31 ideas
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| Full Idea: The logic of ZF Set Theory is classical first-order predicate logic with identity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.121) | |
| A reaction: This logic seems to be unable to deal with very large cardinals, precisely those that are implied by set theory, so there is some sort of major problem hovering here. Boolos is fairly neutral. |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
| Full Idea: Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.130) | |
| A reaction: Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture. |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| Full Idea: The naïve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.127) | |
| A reaction: As clear a summary of Russell's Paradox as you could ever hope for. |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| Full Idea: According to the iterative conception, every set is formed at some stage. There is a relation among stages, 'earlier than', which is transitive. A set is formed at a stage if and only if its members are all formed before that stage. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.126) | |
| A reaction: He gives examples of the early stages, and says the conception is supposed to 'justify' Zermelo set theory. It is also supposed to make the axioms 'natural', rather than just being selected for convenience. And it is consistent. |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| Full Idea: The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless. |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| Full Idea: To the best of my knowledge nothing in mathematics or science requires the existence of very high orders of infinity. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.122) | |
| A reaction: He is referring to particular high orders of infinity implied by set theory. Personally I want to wield Ockham's Razor. Is being implied by set theory a sufficient reason to accept such outrageous entities into our ontology? |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| Full Idea: It is no surprise that we should be able to reason mathematically about many of the things we experience, for they are already 'abstract'. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: He has just given a list of exemplary abstract objects (Idea 10489), but I think there is a more interesting idea here - that our experience of actual physical objects is to some extent abstract, as soon as it is conceptualised. |
| 4913 | Brain lesions can erase whole categories of perception, suggesting they are hard-wired [Carter,R] |
| Full Idea: The discovery that a single brain lesion can erase all knowledge of man-made artefacts, or all knowledge of animals, suggests that these categories somehow hard-wired into the brain - that we all have a set of 'memory pigeonholes'. | |
| From: Rita Carter (Mapping the Mind [1998], p.190) | |
| A reaction: Presumably something can become 'hard-wired' through experience, rather than from birth. The whole idea of 'hard-wired' seems misleading about the brain. What matters is that the brain physically constructs categories. |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| Full Idea: It's a kind of lunacy to think that sound scientific philosophy demands that we think that we see ink-tracks but not words, i.e. word-types. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: This seems to link him with Armstrong's mockery of 'ostrich nominalism'. There seems to be some ambiguity with the word 'see' in this disagreement. When we look at very ancient scratches on stones, why don't we always 'see' if it is words? |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| Full Idea: I am rather a fan of abstract objects, and confident of their existence. Smaller numbers, sets and functions don't offend my sense of reality. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.128) | |
| A reaction: The great Boolos is rather hard to disagree with, but I disagree. Logicians love abstract objects, indeed they would almost be out of a job without them. It seems to me they smuggle them into our ontology by redefining either 'object' or 'exists'. |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| Full Idea: We twentieth century city dwellers deal with abstract objects all the time, such as bank balances, radio programs, software, newspaper articles, poems, mistakes, triangles. | |
| From: George Boolos (Must We Believe in Set Theory? [1997], p.129) | |
| A reaction: I find this claim to be totally question-begging, and typical of a logician. The word 'object' gets horribly stretched in these discussions. We can create concepts which have all the logical properties of objects. Maybe they just 'subsist'? |
| 4910 | Sense organs don't discriminate; they reduce various inputs to the same electrical pulses [Carter,R] |
| Full Idea: Despite their variety, each sense organ translates its stimulus into electrical pulses; rather than discriminating one type of input from another, the sense organs actually make them more alike. | |
