71 ideas
| 18137 | Impredicative definitions are wrong, because they change the set that is being defined? [Bostock] |
| Full Idea: Poincaré suggested that what is wrong with an impredicative definition is that it allows the set defined to alter its composition as more sets are added to the theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 18122 | Classical interdefinitions of logical constants and quantifiers is impossible in intuitionism [Bostock] |
| Full Idea: None of the classical ways of defining one logical constant in terms of others is available in intuitionist logic (and this includes the two quantifiers). | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18114 | There is no single agreed structure for set theory [Bostock] |
| Full Idea: There is so far no agreed set of axioms for set theory which is categorical, i.e. which does pick just one structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: This contrasts with Peano Arithmetic, which is categorical in its second-order version. |
| 18107 | A 'proper class' cannot be a member of anything [Bostock] |
| Full Idea: A 'proper class' cannot be a member of anything, neither of a set nor of another proper class. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18115 | We could add axioms to make sets either as small or as large as possible [Bostock] |
| Full Idea: We could add the axiom that all sets are constructible (V = L), making the universe of sets as small as possible, or add the axiom that there is a supercompact cardinal (SC), making the universe as large as we no know how to. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: Bostock says most mathematicians reject the first option, and are undecided about the second option. |
| 18139 | The Axiom of Choice relies on reference to sets that we are unable to describe [Bostock] |
| Full Idea: The usual accounts of ZF are not restricted to subsets that we can describe, and that is what justifies the axiom of choice. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4 n36) | |
| A reaction: This contrasts interestingly with predicativism, which says we can only discuss things which we can describe or define. Something like verificationism hovers in the background. |
| 18105 | Replacement enforces a 'limitation of size' test for the existence of sets [Bostock] |
| Full Idea: The Axiom of Replacement (or the Axiom of Subsets, 'Aussonderung', Fraenkel 1922) in effect enforces the idea that 'limitation of size' is a crucial factor when deciding whether a proposed set or does not not exist. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) |
| 18108 | First-order logic is not decidable: there is no test of whether any formula is valid [Bostock] |
| Full Idea: First-order logic is not decidable. That is, there is no test which can be applied to any arbitrary formula of that logic and which will tell one whether the formula is or is not valid (as proved by Church in 1936). | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18109 | The completeness of first-order logic implies its compactness [Bostock] |
| Full Idea: From the fact that the usual rules for first-level logic are complete (as proved by Gödel 1930), it follows that this logic is 'compact'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) | |
| A reaction: The point is that the completeness requires finite proofs. |
| 18123 | Substitutional quantification is just standard if all objects in the domain have a name [Bostock] |
| Full Idea: Substitutional quantification and quantification understood in the usual 'ontological' way will coincide when every object in the (ontological) domain has a name. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.3 n23) |
| 18120 | The Deduction Theorem is what licenses a system of natural deduction [Bostock] |
| Full Idea: The Deduction Theorem is what licenses a system of 'natural deduction' in the first place. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) |
| 18125 | Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock] |
| Full Idea: Berry's Paradox can be put in this form, by considering the alleged name 'The least number not named by this name'. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) |
| 18101 | Each addition changes the ordinality but not the cardinality, prior to aleph-1 [Bostock] |
| Full Idea: If you add to the ordinals you produce many different ordinals, each measuring the length of the sequence of ordinals less than it. They each have cardinality aleph-0. The cardinality eventually increases, but we can't say where this break comes. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) |
| 18100 | ω + 1 is a new ordinal, but its cardinality is unchanged [Bostock] |
| Full Idea: If we add ω onto the end of 0,1,2,3,4..., it then has a different length, of ω+1. It has a different ordinal (since it can't be matched with its first part), but the same cardinal (since adding 1 makes no difference). | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: [compressed] The ordinals and cardinals coincide up to ω, but this is the point at which they come apart. |
