16 ideas
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 3291 | Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel] |
| Full Idea: The supposition that a diamond or organism should truly have emergent properties is that they appear at certain complex levels of organisation, but are not explainable (even in principle) in terms of any more fundamental properties of the system. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |
| 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. |
| 3290 | Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel] |
| Full Idea: Given what heat is and what water is, it is literally impossible for water to be heated beyond a certain point at normal atmospheric pressure without boiling. | |
| From: Thomas Nagel (Panpsychism [1979], p.186) |