23 ideas
11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation. | |
From: Ian Rumfitt ("Yes" and "No" [2000], II) | |
A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts. |
11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table. | |
From: Ian Rumfitt ("Yes" and "No" [2000]) | |
A reaction: This is the standard view which Rumfitt sets out to challenge. |
11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious. | |
From: Ian Rumfitt ("Yes" and "No" [2000], III) | |
A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value. |
15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed. | |
From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication | |
A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians. |
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. |
15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time. | |
From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities. |
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. |
11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A. | |
From: Ian Rumfitt ("Yes" and "No" [2000], IV) | |
A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role). |
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. |