| From: Rita Carter (Mapping the Mind [1998], p.174) | |
| A reaction: An illuminating observation, which modern 'naïve realists' should bear in mind. Secondary qualities are entirely unrelated to the nature of the input, and are merely 'what the brain decides to make of it'. Discrimination is in our neurons. |
| 4911 | The recognition sequence is: classify, name, locate, associate, feel [Carter,R, by PG] |
| Full Idea: The sequence of events in the brain for perceptual recognition is first identifying a rough class for the object, then a name, then a location, then some associations, and finally an emotion. | |
| From: report of Rita Carter (Mapping the Mind [1998], p.181) by PG - Db (ideas) | |
| A reaction: This seems to be one of those places where neuro-science trumps philosophy. You can't argue with empirical research, so philosophical theories had better adapt themselves to this sequence. The big modern discovery is the place of emotion in recognition. |
| 4919 | There seems to be no dividing line between a memory and a thought [Carter,R] |
| Full Idea: It has become clear from research that there is no clear dividing line between a memory and a thought. | |
| From: Rita Carter (Mapping the Mind [1998], p.308) | |
| A reaction: This always struck me as an obvious criticism of Descartes, when he claimed that memory was not an essential part of the 'thinking thing'. How can you think or understand without memory of the different phases of your thoughts? No memory, no mind! |
| 4908 | No one knows if animals are conscious [Carter,R] |
| Full Idea: No one knows if animals are conscious. | |
| From: Rita Carter (Mapping the Mind [1998], p.155) | |
| A reaction: This is a report from the front line of brain research, and should be born in mind when over-confident people make pronouncements about this topic. It strikes me as important to grasp that animals MIGHT not be conscious. |
| 4902 | Pain doesn't have one brain location, but is linked to attention and emotion [Carter,R] |
| Full Idea: Scans show there is no such thing as a pain centre; pain springs mainly from the activation of areas associated with attention and emotion. | |
| From: Rita Carter (Mapping the Mind [1998], p. 12) | |
| A reaction: Most brain research points to the complex multi-layered nature of experiences that were traditionally considered simple. We can be distracted from a pain, and an enormous number of factors can affect our degree of dislike of a given pain. |
| 4904 | Proper brains appear at seven weeks, and neonates have as many neurons as adults do [Carter,R] |
| Full Idea: The main sections of the brain, including the cerebral cortex, are visible within seven weeks of conception, and by the time the child is born the brain contains as many neurons - about 100 billion - as it will have as an adult. | |
| From: Rita Carter (Mapping the Mind [1998], p. 17) | |
| A reaction: Of interest in the abortion debate, and also in thinking about personal identity. However, it seems clear that the number of connections, rather than neurons, is what really matters. A small infant may well lack personal identity. |
| 4915 | In primates, brain size correlates closely with size of social group [Carter,R] |
| Full Idea: Brain size in primates is closely associated with the size of the social group in which the animal lives. | |
| From: Rita Carter (Mapping the Mind [1998], p.257) | |
| A reaction: Intriguing. Humans can have huge social groups because of language, which suggests a chicken-or-egg question. Language, intelligence and size of social group must have expanded together in humans. |
| 4917 | Consciousness involves awareness, perception, self-awareness, attention and reflection [Carter,R] |
| Full Idea: Awareness, perception, self-awareness, attention and reflection are all separate components of consciousness, and the quality of our experience varies according to which and how many of them are present. | |
| From: Rita Carter (Mapping the Mind [1998], p.300) | |
| A reaction: Philosophers like to emphasise 'qualia' and 'intentionality'. This remark slices the cake differently. 'Attention' is interesting, dividing consciousness into two areas, with some experience fading away into the darkness. Hume denied self-awareness. |
| 4916 | There is enormous evidence that consciousness arises in the frontal lobes of the brain [Carter,R] |
| Full Idea: A huge volume of evidence suggests that consciousness emerges from the activity of the cerebral cortex, and in particular from the frontal lobes. | |
| From: Rita Carter (Mapping the Mind [1998], p.298) | |
| A reaction: Dualists must face up to this, and even many physicalists have a rather vague notion about the location of awareness, but we are clearly homing in very precise physical substances which have consciousness as a feature. |
| 4905 | Normal babies seem to have overlapping sense experiences [Carter,R] |
