27 ideas
| 18739 | Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew] |
| Full Idea: Three periods can be distinguished in philosophical logic: the syntactic stage, from Russell's definite descriptions to the 1950s, the dominance of possible world semantics from the 50s to 80s, and a current widening of the subject. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 1) | |
| A reaction: [compressed] I've read elsewhere that the arrival of Tarski's account of truth in 1933, taking things beyond the syntactic, was also a landmark. |
| 18741 | Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew] |
| Full Idea: Logical formalization forces the investigator to make the central philosophical concepts precise. It can also show how some philosophical concepts and objects can be defined in terms of others. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: This is the main rationale of the highly formal and mathematical approach to such things. The downside is when you impose 'precision' on language that was never intended to be precise. |
| 18744 | Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew] |
| Full Idea: A (logical) model is a set with functions and relations defined on it that specify the denotation of the non-logical vocabulary. A series of recursive clauses explicate how truth values of complex sentences are compositionally determined from the parts. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: See the ideas on 'Functions in logic' and 'Relations in logic' (in the alphabetical list) to expand this important idea. |
| 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. |
| 18740 | If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew] |
| Full Idea: If there is indeed no property of existence that is expressed by the word 'exist', then it makes no sense to ask for its essence. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 2) | |
| A reaction: As far as I can tell, this was exactly Aristotle's conclusion, so he skirted round the question of 'being qua being', and focused on the nature of objects instead. Grand continental talk of 'Being' doesn't sound very interesting. |
| 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. |
| 18745 | A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew] |
| Full Idea: A Tarskian model can in a sense be seen as a model of a possible state of affairs. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: I include this remark to show how possible worlds semantics built on the arrival of model theory. |
| 18747 | The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew] |
| Full Idea: The notion of a possible worlds model was extended (resulting in the concept of a 'spheres model') in order to obtain a satisfactory logical treatment of counterfactual conditional sentences. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Thus we add 'centred' worlds, and an 'actual' world, to the loose original model. It is important to remember when we discuss 'close' worlds that we are then committed to these presuppositions. |
| 18748 | Epistemic logic introduced impossible worlds [Horsten/Pettigrew] |
| Full Idea: The idea of 'impossible worlds' was introduced into epistemic logic. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 4) | |
| A reaction: Nathan Salmon seems interested in their role in metaphysics (presumably in relation to Meinongian impossible objects, like circular squares, which must necessarily be circular). |
| 18746 | Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew] |
| Full Idea: Each possible worlds model contains a set of possible worlds. For this reason, possible worlds semantics is often charged with smuggling in heavy metaphysical commitments. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 3) | |
| A reaction: To a beginner it looks very odd that you should try to explain possibility by constructing a model of it in terms of 'possible' worlds. |
| 18750 | Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew] |
| Full Idea: When the possible worlds semantics were further extended to model notions of knowledge and of moral obligation, the application was beginning to look distinctly forced and artificial. | |
| From: Horsten,L/Pettigrew,R (Mathematical Methods in Philosophy [2014], 5) | |
| A reaction: They accept lots of successes in modelling necessity and time. |
| 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. |
| 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? |
| 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) |
| 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'. |
| 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) |
| 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. |