33 ideas
| 21793 | Genuine truth is the resolution of the highest contradiction [Hegel] |
| Full Idea: The highest truth, truth as such, is the resolution of the highest opposition and contradiction. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], I: 99), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Art' | |
| A reaction: Uneasy about the word 'highest', and the general Hegelian dream of 'resolving' contradictions, rather than just eliminating at least one component of them. No one else uses the word 'truth' like this. I suppose this Truth has a capital 'T'. |
| 21795 | What I hold true must also be part of my feelings and character [Hegel] |
| Full Idea: Whatever I hold as true, whatever ought to be valid for me, must also be in my feeling, must belong to my being and character. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], I: 97), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Philosophy' | |
| A reaction: I can see that truths do tend to become part of our character, but not that they ought to do so. I suppose I try to live my life enmeshed in the many truths which I have personally selected from the maelstrom of possibilities that engulf us. |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| Full Idea: There are many coherent stopping points in the hierarchy of increasingly strong mathematical systems, starting with strict finitism, and moving up through predicativism to the higher reaches of set theory. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], Intro) |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| Full Idea: Roughly speaking, 'reflection principles' assert that anything true in V [the set hierarchy] falls short of characterising V in that it is true within some earlier level. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 2.1) |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| Full Idea: There is at present no solid argument to the effect that a given statement is absolutely undecidable. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 5.3) |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| Full Idea: Some of the standard large cardinals (in order of increasing (logical) strength) are: inaccessible, Mahlo, weakly compact, indescribable, Erdös, measurable, strong, Wodin, supercompact, huge etc. (...and ineffable). | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) | |
| A reaction: [I don't understand how cardinals can have 'logical strength', but I pass it on anyway] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| Full Idea: To the extent that we are justified in accepting Peano Arithmetic we are justified in accepting its consistency, and so we know how to expand the axiom system so as to overcome the limitation [of Gödel's Second Theorem]. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.1) | |
| A reaction: Each expansion brings a limitation, but then you can expand again. |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| Full Idea: The arithmetical instances of undecidability that arise at one stage of the hierarchy are settled at the next. | |
| From: Peter Koellner (On the Question of Absolute Undecidability [2006], 1.4) |
| 18549 | Nineteenth century aesthetics focused on art rather than nature (thanks to Hegel) [Hegel, by Scruton] |
| Full Idea: Only In the course of the nineteenth century, and in the wake of Hegel's posthumously published lectures on aesthetics, did the topic of art come to replace that of natural beauty as the core subject-matter of aesthetics. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826], 5) by Roger Scruton - Beauty: a very short introduction |
| 22043 | Hegel largely ignores aesthetic pleasure, taste and beauty, and focuses on the meaning of artworks [Hegel, by Pinkard] |
| Full Idea: Unlike his predecessors (including Kant), Hegel does not focus on aesthetic pleasure, nor on good taste, nor even on the nature and criteria for beauty. Instead he focuses on the meaning of artworks and their role in forming mankind's self-consciousness. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Personally I dislike over-intellectualising art. The aim of a work of art is to give a certain experience, not to generate an ensuing sequence of theorising. I doubt whether Vermeer had any 'meaning' in mind in his obsessive work. |
| 22042 | Natural beauty is unimportant, because it doesn't show human freedom [Hegel, by Pinkard] |
| Full Idea: Hegel thinks that natural beauty is of no real significance since it cannot display our freedom to us; nature per se is meaningless. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Terry Pinkard - German Philosophy 1760-1860 11 | |
| A reaction: Presumably freedom is in the creation, and so creativity is what matters in aesthetics. But what are the criteria of good creativity? |
| 20413 | For Hegel the importance of art concerns the culture, not the individual [Hegel, by Eldridge] |
| Full Idea: Hegel locates the significance of art in its role in cultural life in general, not in relation to the psychological needs of individuals. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Richard Eldridge - G.W.F. Hegel (aesthetics) 1 | |
| A reaction: I'm beginning to see that art is a wonderful focus and test case for political attitudes. Roughly, liberalism focuses on individual responses, but more societal views (from right and left) see it in terms of role in the community. Which are you? |