| Full Idea: Connections in a baby's brain probably give the infant the experience of 'seeing' sounds and 'hearing' colours - which occasionally continues into adulthood, where it is known as 'synaesthesia'. | |
| From: Rita Carter (Mapping the Mind [1998], p. 19) | |
| A reaction: A fact to remember when discussing secondary qualities, and the relativism involved in the way we perceive the world. If you have done your philosophy right, you shouldn't be surprised by this discovery. |
| 4918 | In blindsight V1 (normal vision) is inactive, but V5 (movement) lights up [Carter,R] |
| Full Idea: Scans show that a sub-section of the visual cortex called V5 - the area that registers movement - lights up during blindsight, even though V1 - the primary sensory area that is essential for normal sight - is not active. | |
| From: Rita Carter (Mapping the Mind [1998], p.307) | |
| A reaction: The whole point of blindsight is to make us realise that vision involves not one module, but a whole team of them. The inference is that V1 involves consciousness, but other areas of the visual cortex don't. |
| 4912 | Out-of-body experiences may be due to temporary loss of proprioception [Carter,R] |
| Full Idea: Out-of-body experiences may be due to temporary loss of proprioception. | |
| From: Rita Carter (Mapping the Mind [1998], p.187) | |
| A reaction: This is only a speculation, but it is an effect which can be caused by brain injury, and dualists should face the possibility that this evidence (prized by many dualists) can have a physical explanation. |
| 4903 | Scans of brains doing similar tasks produce very similar patterns of activation [Carter,R] |
| Full Idea: The pattern of brain activation during, say, a word retrieval task is usually similar enough among the dozen or so participants who typically take part in such studies for their scans to be overlaid and still show a clear pattern. | |
| From: Rita Carter (Mapping the Mind [1998], p. 17) | |
| A reaction: This doesn't surprise me, though it could be interpreted as supporting type-type identity, or as supporting functionalism. Armstrong and Lewis endorse a sort of reductive functionalism which would fit this observation. |
| 4920 | Thinking takes place on the upper side of the prefrontal cortex [Carter,R] |
| Full Idea: The nuts and bolts of thinking - holding ideas in mind and manipulating them - takes place on the upper side of the prefrontal cortex. | |
| From: Rita Carter (Mapping the Mind [1998], p.312) | |
| A reaction: Keep this firmly in view! Imagine that the skull is transparent, and brain activity moves in waves of colour. Dualism would, in those circumstances, never have even occurred to anyone. |
| 4906 | Babies show highly emotional brain events, but may well be unaware of them [Carter,R] |
| Full Idea: Babies show emotion dramatically, but the areas of the brain that in adults are linked to the conscious experience of emotions are not active in newborn babies. Such emotions may therefore be unconscious. | |
| From: Rita Carter (Mapping the Mind [1998], p. 19) | |
| A reaction: Traditionally, 'unconscious emotion' is a contradiction, but I think we should accept this new evidence and rethink the nature of mind. Not only might emotion be non-conscious, but we should even consider that rational thinking could be too. |
| 4909 | The only way we can control our emotions is by manipulating the outside world that influences them [Carter,R] |
| Full Idea: We try to manipulate our emotions all the time, but all we are doing is arranging the outside world so it triggers certain emotions - we cannot control our reactions directly. | |
| From: Rita Carter (Mapping the Mind [1998], p.155) | |
| A reaction: This seems to me to throw a very illuminating light on a huge amount of human behaviour, such as going to the cinema or listening to music. The romantic movement encouraged direct internal manipulation. Compare sex fantasies with viewing pornography. |
| 4914 | A frog will starve to death surrounded by dead flies [Carter,R] |
| Full Idea: A frog will starve to death surrounded by dead flies. | |
| From: Rita Carter (Mapping the Mind [1998], p.195) | |
| A reaction: A nice warning against assuming that rationality is operating when a frog feels hungry and 'decides' to have lunch. We should take comfort from the fact that humans are NOT this stupid, and philosophers should try to accurately describe our gift. |
| 4907 | The 'locus coeruleus' is one of several candidates for the brain's 'pleasure centre' [Carter,R] |
| Full Idea: Noradrenaline is an excitatory chemical that induces physical and mental arousal and heightens mood. Production is centred in an area of the brain called the locus coeruleus, which is one of several candidates for the brain's 'pleasure' centre. | |
| From: Rita Carter (Mapping the Mind [1998], p. 30) | |
| A reaction: It seems to me very morally desirable that people understand facts of this kind, so that they can be more objective about pleasure. Pleasure is one cog in the machine that makes a person, not the essence of human life. |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |