23 ideas
12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
17536 | If it can't be expressed mathematically, it can't occur in nature? [Heisenberg] |
Full Idea: The solution was to turn around the question How can one in the known mathematical scheme express a given experimental situation? and ask Is it true that only such situations can arise in nature as can be expressed in the mathematical formalism? | |
From: Werner Heisenberg (Physics and Philosophy [1958], 02) | |
A reaction: This has the authority of the great Heisenberg, and is the ultimate expression of 'mathematical physics', beyond anything Galileo or Newton ever conceived. I suppose Pythagoras would have thought that Heisenberg was obviously right. |
12454 | Intuitionists only accept denumerable sets [Brouwer] |
Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
17545 | Quantum theory shows that exact science does not need dogmatic realism [Heisenberg] |
Full Idea: It is only through quantum theory that we have learned that exact science is possible without the basis of dogmatic realism. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 05) |
17538 | Quantum theory does not introduce minds into atomic events [Heisenberg] |
Full Idea: Certainly quantum theory does not contain genuine subjective features, it does not introduce the mind of the physicist as a part of the atomic event. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 03) | |
A reaction: This should be digested by anyone who wants to erect some dodgy anti-realist, idealist, subjective metaphysics on the basis of the Copenhagen interpretation of quantum mechanics. |
17534 | A 'probability wave' is a quantitative version of Aristotle's potential, a mid-way type of reality [Heisenberg] |
Full Idea: The 1924 idea of the 'probability wave' meant a tendency for something. It was a quantitative version of the old concept of 'potentia' in Aristotelian philosophy ...a strange kind of physical reality just in the middle between possibility and reality. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 02) | |
A reaction: [compressed] As far as I can see, he is talking about a disposition or power, which is exactly between a mere theoretical possibility and an actuality. See the Mumford/Lill Anjum proposal for a third modal value, between possible and necessary. |
17553 | We can retain the idea of 'substance', as indestructible mass or energy [Heisenberg] |
Full Idea: One could consider mass and energy as two different forms of the same 'substance' and thereby keep the idea of substance as indestructible. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 07) |
17544 | Basic particles have a mathematical form, which is more important than their substance [Heisenberg] |
Full Idea: The smallest parts of matter are not the fundamental Beings, as in the philosophy of Democritus, but are mathematical forms. Here it is quite evident that the form is more important than the substance of which it is the form. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 04) | |
A reaction: Heisenberg is quite consciously endorsing hylomorphism here, with a Pythagorean twist to it. |
17550 | We give a mathematical account of a system of natural connections in order to clarify them [Heisenberg] |
Full Idea: When we represent a group of connections by a closed and coherent set of concepts, axioms, definitions and laws which in turn is represented by a mathematical scheme we have isolated and idealised them with the purpose of clarification. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 06) | |
A reaction: Attacks on the regularity theory of laws, and the notion that explanation is by laws, tend to downplay this point - that obtaining clarity and precision is a sort of explanation, even if it fails to go deeper. |
10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
22489 | 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot] |
Full Idea: Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'. | |
From: report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro | |
A reaction: [In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it. |
17549 | Seven theories in science: mechanics, heat, electricity, quantum, particles, relativity, life [Heisenberg, by PG] |
Full Idea: Science has seven closed systems of concepts and axioms: Newtonian mechanics; the theory of heat; electricity and magnetism; quantum theory; the theory of elementary particles; general relativity; and the theory of organic life. | |
From: report of Werner Heisenberg (Physics and Philosophy [1958], 06) by PG - Db (ideas) | |
A reaction: [my summary of pp.86-88 and 92] It is interesting to have spelled out that there are number of 'closed' theories, which are only loosely connected to one another. New discoveries launch whole new theories, instead of being subsumed. |
17540 | Energy is that which moves, and is the substance from which everything is made [Heisenberg] |
Full Idea: Energy is the substance from which all elementary particles, all atoms and therefore all things are made, and energy is that which moves. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 04) | |
A reaction: I'm not sure what energy is, but I like this because it says that nature is fundamentally active. Nothing makes sense without that basic assumption (on which Leibniz continually insists). |
17541 | Energy is an unchanging substance, having many forms, and causing all change [Heisenberg] |
Full Idea: Energy is a substance, since its total amount does not change. ...Energy can be changed into motion, into heat, into light and into tension. Energy may be called the fundamental cause for all change in the world. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 04) | |
A reaction: Grandiose stuff. I remain unconvinced that Heisenberg (clever fellow, I'm told) has any idea of what he is talking about. |
17548 | Maxwell introduced real fields, which transferred forces from point to point [Heisenberg] |
Full Idea: In the theory of fields of force one came back to the older idea, that action is transferred from one point to a neighbouring point. ...With Maxwell the fields of force seemed to have acquired the same degree of reality as the body's of Newton's theory. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 06) |
17533 | Radiation interference needs waves, but radiation photoelectric effects needs particles [Heisenberg] |
Full Idea: How could it be that the same radiation that produces interference patterns, and therefore must consist of waves, also produces the photoelectric effect, and therefore must consist of moving particles. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 02) |
17532 | An atom's stability after collisions needs explaining (which Newton's mechanics can't do) [Heisenberg] |
Full Idea: The first new model of the atom could not explain the most characteristic features of the atom, its enormous stability. No planetary system following the laws of Newton's mechanics would ever go back to its original configuration after a collision. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 02) |
17537 | Position is complementary to velocity or momentum, so the whole system is indeterminate [Heisenberg] |
Full Idea: The knowledge of the position of a particle is complementary to the knowledge of its velocity or momentum. If we know one with high accuracy we cannot know the other with high accuracy; still we must know both for determining the behaviour of the system. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 03) | |
A reaction: This is the famous Uncertainty Principle, expressed in plain language by the man himself. At this point we lost our grip on the prospects of determining the behaviour of natural systems. |
17551 | It was formerly assumed that electromagnetic waves could not be a reality in themselves [Heisenberg] |
Full Idea: The idea that electromagnetic waves could be a reality in themselves, independent of any bodies, did at that time not occur to the physicists. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 07) | |
A reaction: 'At that time' is when they thought the waves must travel through something, called the 'ether'. |
17543 | So-called 'empty' space is the carrier of geometry and kinematics [Heisenberg] |
Full Idea: From our modern point of view we would say that the empty space between the atoms was not nothing; it was the carrier of geometry and kinematics. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 04) | |
A reaction: I'm not sure what the 'carrier of geometry and kinematics' means, but it is interesting that he doesn't mention 'fields' (unless they carry the kinematics?) |
17552 | In relativity the length of the 'present moment' is relative to distance from the observer [Heisenberg] |
Full Idea: In classical theory we assume past and future are separated by an infinitely short time interval called the present moment. In relativity it is different: future and past are separated by a finite time interval dependent on the distance from the observer. | |
From: Werner Heisenberg (Physics and Philosophy [1958], 07) | |
A reaction: Not sure I understand this, but it is a revelation to realise that not only is time made relative to observers, but the length of the 'present moment' also becomes relative. The infinitesimal present moment has always bothered me. |