22 ideas
| 10061 | The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave] |
| Full Idea: The If-thenist view seems to apply straightforwardly only to the axiomatised portions of mathematics. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: He cites Lakatos to show that cutting-edge mathematics is never axiomatised. One might reply that if the new mathematics is any good then it ought to be axiomatis-able (barring Gödelian problems). |
| 10065 | Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave] |
| Full Idea: If we identify logic with first-order logic, and mathematics with the collection of first-order theories, then maybe we can continue to maintain the If-thenist position. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: The problem is that If-thenism must rely on rules of inference. That seems to mean that what is needed is Soundness, rather than Completeness. That is, inference by the rules must work properly. |
| 14235 | Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile] |
| Full Idea: If the rule is asserted 'Given any well-determined objects, they can be collected into a set by an application of the 'set of' operation', then on the usual account of 'they' this is a tautology. Collection comes automatically with this form of reference. | |
| From: James Cargile (Paradoxes: Form and Predication [1979], p.115), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? Intro | |
| A reaction: Is this a problem? Given they are well-determined (presumably implying countable) there just is a set of them. That's what set theory is, I thought. Of course, the iterative view talks of 'constructing' the sets, but the construction looks unstoppable. |
| 10049 | Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave] |
| Full Idea: Containing only logical notions is not a necessary condition for being a logical truth, since a logical truth such as 'all men are men' may contain non-logical notions such as 'men'. | |
| From: Alan Musgrave (Logicism Revisited [1977], §3) | |
| A reaction: [He attributes this point to Russell] Maybe it is only a logical truth in its general form, as ∀x(x=x). Of course not all 'banks' are banks. |
| 10050 | A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave] |
| Full Idea: The standard modern view of logical truth is that a statement is logically true if it comes out true in all interpretations in all (non-empty) domains. | |
| From: Alan Musgrave (Logicism Revisited [1977], §3) |
| 10058 | No two numbers having the same successor relies on the Axiom of Infinity [Musgrave] |
| Full Idea: The axiom of Peano which states that no two numbers have the same successor requires the Axiom of Infinity for its proof. | |
| From: Alan Musgrave (Logicism Revisited [1977], §4 n) | |
| A reaction: [He refers to Russell 1919:131-2] The Axiom of Infinity is controversial and non-logical. |
| 10062 | Formalism seems to exclude all creative, growing mathematics [Musgrave] |
| Full Idea: Formalism seems to exclude from consideration all creative, growing mathematics. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: [He cites Lakatos in support] I am not immediately clear why spotting the remote implications of a formal system should be uncreative. The greatest chess players are considered to be highly creative and imaginative. |
| 10063 | Formalism is a bulwark of logical positivism [Musgrave] |
| Full Idea: Formalism is a bulwark of logical positivist philosophy. | |
| From: Alan Musgrave (Logicism Revisited [1977], §5) | |
| A reaction: Presumably if you drain all the empirical content out of arithmetic and geometry, you are only left with the bare formal syntax, of symbols and rules. That seems to be as analytic as you can get. |
| 5791 | Reduction is either by elimination, or by explanation [Searle] |
| Full Idea: One sense of 'reduction' is eliminative, in getting rid of a phenomenon by showing that it is really something else (as the earth's rotation eliminates 'sunsets'), but another sense does not get rid of it (as in the explanation of solidity by molecules). | |
| From: John Searle (The Mystery of Consciousness [1997], Ch.2) | |
| A reaction: These are bad analogies. You can't 'eliminate' a sunset - you just accept that the event is relative to a viewpoint. If we are discussing ontology, we will not admit the existence of sunsets, but we won't have an ontological category of 'solidity' either. |
| 5799 | Eliminative reduction needs a gap between appearance and reality, as in sunsets [Searle] |
| Full Idea: Eliminative reductions require a distinction between reality and appearance; for example, the sun appears to set but the reality is that the earth rotates. | |
| From: John Searle (The Mystery of Consciousness [1997], Concl 2.10) | |
| A reaction: A bad analogy. You don't 'eliminate' sunsets. It is just 'Galilean' relativity - you thought it was your train moving, then you discover it was the other one. You don't eliminate hallucinations when you show that they don't correspond to reality. |
| 5790 | A property is 'emergent' if it is caused by elements of a system, when the elements lack the property [Searle] |
| Full Idea: An emergent property of a system is causally explained by elements of the system, but it is not a property of the elements, and cannot be explained by a summation of their properties. The behaviour of H2O explains liquidity, but molecules aren't liquid. | |
| From: John Searle (The Mystery of Consciousness [1997], Ch.1) | |
| A reaction: The genie is 'emergent' from the lamp, and so (in Searle's meaning) is the lamp's solidity. I agree that the mind is 'emergent' in Searle's very weak sense, if that only means that one neuron can't be conscious, but lots together can. |
| 5792 | Explanation of how we unify our mental stimuli into a single experience is the 'binding problem' [Searle] |
| Full Idea: The 'binding problem' is how to explain how the brain binds all our different stimuli into a single unified experience of an object. | |
| From: John Searle (The Mystery of Consciousness [1997], Ch.2) | |
| A reaction: This may be the best way of expressing what philosophers call (after Chalmers) the 'Hard Question'. Large objects are held together by gravity, and small objects by electro-magnetism. We don't see a 'binding problem' in the function of a leaf. |