| 18102 | A cardinal is the earliest ordinal that has that number of predecessors [Bostock] |
| Full Idea: It is the usual procedure these days to identify a cardinal number with the earliest ordinal number that has that number of predecessors. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: This sounds circular, since you need to know the cardinal in order to decide which ordinal is the one you want, but, hey, what do I know? |
| 18106 | Aleph-1 is the first ordinal that exceeds aleph-0 [Bostock] |
| Full Idea: The cardinal aleph-1 is identified with the first ordinal to have more than aleph-0 members, and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.4) | |
| A reaction: That is, the succeeding infinite ordinals all have the same cardinal number of members (aleph-0), until the new total is triggered (at the number of the reals). This is Continuum Hypothesis territory. |
| 18095 | Instead of by cuts or series convergence, real numbers could be defined by axioms [Bostock] |
| Full Idea: In addition to cuts, or converging series, Cantor suggests we can simply lay down a set of axioms for the real numbers, and this can be done without any explicit mention of the rational numbers [note: the axioms are those for a complete ordered field]. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: It is interesting when axioms are best, and when not. Set theory depends entirely on axioms. Horsten and Halbach are now exploring treating truth as axiomatic. You don't give the 'nature' of the thing - just rules for its operation. |
| 18099 | The number of reals is the number of subsets of the natural numbers [Bostock] |
| Full Idea: It is not difficult to show that the number of the real numbers is the same as the number of all the subsets of the natural numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.5) | |
| A reaction: The Continuum Hypothesis is that this is the next infinite number after the number of natural numbers. Why can't there be a number which is 'most' of the subsets of the natural numbers? |
| 18093 | For Eudoxus cuts in rationals are unique, but not every cut makes a real number [Bostock] |
| Full Idea: As Eudoxus claimed, two distinct real numbers cannot both make the same cut in the rationals, for any two real numbers must be separated by a rational number. He did not say, though, that for every such cut there is a real number that makes it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4) | |
| A reaction: This is in Bostock's discussion of Dedekind's cuts. It seems that every cut is guaranteed to produce a real. Fine challenges the later assumption. |
| 18110 | Infinitesimals are not actually contradictory, because they can be non-standard real numbers [Bostock] |
| Full Idea: Non-standard natural numbers will yield non-standard rational and real numbers. These will include reciprocals which will be closer to 0 than any standard real number. These are like 'infinitesimals', so that notion is not actually a contradiction. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18156 | Modern axioms of geometry do not need the real numbers [Bostock] |
| Full Idea: A modern axiomatisation of geometry, such as Hilbert's (1899), does not need to claim the existence of real numbers anywhere in its axioms. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.ii) | |
| A reaction: This is despite the fact that geometry is reduced to algebra, and the real numbers are the equivalent of continuous lines. Bostock votes for a Greek theory of proportion in this role. |
| 18097 | The Peano Axioms describe a unique structure [Bostock] |
| Full Idea: The Peano Axioms are categorical, meaning that they describe a unique structure. | |
| From: David Bostock (Philosophy of Mathematics [2009], 4.4 n20) | |
| A reaction: So if you think there is nothing more to the natural numbers than their structure, then the Peano Axioms give the essence of arithmetic. If you think that 'objects' must exist to generate a structure, there must be more to the numbers. |
| 18148 | Hume's Principle is a definition with existential claims, and won't explain numbers [Bostock] |
| Full Idea: Hume's Principle will not do as an implicit definition because it makes a positive claim about the size of the universe (which no mere definition can do), and because it does not by itself explain what the numbers are. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18145 | Many things will satisfy Hume's Principle, so there are many interpretations of it [Bostock] |
| Full Idea: Hume's Principle gives a criterion of identity for numbers, but it is obvious that many other things satisfy that criterion. The simplest example is probably the numerals (in any notation, decimal, binary etc.), giving many different interpretations. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18149 | There are many criteria for the identity of numbers [Bostock] |
