28 ideas
| 23249 | The early philosophers thought that reason has its own needs and desires [Frede,M] |
| Full Idea: It is part of the notion of reason according to these philosophers [Socrates, Plato, Aristotle, Stoics] that reason has its own needs and desires. | |
| From: Michael Frede (Intro to 'Rationality in Greek Thought' [1996], p.5) | |
| A reaction: This sounds as if reason is treated as a separate person within a person. Anyone solving a logical puzzle feels that reason has its own compulsion. 'Boulesis' is the desire characteristic of reason. |
| 15647 | Truth definitions don't produce a good theory, because they go beyond your current language [Halbach] |
| Full Idea: It is far from clear that a definition of truth can lead to a philosophically satisfactory theory of truth. Tarski's theorem on the undefinability of the truth predicate needs resources beyond those of the language for which it is being defined. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: The idea is that you need a 'metalanguage' for the definition. If I say 'p' is a true sentence in language 'L', I am not making that observation from within language L. The dream is a theory confined to the object language. |
| 15649 | In semantic theories of truth, the predicate is in an object-language, and the definition in a metalanguage [Halbach] |
| Full Idea: In semantic theories of truth (Tarski or Kripke), a truth predicate is defined for an object-language. This definition is carried out in a metalanguage, which is typically taken to include set theory or another strong theory or expressive language. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Presumably the metalanguage includes set theory because that connects it with mathematics, and enables it to be formally rigorous. Tarski showed, in his undefinability theorem, that the meta-language must have increased resources. |
| 15655 | Should axiomatic truth be 'conservative' - not proving anything apart from implications of the axioms? [Halbach] |
| Full Idea: If truth is not explanatory, truth axioms should not allow proof of new theorems not involving the truth predicate. It is hence said that axiomatic truth should be 'conservative' - not implying further sentences beyond what the axioms can prove. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: [compressed] |
| 15654 | If truth is defined it can be eliminated, whereas axiomatic truth has various commitments [Halbach] |
| Full Idea: If truth can be explicitly defined, it can be eliminated, whereas an axiomatized notion of truth may bring all kinds of commitments. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: The general principle that anything which can be defined can be eliminated (in an abstract theory, presumably, not in nature!) raises interesting questions about how many true theories there are which are all equivalent to one another. |
| 15650 | Axiomatic theories of truth need a weak logical framework, and not a strong metatheory [Halbach] |
| Full Idea: Axiomatic theories of truth can be presented within very weak logical frameworks which require very few resources, and avoid the need for a strong metalanguage and metatheory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) |
| 15648 | Instead of a truth definition, add a primitive truth predicate, and axioms for how it works [Halbach] |
| Full Idea: The axiomatic approach does not presuppose that truth can be defined. Instead, a formal language is expanded by a new primitive predicate of truth, and axioms for that predicate are then laid down. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1) | |
| A reaction: Idea 15647 explains why Halbach thinks the definition route is no good. |
| 15656 | Deflationists say truth merely serves to express infinite conjunctions [Halbach] |
| Full Idea: According to many deflationists, truth serves merely the purpose of expressing infinite conjunctions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.3) | |
| A reaction: That is, it asserts sentences that are too numerous to express individually. It also seems, on a deflationist view, to serve for anaphoric reference to sentences, such as 'what she just said is true'. |
| 15657 | To prove the consistency of set theory, we must go beyond set theory [Halbach] |
| Full Idea: The consistency of set theory cannot be established without assumptions transcending set theory. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 2.1) |
| 15652 | We can use truth instead of ontologically loaded second-order comprehension assumptions about properties [Halbach] |
| Full Idea: The reduction of 2nd-order theories (of properties or sets) to axiomatic theories of truth may be conceived as a form of reductive nominalism, replacing existence assumptions (for comprehension axioms) by ontologically innocent truth assumptions. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I like this very much, as weeding properties out of logic (without weeding them out of the world). So-called properties in logic are too abundant, so there is a misfit with their role in science. |
| 15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |
| Full Idea: Quantification over (certain) properties can be mimicked in a language with a truth predicate by quantifying over formulas. Instead of saying that Tom has the property of being a poor philosopher, we can say 'x is a poor philosopher' is true of Tom. | |
| From: Volker Halbach (Axiomatic Theories of Truth (2005 ver) [2005], 1.1) | |
| A reaction: I love this, and think it is very important. He talks of 'mimicking' properties, but I see it as philosophers mistakenly attributing properties, when actually what they were doing is asserting truths involving certain predicates. |
| 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. |
| 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. |
| 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. |