32 ideas
| 1749 | If all laws were abolished, philosophers would still live as they do now [Aristippus elder] |
| Full Idea: If all laws were abolished, philosophers would still live as they do now. | |
| From: Aristippus the elder (fragments/reports [c.395 BCE]), quoted by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.4 | |
| A reaction: Presumably philosophers develop inner laws which other people lack. |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 4608 | Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil] |
| Full Idea: Dennett identifies a hierarchy of minds running from 'Darwinian' (hard-wired solutions to problems), to 'Skinnerian' (trial-and-error), to 'Popperian' (anticipating possible experience), to 'Gregorian' (self-conscious representation, probably linguistic). | |
| From: report of Daniel C. Dennett (Kinds of Minds [1996]) by John Heil - Philosophy of Mind Ch.5 | |
| A reaction: Interesting. The concept of an experiment seems a major step (assessing reality against an internal map), and the ability to think about one's own thoughts certainly strikes me as the mark of a top level mind. Maybe that is the importance of language. |
| 4880 | Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett] |
| Full Idea: 'Sentience' comes in every imaginable grade or intensity, from the simplest and most 'robotic', to the most exquisitely sensitive, hyper-reactive 'human'. We have to draw a line for moral policy, but it is unlikely we will ever discover a threshold. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.4) | |
| A reaction: This is the only plausible view, if you take the theory of evolution seriously. We can even observe low-grade marginal sentience in our own minds, and then shoot up the scale when we focus our minds properly on an object. |
| 4873 | What is it like to notice an uncomfortable position when you are asleep? [Dennett] |
| Full Idea: What is it like to notice, while sound asleep, that your left arm has become twisted into a position in which it is putting undue strain on your left shoulder? Like nothing. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.1) | |
| A reaction: A nice question, and all part of Dennett's accurate campaign to show that consciousness is not an all-or-nothing thing. As when we are barely aware of driving, innumerable things happen in the shadowy corners of thought. |
| 4881 | Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett] |
| Full Idea: An important step towards becoming a person is the step up from a first-order intentional system to a second-order system (which has beliefs and desires about beliefs and desires). | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.5) | |
| A reaction: Call it 'meta-thought'. I agree. Dennett thinks language is crucial to this, but the hallmark of intelligence and full-blown personhood is meta- and meta-meta-thought. Maybe the development of irony is a step up the evolutionary scale. Sarcasm is GOOD. |
| 4875 | We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett] |
| Full Idea: We are descended from robots, and composed of robots, and all the intentionality we enjoy is derived from the more fundamental intentionality of billions of crude intentional systems. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.2) | |
| A reaction: A more grand view of intentionality (such as Searle's) seems more attractive than this, but the crucial fact about Dennett is that he takes the implications of evolution much more seriously than other philosophers. He's probably right. |
| 4879 | There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett] |
| Full Idea: There is no more fear or anger in adrenaline than there is silliness in a bottle of whiskey. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.3) | |
| A reaction: Not exactly an argument, but a nice rhetorical point against absurd claims about identity and reduction and elimination. We may say that there is no fear without adrenaline, and no adrenaline in a live brain without fear. |
| 4876 | Maybe there is a minimum brain speed for supporting a mind [Dennett] |
| Full Idea: Perhaps there is a minimum speed for a mind, rather like the minimum escape velocity required to overcome gravity and leave the planet. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.3) | |
| A reaction: Dennett rejects this speculation, but he didn't stop to imagine what it would be LIKE if your brain slowed down, and he never considers Edelman's view that mind is a process. Put the two together… |
| 4878 | The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett] |
| Full Idea: I think there are only two good reasons why, when you make a mind, the materials matter: speed, and the ubiquity of transducers and effectors throughout the nervous system. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.3) | |
| A reaction: This sounds roughly right, because it gives you something between multiple realisability (minds made of cans and string), and type-type identity (minds ARE a particular material). Call it 'biological functionalism'? |
| 4874 | The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett] |
| Full Idea: The ancestor and chief rival of the language-of-thought hypothesis is the picture theory of ideas - that thoughts are about what they are about because they resemble their objects. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.2) | |
| A reaction: When you place them side by side, neither seems quite right. How can a mental state resemble an object, and how can an inner language inherently capture the features of an object? Maybe we lack the words for the correct theory. |
| 4882 | Concepts are things we (unlike dogs) can think about, because we have language [Dennett] |
| Full Idea: A dog cannot consider its concepts. Concepts are not things in a dog's world in the way that cats are. Concepts are things in our world, because we have language. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.6) | |
| A reaction: Dogs must have concepts, though, or much of their behaviour (like desperation to go for a walk, or to eat) is baffling. This is as good a proposal as I have ever encountered for the value of language. Meta-thought is a huge evolutionary advantage. |
| 3558 | Only the Cyrenaics reject the idea of a final moral end [Aristippus elder, by Annas] |
| Full Idea: The Cyrenaics are the most radical ancient moral philosophers, since they are the only school explicitly to reject the importance of achieving an overall final end. | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Julia Annas - The Morality of Happiness 11.1 | |
| A reaction: This looks like dropping out, but it could also be Keats's 'negative capability', of simply participating in existence without needing to do anything about it. |
| 5835 | The road of freedom is the surest route to happiness [Aristippus elder, by Xenophon] |
| Full Idea: The surest road to happiness is not the path through rule nor through servitude, but through liberty. | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Xenophon - Memorabilia of Socrates 2.1.9 | |
| A reaction: The great anarchist slogan. Personally I don't believe it, because I agree a little with Hobbes that authority is required to make cooperation flourish, and that is essential for full happiness. If I were a slave, I would agree with Aristippus. |
| 3018 | People who object to extravagant pleasures just love money [Aristippus elder, by Diog. Laertius] |
| Full Idea: When blamed for buying expensive food he asked "Would you have bought it for just three obols?" When the person said yes, he said,"Then it is not that I am fond of pleasure, but that you are fond of money". | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.4 |
| 1751 | Pleasure is the good, because we always seek it, it satisfies us, and its opposite is the most avoidable thing [Aristippus elder, by Diog. Laertius] |
| Full Idea: Pleasure is the good because we desire it from childhood, when we have it we seek nothing further, and the most avoidable thing is its opposite, pain. | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.8 |
| 1755 | Errors result from external influence, and should be corrected, not hated [Aristippus elder, by Diog. Laertius] |
| Full Idea: Errors ought to meet with pardon, for a man does not err intentionally, but influenced by some external circumstances. We should not hate someone who has erred, but teach him better. | |
| From: report of Aristippus the elder (fragments/reports [c.395 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.9 |
| 4872 | Most people see an abortion differently if the foetus lacks a brain [Dennett] |
| Full Idea: If a fetus that is being considered for abortion is known to be anencephalic (lacking a brain), this dramatically changes the issue for most people, though not for all. | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.1) | |
| A reaction: A very effective point, as it is hard to see what grounds could be given for not aborting in this case. But the brain then clearly becomes the focus of why abortion is often rejected by many people. |
| 4877 | Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett] |
| Full Idea: Might plants just be 'very slow animals', enjoying sentience that has been overlooked by us because of our human timescale chauvinism? | |
| From: Daniel C. Dennett (Kinds of Minds [1996], Ch.3) | |
| A reaction: Delightful thought, arising from pondering the significance of the speed of operation of the brain. I think it is false, because I think high speed is essential to mind, and Dennett seems not to. |