| Full Idea: There is not just one way of giving a criterion of identity for numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18143 | Frege makes numbers sets to solve the Caesar problem, but maybe Caesar is a set! [Bostock] |
| Full Idea: The Julius Caesar problem was one reason that led Frege to give an explicit definition of numbers as special sets. He does not appear to notice that the same problem affects his Axiom V for introducing sets (whether Caesar is or is not a set). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: The Julius Caesar problem is a sceptical acid that eats into everything in philosophy of mathematics. You give all sorts of wonderful accounts of numbers, but at what point do you know that you now have a number, and not something else? |
| 18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
| Full Idea: There is no ground for saying that a number IS a position, if the truth is that there is nothing to determine which number is which position. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.4) | |
| A reaction: If numbers lose touch with the empirical ability to count physical objects, they drift off into a mad world where they crumble away. |
| 18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
| Full Idea: Structuralism begins from a false premise, namely that numbers have no properties other than their relations to other numbers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 6.5) | |
| A reaction: Well said. Describing anything purely relationally strikes me as doomed, because you have to say why those things relate in those ways. |
| 18141 | Nominalism about mathematics is either reductionist, or fictionalist [Bostock] |
| Full Idea: Nominalism has two main versions, one which tries to 'reduce' the objects of mathematics to something simpler (Russell and Wittgenstein), and another which claims that such objects are mere 'fictions' which have no reality (Field). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9) |
| 18157 | Nominalism as based on application of numbers is no good, because there are too many applications [Bostock] |
| Full Idea: The style of nominalism which aims to reduce statements about numbers to statements about their applications does not work for the natural numbers, because they have many applications, and it is arbitrary to choose just one of them. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5.iii) |
| 18150 | Actual measurement could never require the precision of the real numbers [Bostock] |
| Full Idea: We all know that in practice no physical measurement can be 100 per cent accurate, and so it cannot require the existence of a genuinely irrational number, rather than some of the rational numbers close to it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.3) |
| 18158 | Ordinals are mainly used adjectively, as in 'the first', 'the second'... [Bostock] |
| Full Idea: The basic use of the ordinal numbers is their use as ordinal adjectives, in phrases such as 'the first', 'the second' and so on. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: That is because ordinals seem to attach to particulars, whereas cardinals seem to attach to groups. Then you say 'three is greater than four', it is not clear which type you are talking about. |
| 18127 | Simple type theory has 'levels', but ramified type theory has 'orders' [Bostock] |
| Full Idea: The simple theory of types distinguishes sets into different 'levels', but this is quite different from the distinction into 'orders' which is imposed by the ramified theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.1) | |
| A reaction: The ramified theory has both levels and orders (p.235). Russell's terminology is, apparently, inconsistent. |
| 18144 | Neo-logicists agree that HP introduces number, but also claim that it suffices for the job [Bostock] |
| Full Idea: The neo-logicists take up Frege's claim that Hume's Principle introduces a new concept (of a number), but unlike Frege they go on to claim that it by itself gives a complete account of that concept. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: So the big difference between Frege and neo-logicists is the Julius Caesar problem. |
| 18147 | Neo-logicists meet the Caesar problem by saying Hume's Principle is unique to number [Bostock] |
| Full Idea: The response of neo-logicists to the Julius Caesar problem is to strengthen Hume's Principle in the hope of ensuring that only numbers will satisfy it. They say the criterion of identity provided by HP is essential to number, and not to anything else. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) |
| 18146 | If Hume's Principle is the whole story, that implies structuralism [Bostock] |
| Full Idea: If Hume's Principle is all we are given, by way of explanation of what the numbers are, the only conclusion to draw would seem to be the structuralists' conclusion, ...studying all systems that satisfy that principle. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.A.2) | |
