23 ideas
| 19456 | Philosophy is distinguished from other sciences by its complete lack of presuppositions [Feuerbach] |
| Full Idea: Philosophy does not presuppose anything. It is precisely in this fact of non-presupposition that its beginning lies - a beginning by virtue of which it is set apart from all the other sciences. | |
| From: Ludwig Feuerbach (On 'The Beginning of Philosophy' [1841], p.135) | |
| A reaction: Most modern philosophers seem to laugh at such an idea, because everything is theory-laden, culture-laden, language-laden etc. As an aspiration I love it, and think good philosophers get quite close to the goal (which, I admit, is not fully attainable). |
| 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. |
| 2590 | Dispositions need mental terms to define them [Putnam] |
| Full Idea: The chief difficulty with the behaviour-disposition account is the virtual impossibility of specifying a disposition except as a 'disposition of x to behave as though x were in pain'. | |
| From: Hilary Putnam (The Nature of Mental States [1968], p.57) | |
| A reaction: This has become the best-known objection to behaviourism - that you can't specify a piece of behaviour clearly unless you mention the mental state which it is expressing. The defence is to go on endlessly mentioning further behaviour. |
| 2591 | Total paralysis would mean that there were mental states but no behaviour at all [Putnam] |
| Full Idea: Two animals with all motor nerves cut will have the same actual and potential behaviour (i.e. none), but if only one has uncut pain fibres, it will feel pain where the other won't. | |
| From: Hilary Putnam (The Nature of Mental States [1968], p.57) | |
| A reaction: This is a splendidly literal and practical argument against behaviourism - if you prevent all the behaviour, you don't thereby prevent the experience. Clearly we have to say something about what is inside the 'black box' of the mind. |
| 2588 | Is pain a functional state of a complete organism? [Putnam] |
| Full Idea: I propose the hypothesis that pain, or the state of being in pain, is a functional state of a whole organism. | |
| From: Hilary Putnam (The Nature of Mental States [1968], p.54) | |
| A reaction: This sounds wrong right from the start. Pain hurts. The fact that it leads to avoidance behaviour etc. seems much more like a by-product of pain than its essence. |
| 2589 | Functionalism is compatible with dualism, as pure mind could perform the functions [Putnam] |
| Full Idea: The functional-state hypothesis is not incompatible with dualism, as a system consisting of a body and a soul could meet the required conditions. | |
| From: Hilary Putnam (The Nature of Mental States [1968], p.55) | |
| A reaction: He doesn't really believe this, of course. This claim led to all the weak objections to functionalism involving silly implementations of minds. A brain is the only plausible way to implement our mental functions. |
| 2592 | Functional states correlate with AND explain pain behaviour [Putnam] |
| Full Idea: The presence of a certain functional state is not merely 'correlated with' but actually explains the pain behaviour on the part of the organism. | |
| From: Hilary Putnam (The Nature of Mental States [1968], p.58) | |
| A reaction: Does it offer any further explanation beyond saying that it is the brain state that causes the behaviour? The pain is just a link between damage and avoidance. I wish that is all that pain was. |
| 2587 | Temperature is mean molecular kinetic energy, but they are two different concepts [Putnam] |
| Full Idea: The concept of temperature is not the same as the concept of mean molecular kinetic energy. But temperature is mean molecular kinetic energy. | |
| From: Hilary Putnam (The Nature of Mental States [1968], p.52) | |
| A reaction: This is the standard analogy for mind-brain identity, and it seems fair enough to me. The mind is the activity of the brain. It is rather unhelpful to think of weather in terms of chemistry, but it is actions of chemicals. |
| 6376 | Neuroscience does not support multiple realisability, and tends to support identity [Polger on Putnam] |
| Full Idea: Putnam was too quick to assert neuroscientific support for multiple realizability; current evidence does not reveal it, and there is some reason to think the enterprises of neuroscience are premised on the hypothesis of brain-state identity. | |
| From: comment on Hilary Putnam (The Nature of Mental States [1968]) by Thomas W. Polger - Natural Minds Ch.1.4 | |
| A reaction: I have always been suspicious of the glib claim that mental states were multiply realisable. I see no reason to think that octupi see colours as we do, or experience fear as we do, even though their behaviour has to be similar, for survival. |
| 2330 | If humans and molluscs both feel pain, it can't be a single biological state [Putnam, by Kim] |
| Full Idea: Mental states have vastly diverse physical/biological realizations in different species and structures (e.g. pain in humans and in molluscs), so no mental state can be identified with any single physical/biological state. | |
| From: report of Hilary Putnam (The Nature of Mental States [1968]) by Jaegwon Kim - Mind in a Physical World n p.120 | |
| A reaction: But maybe mollusc and human nervous systems ARE the same in the respects that matter. We don't know enough about pain to deny that possibility. |