| 5786 | A system is either conscious or it isn't, though the intensity varies a lot [Searle] |
| Full Idea: A system is either conscious or it isn't, but within the field of consciousness there are states of intensity ranging from drowsiness to full awareness. | |
| From: John Searle (The Mystery of Consciousness [1997], Ch.1) | |
| A reaction: I think this all-or-nothing view is the last vestiges of Cartesian dualism, and is quite wrong. Heaps of neuroscience (about blindsight, subliminal awareness, neurosis etc.) says we will never understand the mind if we think it is only the conscious part. |
| 5794 | Consciousness has a first-person ontology, which only exists from a subjective viewpoint [Searle] |
| Full Idea: Consciousness has a first-person or subjective ontology, by which I mean that conscious states only exist when experienced by a subject and they exist only from the first-person point of view of that subject. | |
| From: John Searle (The Mystery of Consciousness [1997], Ch.5 App) | |
| A reaction: I think this is nonsense, and I don't think Searle believes it. He ruthlessly attacks so-called 'eliminativists', but the definition he gives here would make him an eliminativist about other minds. There is no such thing as 'first-person' ontology. |
| 5795 | There isn't one consciousness (information-processing) which can be investigated, and another (phenomenal) which can't [Searle] |
| Full Idea: There are not two kinds of consciousness, an information-processing consciousness that is amenable to scientific investigation and a phenomenal, what-it-subjectively-feels-like form of consciousness that will forever remain mysterious. | |
| From: John Searle (The Mystery of Consciousness [1997], Concl.1) | |
| A reaction: Fodor appears to be the main target of this remark. The view that we can explain intentionality but not qualia is currently very fashionable. I am sympathetic to Searle here. Consciousness isn't an epiphenomenon, it is essential to all thought. |
| 5788 | The use of 'qualia' seems to imply that consciousness and qualia are separate [Searle] |
| Full Idea: I am hesitant to use the word 'quale/qualia', because it gives the impression that there are two separate phenomena, consciousness and qualia. | |
| From: John Searle (The Mystery of Consciousness [1997], Ch.1) | |
| A reaction: He is trying to resist going back to 'sense-data', sitting uneasily between reality and our experience of it. Personally I am quite happy with qualia as an aspect of consciousness - just as I am happy with consciousness as an 'aspect' of brain. |
| 5789 | I now think syntax is not in the physics, but in the eye of the beholder [Searle] |
| Full Idea: It seems to me now that syntax is not intrinsic to the physics of the system, but is in the eye of the beholder. | |
| From: John Searle (The Mystery of Consciousness [1997], Ch.1) | |
| A reaction: This seems right, in that whether strung beads are a toy or an abacus depends on the user. It doesn't follow that the 'beholder' stands outside the physics. A beholder is another physical system, of a particular type of high complexity. |
| 5798 | Consciousness has a first-person ontology, so it cannot be reduced without omitting something [Searle] |
| Full Idea: Consciousness has a first-person or subjective ontology and so cannot be reduced to anything that has third-person or objective ontology. If you try to reduce or eliminate one in favour of the other you leave something out. | |
| From: John Searle (The Mystery of Consciousness [1997], Concl 2.10) | |
| A reaction: Misconceived. There is no such thing as 'first-person' ontology, though there are subjective viewpoints, but then a camera has a viewpoint which is lost if you eliminate it. If consciousness is physical events, that leaves viewpoints untouched. |
| 5787 | There is non-event causation between mind and brain, as between a table and its solidity [Searle] |
| Full Idea: The solidity of a table is explained causally by the behaviour of the molecules of which it is composed, but the solidity is not an extra event, it is just a feature of the table. This non-event causation models the relationship of mind and brain. | |
| From: John Searle (The Mystery of Consciousness [1997], Ch.1) | |
| A reaction: He calls it 'non-event' causation, while referring to the 'behaviour of molecules'. Ask a physicist what a 'feature' is. Better to think of it as one process 'emerging' as another process at the macro-level. |
| 5797 | The pattern of molecules in the sea is much more complex than the complexity of brain neurons [Searle] |
| Full Idea: The pattern of molecules in the ocean is vastly more complex than any pattern of neurons in my brain. | |
| From: John Searle (The Mystery of Consciousness [1997], Concl 2.6) | |
| A reaction: A nice warning for anyone foolish enough to pin their explanatory hopes simply on 'complexity', but we would not be so foolish. A subtler account of complexity (e.g. by Edelman and Tononi) might make brains much more complex than oceans. |
| 5796 | If tree rings contain information about age, then age contains information about rings [Searle] |
| Full Idea: You could say that tree-rings contain information about the age of a tree, but you could as well say that the age of a tree in years contains information about the number of rings in a tree stump. ..'Information' is not a real causal feature of the world. | |
| From: John Searle (The Mystery of Consciousness [1997], Concl 2.5) | |
| A reaction: A nice point for fans of 'information' to ponder. However, you cannot deny the causal connection between the age and the rings. Information has a subjective aspect, but you cannot, for example, eliminate the role of DNA in making organisms. |
| 10060 | Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave] |
| Full Idea: Logical positivists did not adopt old-style logicism, but rather logicism spiced with varying doses of If-thenism. | |
| From: Alan Musgrave (Logicism Revisited [1977], §4) | |
| A reaction: This refers to their account of mathematics as a set of purely logical truths, rather than being either empirical, or a priori synthetic. |