35 ideas
11223 | Definitions usually have a term, a 'definiendum' containing the term, and a defining 'definiens' [Gupta] |
Full Idea: Many definitions have three elements: the term that is defined, an expression containing the defined term (the 'definiendum'), and another expression (the 'definiens') that is equated by the definition with this expression. | |
From: Anil Gupta (Definitions [2008], 2) | |
A reaction: He notes that the definiendum and the definiens are assumed to be in the 'same logical category', which is a right can of worms. |
11215 | Notable definitions have been of piety (Plato), God (Anselm), number (Frege), and truth (Tarski) [Gupta] |
Full Idea: Notable examples of definitions in philosophy have been Plato's (e.g. of piety, in 'Euthyphro'), Anselm's definition of God, the Frege-Russell definition of number, and Tarski's definition of truth. | |
From: Anil Gupta (Definitions [2008], Intro) | |
A reaction: All of these are notable for the extensive metaphysical conclusions which then flow from what seems like a fairly neutral definition. We would expect that if we were defining essences, but not if we were just defining word usage. |
11225 | A definition needs to apply to the same object across possible worlds [Gupta] |
Full Idea: In a modal logic in which names are non-vacuous and rigid, not only must existence and uniqueness in a definition be shown to hold necessarily, it must be shown that the definiens is satisfied by the same object across possible worlds. | |
From: Anil Gupta (Definitions [2008], 2.4) |
11227 | The 'revision theory' says that definitions are rules for improving output [Gupta] |
Full Idea: The 'revision theory' of definitions says definitions impart a hypothetical character, giving a rule of revision rather than a rule of application. ...The output interpretation is better than the input one. | |
From: Anil Gupta (Definitions [2008], 2.7) | |
A reaction: Gupta mentions the question of whether such definitions can extend into the trans-finite. |
11224 | Traditional definitions are general identities, which are sentential and reductive [Gupta] |
Full Idea: Traditional definitions are generalized identities (so definiendum and definiens can replace each other), in which the sentential is primary (for use in argument), and they involve reduction (and hence eliminability in a ground language). | |
From: Anil Gupta (Definitions [2008], 2.2) |
11226 | Traditional definitions need: same category, mention of the term, and conservativeness and eliminability [Gupta] |
Full Idea: A traditional definition requires that the definiendum contains the defined term, that definiendum and definiens are of the same logical category, and the definition is conservative (adding nothing new), and makes elimination possible. | |
From: Anil Gupta (Definitions [2008], 2.4) |
11221 | A definition can be 'extensionally', 'intensionally' or 'sense' adequate [Gupta] |
Full Idea: A definition is 'extensionally adequate' iff there are no actual counterexamples to it. It is 'intensionally adequate' iff there are no possible counterexamples to it. It is 'sense adequate' (or 'analytic') iff it endows the term with the right sense. | |
From: Anil Gupta (Definitions [2008], 1.4) |
11217 | Chemists aim at real definition of things; lexicographers aim at nominal definition of usage [Gupta] |
Full Idea: The chemist aims at real definition, whereas the lexicographer aims at nominal definition. ...Perhaps real definitions investigate the thing denoted, and nominal definitions investigate meaning and use. | |
From: Anil Gupta (Definitions [2008], 1.1) | |
A reaction: Very helpful. I really think we should talk much more about the neglected chemists when we discuss science. Theirs is the single most successful branch of science, the paradigm case of what the whole enterprise aims at. |
11216 | If definitions aim at different ideals, then defining essence is not a unitary activity [Gupta] |
Full Idea: Some definitions aim at precision, others at fairness, or at accuracy, or at clarity, or at fecundity. But if definitions 'give the essence of things' (the Aristotelian formula), then it may not be a unitary kind of activity. | |
From: Anil Gupta (Definitions [2008], 1) | |
A reaction: We don't have to accept this conclusion so quickly. Human interests may shift the emphasis, but there may be a single ideal definition of which these various examples are mere parts. |