| A reaction: Any approach that implies a set of matching interpretations will always imply structuralism. To avoid it, you need to pin the target down uniquely. |
| 18129 | Many crucial logicist definitions are in fact impredicative [Bostock] |
| Full Idea: Many of the crucial definitions in the logicist programme are in fact impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) |
| 18111 | Treating numbers as objects doesn't seem like logic, since arithmetic fixes their totality [Bostock] |
| Full Idea: If logic is neutral on the number of objects there are, then logicists can't construe numbers as objects, for arithmetic is certainly not neutral on the number of numbers there are. They must be treated in some other way, perhaps as numerical quantifiers. | |
| From: David Bostock (Philosophy of Mathematics [2009], 5.5) |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| Full Idea: In its higher reaches, which posit sets of huge cardinalities, set theory is just a fairy story. | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.5.iii) | |
| A reaction: You can't say the higher reaches are fairy stories but the lower reaches aren't, if the higher is directly derived from the lower. The empty set and the singleton are fairy stories too. Bostock says the axiom of infinity triggers the fairy stories. |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| Full Idea: A common view is that although a fairy tale may provide very useful predictions, it cannot provide explanations for why things happen as they do. In order to do that a theory must also be true (or, at least, an approximation to the truth). | |
| From: David Bostock (Philosophy of Mathematics [2009], 9.B.5) | |
| A reaction: Of course, fictionalism offers an explanation of mathematics as a whole, but not of the details (except as the implications of the initial fictional assumptions). |
| 18140 | The best version of conceptualism is predicativism [Bostock] |
| Full Idea: In my personal opinion, predicativism is the best version of conceptualism that we have yet discovered. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: Since conceptualism is a major player in the field, this makes predicativism a very important view. I won't vote Predicativist quite yet, but I'm tempted. |
| 18138 | Conceptualism fails to grasp mathematical properties, infinity, and objective truth values [Bostock] |
| Full Idea: Three simple objections to conceptualism in mathematics are that we do not ascribe mathematical properties to our ideas, that our ideas are presumably finite, and we don't think mathematics lacks truthvalue before we thought of it. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.4) | |
| A reaction: [compressed; Bostock refers back to his Ch 2] Plus Idea 18134. On the whole I sympathise with conceptualism, so I will not allow myself to be impressed by any of these objections. (So, what's actually wrong with them.....?). |
| 18131 | If abstracta only exist if they are expressible, there can only be denumerably many of them [Bostock] |
| Full Idea: If an abstract object exists only when there is some suitable way of expressing it, then there are at most denumerably many abstract objects. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.2) | |
| A reaction: Fine by me. What an odd view, to think there are uncountably many abstract objects in existence, only a countable portion of which will ever be expressed! [ah! most people agree with me, p.243-4] |
| 18134 | Predicativism makes theories of huge cardinals impossible [Bostock] |
| Full Idea: Classical mathematicians say predicative mathematics omits areas of great interest, all concerning non-denumerable real numbers, such as claims about huge cardinals. There cannot be a predicative version of this theory. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I'm not sure that anyone will really miss huge cardinals if they are prohibited, though cryptography seems to flirt with such things. Are we ever allowed to say that some entity conjured up by mathematicians is actually impossible? |
| 18135 | If mathematics rests on science, predicativism may be the best approach [Bostock] |
| Full Idea: It has been claimed that only predicative mathematics has a justification through its usefulness to science (an empiricist approach). | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [compressed. Quine is the obvious candidate] I suppose predicativism gives your theory roots, whereas impredicativism is playing an abstract game. |
| 18136 | If we can only think of what we can describe, predicativism may be implied [Bostock] |
| Full Idea: If we accept the initial idea that we can think only of what we ourselves can describe, then something like the theory of predicativism quite naturally results | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: I hate the idea that we can only talk of what falls under a sortal, but 'what we can describe' is much more plausible. Whether or not you agree with this approach (I'm pondering it), this makes predicativism important. |