| 20394 | The purpose of art is to reveal to Spirit its own nature [Hegel, by Davies,S] |
| Full Idea: According to Hegel, the goal of art was to serve as a phase in a process by which Spirit would come to understand its own nature. | |
| From: report of Georg W.F.Hegel (Lectures on Aesthetics [1826]) by Stephen Davies - The Philosophy of Art (2nd ed) 2.7 | |
| A reaction: I try very hard to understand ideas like this. Really really hard. However, since I see little sign of 'Spirit' really understanding its own nature, I'm guessing that the project is not going well. |
| 21794 | The main purpose of art is to express the unity of human life [Hegel] |
| Full Idea: Art's primary function, for Hegel, is to give expression to the unity and wholeness of life - especially human life - that the contingencies of everyday existence frequently conceal. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826]), quoted by Stephen Houlgate - An Introduction to Hegel 09 'Beauty' | |
| A reaction: I don't find the view that human life is 'unified' and 'whole' vary illuminating, and I have no objection to art which reflects the fragmentary and unstable aspects of life. I suspect Hegel would just prefer it if life were a unity. |
| 20415 | Art forms a bridge between the sensuous world and the world of pure thought [Hegel] |
| Full Idea: Spirit generates out of itself works of fine art as the first reconciling middle term between pure thought and what is merely external, sensuous and transient - between finite natural reality and the infinite freedom of conceptual thinking. | |
| From: Georg W.F.Hegel (Lectures on Aesthetics [1826], p.8), quoted by Richard Eldridge - G.W.F. Hegel (aesthetics) | |
| A reaction: This apparently says that there is necessarily an intellectual and conceptual component in art. This means little to me. Does he include portraits? Dutch domestic scenes? Would photography qualify? |
| 20624 | Work degrades into heat, but not vice versa [Close] |
| Full Idea: William Thomson, Lord Kelvin, declared (in 1865) the second law of thermodynamics: mechanical work inevitably tends to degrade into heat, but not vice versa. | |
| From: Frank Close (Theories of Everything [2017], 3 'Perpetual') | |
| A reaction: The basis of entropy, which makes time an essential part of physics. Might this be the single most important fact about the physical world? |
| 20623 | First Law: energy can change form, but is conserved overall [Close] |
| Full Idea: The first law of thermodynamics : energy can be changed from one form to another, but is always conserved overall. | |
| From: Frank Close (Theories of Everything [2017], 3 'Perpetual') | |
| A reaction: So we have no idea what energy is, but we know it's conserved. (Daniel Bernoulli showed the greater the mean energy, the higher the temperature. James Joule showed the quantitative equivalence of heat and work p.26-7) |
| 20625 | Third Law: total order and minimum entropy only occurs at absolute zero [Close] |
| Full Idea: The third law of thermodynamics says that a hypothetical state of total order and minimum entropy can be attained only at the absolute zero temperature, minus 273 degrees Celsius. | |
| From: Frank Close (Theories of Everything [2017], 3 'Arrow') | |
| A reaction: If temperature is energetic movement of atoms (or whatever), then obviously zero movement is the coldest it can get. So is absolute zero an energy state, or an absence of energy? I have no idea what 'total order' means. |
| 20622 | All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close] |
| Full Idea: There is no absolute state of rest; only relative motions are unambiguous. Contrast this with acceleration, however, which has the same magnitude in all inertial frames. | |
| From: Frank Close (Theories of Everything [2017], 3 'Newton's') | |
| A reaction: It seems important to remember this, before we start trumpeting about the whole of physics being relative. ....But see Idea 20634! |
| 20628 | The electric and magnetic are tightly linked, and viewed according to your own motion [Close] |
| Full Idea: Electric and magnetic phenomena are profoundly intertwined; what you interpret as electric or magnetic thus depends on your own motion. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: This sounds like an earlier version of special relativity. |
| 20635 | The general relativity equations relate curvature in space-time to density of energy-momentum [Close] |
| Full Idea: The essence of general relativity relates 'curvature in space-time' on one side of the equation to the 'density of momentum and energy' on the other. ...In full, Einstein required ten equations of this type. | |
| From: Frank Close (Theories of Everything [2017], 5 'Gravity') | |
| A reaction: Momentum involves mass, and energy is equivalent to mass (e=mc^2). |
| 20642 | Photon exchange drives the electro-magnetic force [Close] |
| Full Idea: The exchange of photons drives the electro-magnetic force. | |
| From: Frank Close (Theories of Everything [2017], 6 'Superstrings') | |
| A reaction: So light, which we just think of as what is visible, is a mere side-effect of the engine room of nature - the core mechanism of the whole electro-magnetic field. |