11218 | Stipulative definition assigns meaning to a term, ignoring prior meanings [Gupta] |
Full Idea: Stipulative definition imparts a meaning to the defined term, and involves no commitment that the assigned meaning agrees with prior uses (if any) of the term | |
From: Anil Gupta (Definitions [2008], 1.3) | |
A reaction: A nice question is how far one can go in stretching received usage. If I define 'democracy' as 'everyone is involved in decisions', that is sort of right, but pushing the boundaries (children, criminals etc). |
11220 | Ostensive definitions look simple, but are complex and barely explicable [Gupta] |
Full Idea: Ostensive definitions look simple (say 'this stick is one meter long', while showing a stick), but they are effective only because a complex linguistic and conceptual capacity is operative in the background, of which it is hard to give an account. | |
From: Anil Gupta (Definitions [2008], 1.2) | |
A reaction: The full horror of the situation is brought out in Quine's 'gavagai' example (Idea 6312) |
14965 | Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta] |
Full Idea: The basic principles governing truth are Truth Elimination (sentence A follows from ''A' is true') and the converse Truth Introduction (''A' is true' follows from A), which combine into Tarski's T-schema - 'A' is true if and only if A. | |
From: Anil Gupta (Truth [2001], 5.1) | |
A reaction: Introduction and Elimination rules are the basic components of natural deduction systems, so 'true' now works in the same way as 'and', 'or' etc. This is the logician's route into truth. |
14968 | A weakened classical language can contain its own truth predicate [Gupta] |
Full Idea: If a classical language is expressively weakened - for example, by dispensing with negation - then it can contain its own truth predicate. | |
From: Anil Gupta (Truth [2001], 5.2) | |
A reaction: Thus the Tarskian requirement to move to a metalanguage for truth is only a requirement of a reasonably strong language. Gupta uses this to criticise theories that dispense with the metalanguage. |
11222 | The ordered pair <x,y> is defined as the set {{x},{x,y}}, capturing function, not meaning [Gupta] |
Full Idea: The ordered pair <x,y> is defined as the set {{x},{x,y}}. This does captures its essential uses. Pairs <x,y> <u,v> are identical iff x=u and y=v, and the definition satisfies this. Function matters here, not meaning. | |
From: Anil Gupta (Definitions [2008], 1.5) | |
A reaction: This is offered as an example of Carnap's 'explications', rather than pure definitions. Quine extols it as a philosophical paradigm (1960:§53). |
14964 | The Liar reappears, even if one insists on propositions instead of sentences [Gupta] |
Full Idea: There is the idea that the Liar paradox is solved simply by noting that truth is a property of propositions (not of sentences), and the Liar sentence does not express a proposition. But we then say 'I am not now expressing a true proposition'! | |
From: Anil Gupta (Truth [2001], 5.1) | |
A reaction: Disappointed to learn this, since I think focusing on propositions (which are unambiguous) rather than sentences solves a huge number of philosophical problems. |
14969 | Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta] |
Full Idea: An example of the Strengthened Liar is the following statement SL: 'Either SL is neither-true-nor-false or it is not true'. This raises a serious problem for any theory that assesses the paradoxes to be neither true nor false. | |
From: Anil Gupta (Truth [2001], 5.4.2) | |
A reaction: If the sentence is either true or false it reduces to the ordinary Liar. If it is neither true nor false, then it is true. |
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 Ampère, 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), Ampère'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] |
7604 | Amos was the first prophet to emphasise justice and compassion [Amos, by Armstrong,K] |
Full Idea: Amos was the first prophet to emphasise social justice and compassion. | |
From: report of Amos (30: Book of Amos [c.740 BCE]) by Karen Armstrong - A History of God | |
A reaction: It increasingly strikes me that early religious thinkers were actually working out the rules for good community living, but seeing them through the distorting spectacles of religion as a means to post-life salvation. |