| 18132 | The predicativity restriction makes a difference with the real numbers [Bostock] |
| Full Idea: It is with the real numbers that the restrictions imposed by predicativity begin to make a real difference. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) |
| 18133 | The usual definitions of identity and of natural numbers are impredicative [Bostock] |
| Full Idea: The predicative approach cannot accept either the usual definition of identity or the usual definition of the natural numbers, for both of these definitions are impredicative. | |
| From: David Bostock (Philosophy of Mathematics [2009], 8.3) | |
| A reaction: [Bostock 237-8 gives details] |
| 4938 | Prior to language, concepts are universals created by self-mapping of brain activity [Edelman/Tononi] |
| Full Idea: Before language is present, concepts depend on the brain's ability to construct 'universals' through higher-order mapping of the activity of the brain's own perceptual and motor maps. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.15) | |
| A reaction: It should be of great interest to philosophers that one can begin to give a neuro-physiological account of universals. A physical system can be ordered as a database, and universals are the higher branches of a tree-structure of information. |
| 4934 | Cultures have a common core of colour naming, based on three axes of colour pairs [Edelman/Tononi] |
| Full Idea: We seem to have a set of colour axes (red-green, blue-yellow, and light-dark). Color naming in different cultures tend to have universal categories based on these axes, with a few derived or composite categories (e.g. orange, purple, pink, brown, grey). | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.13) | |
| A reaction: This confirms my view of all supposed relativism: that there are degrees of cultural and individual relativism possible, but it is daft to think this goes all the way down, as nature has 'joints', and our minds are part of nature. |
| 4924 | A conscious human being rapidly reunifies its mind after any damage to the brain [Edelman/Tononi] |
| Full Idea: It seems that after a massive stroke or surgical resection, a conscious human being is rapidly "resynthesised" or reunified within the limits of a solipsistic universe that, to outside appearances, is warped and restricted. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch. 3) | |
| A reaction: Note that there are two types of 'unity of mind'. This comment refers to the unity of seeing oneself as a single person, rather than the smooth unbroken quality of conscious experience. I presume that there is no point in a mind without the first unity. |
| 4932 | A conscious state endures for about 100 milliseconds, known as the 'specious present' [Edelman/Tononi] |
| Full Idea: The 'specious present' (William James), a rough estimate of the duration of a single conscious state, is of the order of 100 milliseconds, meaning that conscious states can change very rapidly. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.12) | |
| A reaction: A vital feature of our subjective experience of time. I wonder what the figure is for a fly? It suggests that conscious experience really is like a movie film, composed of tiny independent 'frames' of very short duration. |
| 4931 | Consciousness is a process (of neural interactions), not a location, thing, property, connectivity, or activity [Edelman/Tononi] |
| Full Idea: Consciousness is neither a thing, nor a simple property. ..The conscious 'dynamic core' of the brain is a process, not a thing or a place, and is defined in terms of neural interactions, not in terms of neural locations, connectivity or activity. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.12) | |
| A reaction: This must be of great interest to philosophers. Edelman is adamant that it is not any specific neurons. The nice question is: what would it be like to have your brain slowed down? Presumably we would experience steps in the process. Is he a functionalist? |
| 4923 | The three essentials of conscious experience are privateness, unity and informativeness [Edelman/Tononi] |
| Full Idea: The fundamental aspects of conscious experience that are common to all its phenomenological manifestations are: privateness, unity, and informativeness. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch. 3) | |
| A reaction: Interesting, coming from neuroscientists. The list strikes me as rather passive. It is no use having good radar if you can't make decisions. Privacy and unity are overrated. Who gets 'informed'? Personal identity must be basic. |
| 4941 | Consciousness can create new axioms, but computers can't do that [Edelman/Tononi] |
| Full Idea: Conscious human thought can create new axioms, which a computer cannot do. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.17) | |
| A reaction: A nice challenge for the artificial intelligence community! I don't understand their confidence in making this assertion. Nothing in Gödel's Theorem seems to prevent the reassignment of axioms, and Quine implies that it is an easy and trivial game. |