| 20627 | Electric fields have four basic laws (two by Gauss, one by Ampčre, one by Faraday) [Close] |
| Full Idea: Four basic laws of electric and magnetic fields: Gauss's Law (about the flux produced by a field), Gauss's law of magnets (there can be no monopoles), Ampčre's Law (fields on surfaces), and Farday's Law (accelerated magnets produce fields). | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: [Highly compressed, for an overview. Close explains them] |
| 20630 | Light isn't just emitted in quanta called photons - light is photons [Close] |
| Full Idea: Planck had assumed that light is emitted in quanta called photons. Einstein went further - light is photons. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: The point is that light travels as entities which are photons, rather than the emissions being quantized packets of some other stuff. |
| 20637 | In general relativity the energy and momentum of photons subjects them to gravity [Close] |
| Full Idea: In Einstein's general theory, gravity acts also on energy and momentum, not simply on mass. For example, massless photons of light feel the gravitational attraction of the Sun and can be deflected. | |
| From: Frank Close (Theories of Everything [2017], 5 'Planck') | |
| A reaction: Ah, a puzzle solved. How come massless photons are bent by gravity? |
| 20629 | Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close] |
| Full Idea: Faradays' measurements predicted the speed of electro-magnetic waves, which happened to be the speed of light, so Maxwell made an inspired leap: light is an electromagnetic wave! | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: Put that way, it doesn't sound like an 'inspired' leap, because travelling at exactly the same speed seems a pretty good indication that they are the same sort of thing. (But I'm not denying that Maxwell was a special guy!) |
| 20632 | In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close] |
| Full Idea: Dirac created quantum electrodynamics (QED): the universal electro-magnetic field can exist in discreet states of energy (with photons appearing and disappearing by energy excitations. This combined classical ideas, quantum theory and special relativity. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: Close says this is the theory of everything in atomic structure, but not in nuclei (which needs QCD and QFD). So if there are lots of other 'fields' (e.g. gravitational, weak, strong, Higgs), how do they all fit together? Do they talk to one another? |
| 20639 | Quantum fields contain continual rapid creation and disappearance [Close] |
| Full Idea: Quantum field theory implies that the vacuum of space is filled with particles and antiparticles which bubble in and out of existence on faster and faster timescales over shorter and shorter distances. | |
| From: Frank Close (Theories of Everything [2017], 6 'Intro') | |
| A reaction: Ponder this sentence until you head aches. Existence, but not as we know it, Jim. Close says calculations in QED about the electron confirm this. |
| 20641 | Electrons get their mass by interaction with the Higgs field [Close] |
| Full Idea: The electron gets its mass by interaction with the ubiquitous Higgs field. | |
| From: Frank Close (Theories of Everything [2017], 6 'Hierarchy') | |
| A reaction: I thought I understood mass until I read this. Is it just wrong to say the mass of a table is the 'amount of stuff' in it? |
| 20631 | Dirac showed how electrons conform to special relativity [Close] |
| Full Idea: In 1928 Paul Dirac discovered the quantum equation that describes the electron and conforms to the requirements special relativity theory. | |
| From: Frank Close (Theories of Everything [2017], 3 'Light!') | |
| A reaction: This sounds like a major step in the unification of physics. Quantum theory and General relativity remain irreconcilable. |
| 20626 | Modern theories of matter are grounded in heat, work and energy [Close] |
| Full Idea: The link between temperature, heat, work and energy is at the root of our historical ability to construct theories of matter, such as Newton's dynamics, while ignoring, and indeed being ignorant of - atomic dimensions. | |
| From: Frank Close (Theories of Everything [2017], 3 'Arrow') | |
| A reaction: That is, presumably, that even when you fill in the atoms, and the standard model of physics, these aspects of matter do the main explaiining (of the behaviour, rather than of the structure). |
| 20633 | The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close] |
| Full Idea: In 2012 it was confirmed that we are immersed in an electroweak plasma - the Higgs field. We curently have no knowledge of what this stuff might consist of. | |
| From: Frank Close (Theories of Everything [2017], 4 'Higgs') | |
| A reaction: The second sentence has my full attention. So we don't understand a field properly until we understand the 'stuff' it is made of? So what are all the familiar fields made of? Tell me more! |
| 20640 | Space-time is indeterminate foam over short distances [Close] |
| Full Idea: At very short distances, space-time itself becomes some indeterminate foam. | |
| From: Frank Close (Theories of Everything [2017], 6 'Intro') | |
| A reaction: [see Close for a bit more detail of this weird idea] |