation [Flanagan] |
| Full Idea: Behaviourism was notorious in its heyday for having nothing to say about mental causation. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.141) | |
| A reaction: This is a bit unfair, as Ryle (idea 2622, following Spinoza, 4862) was one of the first to point out the paradox of 'double causation'. You have to be a mentalist to worry about mental causation, and eliminativists aren't bothered. |
| 5339 | Cars and bodies obey principles of causation, without us knowing any 'strict laws' about them [Flanagan] |
| Full Idea: Although everyone thinks cars and bodies obey the principles of causation, no one thinks it a deficiency that we don't know strict laws of automechanics or anatomy. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 65) | |
| A reaction: This attacks Davidson's claim that there are no strict psycho-physical laws, and I agree with Flanagan. Huge dreams of free will and human dignity are being pinned on the flimsy point that we have no strict laws here. But brains are very complicated. |
| 5342 | Physicalism doesn't deny that the essence of an experience is more than its neural realiser [Flanagan] |
| Full Idea: One may be committed to the truth of physicalism without being committed to the claim that the essence of an experience is captured fully by a description of its neural realiser. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 90) | |
| A reaction: This is a reply to the Leibniz Mill question (idea 2109) about what is missing from a materialist view. Flanagan's point is that just as the essence of a panorama is the view from the hill, so the essence of consciousness requires you to be that brain. |
| 5335 | Emotions are usually very apt, rather than being non-rational and fickle [Flanagan] |
| Full Idea: One can question the idea that emotions are non-rational, fickle and flighty; on the contrary, emotions normally seem to be very apt. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 16) | |
| A reaction: This is the modern view of emotion which is emerging from neuroscience, which is greatly superior to traditional views, apart from Aristotle, who felt that wisdom and virtue arose precisely when emotions were apt for the situation. |
| 5348 | Intellectualism admires the 'principled actor', non-intellectualism admires the 'good character' [Flanagan] |
| Full Idea: There are two main pictures of the good person: there is the 'good character', and there is the 'principled actor'. ..The first picture is non-intellectualist, and the second is intellectualist. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.145) | |
| A reaction: The second ideal elevates the principle itself above the actor who carries it out. Presumably consistency is a virtue, so a good character will at least pay some attention to principles. A good magistrate comes out the same in both views. |
| 5355 | Cognitivists think morals are discovered by reason [Flanagan] |
| Full Idea: Cognitivists think morals are discovered by reason. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.301n) | |
| A reaction: I take cognitivism to be (strictly) the view that morals are knowable in principle. Our intellects might not be up to the task (and so we might have to ask the gods what is right). There is also the possibility that morals might be known by intuition. |
| 5336 | Ethics is the science of the conditions that lead to human flourishing [Flanagan] |
| Full Idea: Ethics is the normative science that studies the objective conditions that lead to flourishing of persons. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p. 17) | |
| A reaction: This is a nice slogan for the virtue theory account of the nature of ethics. I think it is the view with which I agree. I am intrigued that he has smuggled the word 'science' in, which is a nice challenge to conventional views of science. |
| 12759 | There are atoms of substance, but no atoms of bulk or extension [Leibniz] |
| Full Idea: Although there are atoms of substance, namely monads, which lack parts, there are no atoms of bulk [moles], that is, atoms of the least possible extension, nor are there any ultimate elements, since a continuum cannot be composed out of points. | |
| From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §11) | |
| A reaction: Leibniz has a constant battle for the rest of his career to explain what these 'atoms of substance' are, since they have location but no extension, they are self-sufficient yet generate force, and are non-physical but interact with matter. |
| 12718 | Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz] |
| Full Idea: I understand matter as either secondary or primary. Secondary matter is, indeed, a complete substance, but it is not merely passive; primary matter is merely passive, but it is not a complete substance. So we must add a soul or form... | |
| From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §12), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4 | |
| A reaction: It sounds as if primary matter is redundant, but Garber suggests that secondary matter is just the combination of primary matter with form. |
| 11854 | If there is some trace of God in things, that would explain their natural force [Leibniz] |
| Full Idea: If the law of God does indeed leave some vestige of him expressed in things...then it must be granted that there is a certain efficacy residing in things, a form or force such as we usually designate by the name of nature, from which the phenomena follow. | |
| From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §06) | |
| A reaction: I wouldn't rate this as a very promising theory of powers, but it seems to me important that Leibniz recognises the innate power in things as needing explanation. If you remove divine power, you are left with unexplained intrinsic powers. |
| 12758 | It is plausible to think substances contain the same immanent force seen in our free will [Leibniz] |
| Full Idea: If we attribute an inherent force to our mind, a force acting immanently, then nothing forbids us to suppose that the same force would be found in other souls or forms, or, if you prefer, in the nature of substances. | |
| From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], §10) | |
| A reaction: This is the kind of bizarre idea that you are driven to, once you start thinking that God must have a will outside nature, and then that we have the same thing. Why shouldn't such a thing pop up all over the place? Only Leibniz spots the slippery slope. |
| 19408 | To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz] |
| Full Idea: To say that nature itself or the substance of all things is God is a pernicious doctrine, recently introduced into the world or renewed by a subtle or profane author. | |
| From: Gottfried Leibniz (On Nature Itself (De Ipsa Natura) [1698], 8) | |
| A reaction: The dastardly profane author is, of course, Spinoza, whom Leibniz had met in 1676. The doctrine may be pernicious to religious orthodoxy, but to me it is rather baffling, since in my understanding nature and God have almost nothing in common. |
| 5350 | The Hindu doctrine of reincarnation only appeared in the eighth century CE [Flanagan] |
| Full Idea: The doctrine of a cycle of rebirths and reincarnations that are normally required before one achieve nirvana was only proposed in the eighth century CE, and then spread like wildfire among Hindus and, to a lesser extent, among Buddhists. | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.166n) | |
| A reaction: Intriguing. Plato had proposed it in the fourth century BCE. Presumably Hindus had always been dualists, and then suddenly saw and exciting possibility that followed from it. The doctrine strikes me as (to put it mildly) implausible. |
| 5352 | The idea of the soul gets some support from the scientific belief in essential 'natural kinds' [Flanagan] |
| Full Idea: The idea of the soul could be easily trashed if science does not countenance essences, but science does countenance essences in the form of what are known as 'natural kinds' (such as water, salt and gold). | |
| From: Owen Flanagan (The Problem of the Soul [2002], p.181) | |
| A reaction: The existence of any essences at all does indeed make the existence of a soul naturally possible, but scientific natural kinds are usually postulated on a basis of chemical stability. Animals, for example, are no longer usually classified that way. |