| 4930 | Consciousness arises from high speed interactions between clusters of neurons [Edelman/Tononi] |
| Full Idea: Our hypothesis is that the activity of a group of neurons can contribute directly to conscious experience if it is part of a functional cluster, characterized by strong interactions among a set of neuronal groups over a period of hundreds of milliseconds. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.12) | |
| A reaction: This is their 'dynamic core' hypothesis. It doesn't get at the Hard Questions about consciousness, but this is a Nobel prize winner hot on the trail of the location of the action. It gives support to functionalism, because the neurons vary. |
| 4929 | Dreams and imagery show the brain can generate awareness and meaning without input [Edelman/Tononi] |
| Full Idea: Dreaming and imagery are striking phenomenological demonstrations that the adult brain can spontaneously and intrinsically produce consciousness and meaning without any direct input from the periphery. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.11) | |
| A reaction: This offers some support for Searle's claim that brain's produce 'intrinsic' (rather than 'derived') intentionality. Of course, one can have a Humean impressions/ideas theory about how the raw material got there. We SEE meaning in our experiences. |
| 4940 | Physicists see information as a measure of order, but for biologists it is symbolic exchange between animals [Edelman/Tononi] |
| Full Idea: Physicists may define information as a measure of order in a far-from-equilibrium state, but it is best seen as a biological concept which emerged in evolution with animals that were capable of mutual symbolic exchange. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.17) | |
| A reaction: The physicists' definition seems to open the road to the possibility of non-conscious intentionality (Dennett), where the biological view seems to require consciousness of symbolic meanings (Searle). Tree-rings contain potential information? |
| 4935 | The sensation of red is a point in neural space created by dimensions of neuronal activity [Edelman/Tononi] |
| Full Idea: The pure sensation of red is a particular neural state identified by a point within the N-dimensional neural space defined by the integrated activity of all the group of neurons that constitute the dynamic core. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.13) | |
| A reaction: This hardly answers the Hard Question (why experience it? why that experience?), but it is interesting to see a neuroscientist fishing for an account of qualia. He says three types of neuron firing generate the dimensions of the 'space'. |
| 4936 | The self is founded on bodily awareness centred in the brain stem [Edelman/Tononi] |
| Full Idea: Structures in the brain stem map the state of the body and its relation to the environment, on the basis of signals with proprioceptive, kinesthetic, somatosensory and autonomic components. We may call these the dimensions of the proto-self. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.13) | |
| A reaction: It seems to me that there is no free will, but moral responsibility depends on the existence of a Self, and philosophers had better fight for it (are you listening, Hume?). Fortunately neuroscientists seem to endorse it fairly unanimously. |
| 4939 | A sense of self begins either internally, or externally through language and society [Edelman/Tononi] |
| Full Idea: Two extreme views on the development of the self are 'internalist' and 'externalist'. The first starts with a baby's subjective experience, and increasing differentiation as self-consciousness develops. The externalist view requires language and society. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.15) | |
| A reaction: Edelman rightly warns against this simple dichotomy, but if I have to vote, it is for internalism. I take a sense of self as basic to any mind, even a slug's. What is a mind for, if not to look after the creature? Self makes sensation into mind. |
| 4925 | Brains can initiate free actions before the person is aware of their own decision [Edelman/Tononi] |
| Full Idea: Libet concluded that the cerebral initiation of a spontaneous, freely voluntary act can begin unconsciously, that is, before there is any recallable awareness that a decision to act has already been initiated cerebrally. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch. 6) | |
| A reaction: We should accept this result. 'Free will' was always a bogus metaphysical concept (invented, I think, because God had to be above natural laws). A person is the source of responsibility, and is the controller of the brain, but not entirely conscious. |
| 4933 | Consciousness is a process, not a thing, as it maintains unity as its composition changes [Edelman/Tononi] |
| Full Idea: The conscious 'dynamic core' of the brain can maintain its unity over time even if its composition may be constantly changing, which is the signature of a process as opposed to a thing. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.12) | |
| A reaction: This is the functionalists' claim that the mind is 'multiply realisable', since different neurons can maintain the same process. 'Process' strikes me as a much better word than 'function'. These theories capture passive mental life better than active. |
| 4928 | Brain complexity balances segregation and integration, like a good team of specialists [Edelman/Tononi] |
| Full Idea: A theoretical analysis of complexity suggests that neuronal complexity strikes an optimum balance between segregation and integration, which fits the view of the brain as a collection of specialists who talk to each other a lot. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.11) | |
| A reaction: This is a theoretical point, but comes from a leading neuroscientist, and seems to endorse Fodor's modularity proposal. For a philosopher, one of the issues here is how to reconcile the segregation with the Cartesian unity and personal identity of a mind. |
| 4927 | Information-processing views of the brain assume the existence of 'information', and dubious brain codes [Edelman/Tononi] |
| Full Idea: So-called information-processing views of the brain have been criticized because they typically assume the existence in the world of previously defined information, and often assume the existence of precise neural codes for which there is no evidence. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.11) | |
| A reaction: Fodor is the target here. Searle is keen that 'intrinsic intentionality' is required to see something as 'information'. It is hard to see how anything acquires significance as it flows through a mechanical process. |
| 4922 | Consciousness involves interaction with persons and the world, as well as brain functions [Edelman/Tononi] |
| Full Idea: We emphatically do not identify consciousness in its full range as arising solely in the brain, since we believe that higher brain functions require interactions both with the world and with other persons. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Pref) | |
| A reaction: Would you gradually lose higher brain functions if you lived entirely alone? Intriguingly, this sounds like a neuroscientist asserting the necessity for broad content in order to understand the brain. |
| 5793 | Concepts and generalisations result from brain 'global mapping' by 'reentry' [Edelman/Tononi, by Searle] |
| Full Idea: When you get maps all over the brain signalling to each other by reentry you have what Edelman calls 'global mapping', and this allows the system not only to have perceptual categories and generalisation, but also to coordinate perception and action. | |
| From: report of G Edelman / G Tononi (Consciousness: matter becomes imagination [2000]) by John Searle - The Mystery of Consciousness Ch.3 | |
| A reaction: This is the nearest we have got to a proper scientific account of thought (as opposed to untested speculation about Turing machines). Something like this account must be right. A concept is a sustained process, not a static item. |
| 4926 | Concepts arise when the brain maps its own activities [Edelman/Tononi] |
| Full Idea: We propose that concepts arise from the mapping by the brain itself of the activity of the brain's own areas and regions. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch. 9) | |
| A reaction: Yes. One should add that the brain appears to be physically constructed with the logic of a filing system, which would mean that our concepts were labels for files within the system. Nature generates some of the files, and thinking creates the others. |
| 18121 | In logic a proposition means the same when it is and when it is not asserted [Bostock] |
| Full Idea: In Modus Ponens where the first premise is 'P' and the second 'P→Q', in the first premise P is asserted but in the second it is not. Yet it must mean the same in both premises, or it would be guilty of the fallacy of equivocation. | |
| From: David Bostock (Philosophy of Mathematics [2009], 7.2) | |
| A reaction: This is Geach's thought (leading to an objection to expressivism in ethics, that P means the same even if it is not expressed). |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 4937 | Systems that generate a sense of value are basic to the primitive brain [Edelman/Tononi] |
| Full Idea: Early and central in the development of the brain are the dimensions provided by value systems indicating salience for the entire organism. | |
| From: G Edelman / G Tononi (Consciousness: matter becomes imagination [2000], Ch.13) | |
| A reaction: This doesn't quite meet Hume's challenge to find values in the whole of nature, but it matches Charles Taylor's claim that for humans values are knowable a priori. Conditional values can be facts of the whole of nature. "If there is life, x has value..". |