14 ideas
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| Full Idea: The modal structuralist thinks of mathematical structures as possibilities. The application of mathematics is just the realisation that a possible structure is actualised. As structures are possibilities, realist ontological problems are avoided. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Michèle Friend - Introducing the Philosophy of Mathematics 4.3 | |
| A reaction: Friend criticises this and rejects it, but it is appealing. Mathematics should aim to be applicable to any possible world, and not just the actual one. However, does the actual world 'actualise a mathematical structure'? |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| Full Idea: Hellman represents statements of pure mathematics as elliptical for modal conditionals of a certain sort. | |
| From: report of Geoffrey Hellman (Mathematics without Numbers [1989]) by Charles Chihara - A Structural Account of Mathematics 5.3 | |
| A reaction: It's a pity there is such difficulty in understanding conditionals (see Graham Priest on the subject). I intuit a grain of truth in this, though I take maths to reflect the structure of the actual world (with possibilities being part of that world). |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| Full Idea: The usual way to show that a sentence is possible is to show that it has a model, but for Hellman presumably a sentence is possible if it might have a model (or if, possibly, it has a model). It is not clear what this move brings us. | |
| From: comment on Geoffrey Hellman (Mathematics without Numbers [1989]) by Stewart Shapiro - Philosophy of Mathematics 7.3 | |
| A reaction: I can't assess this, but presumably the possibility of the model must be demonstrated in some way. Aren't all models merely possible, because they are based on axioms, which seem to be no more than possibilities? |
| 7621 | Special relativity, unlike general relativity, was operationalist in spirit [Putnam on Einstein] |
| Full Idea: Einstein's interpretation of special relativity was operationalist in spirit (in marked contrast to the interpretation he gave to general relativity). | |
| From: comment on Albert Einstein (works [1915]) by Hilary Putnam - Reason, Truth and History Ch.5 | |
| A reaction: The late twentieth century was polluted with daft relativism, and I hold Einstein partly responsible, suspecting that he was a bad philosopher. The later development of Einstein's view noted here is interesting. |
| 22395 | Moral judgements are hypothetical, because they depend on interests and desires [Foot] |
| Full Idea: Moral judgements are hypothetical imperatives in the sense that they give reasons for acting only in conjunction with interests and desires. | |
| From: Philippa Foot (Reply to Professor Frankena [1975], p.177) | |
| A reaction: This is a splendid claim, which points to a more sensibly naturalistic ethics. There seem to be occasions for moral behaviour where I have no interests or desires, such as when a stranger asks me for a favour and I'm feeling tired. |
| 22955 | Einstein took causation to be the bedrock of physics [Einstein, by Coveney/Highfield] |
| Full Idea: It is difficult to overplay Einstein's commitment to the concept of causality as the bedrock of physics. | |
| From: report of Albert Einstein (works [1915]) by P Coveney / R Highfield - The Arrow of Time 3 'problem' | |
| A reaction: I normally avoid arguments from authority, but this carries a bit of weight (e.g. when Russell tries to oppose it). What happens to Einstein's theories if you remove causation from them? |
| 20638 | General relativity assumes laws of nature are the same in all frames of reference [Einstein, by Close] |
| Full Idea: Einstein came to general relativity from the principles that the laws of nature are the same in all frames of reference. | |
| From: report of Albert Einstein (works [1915]) by Frank Close - Theories of Everything 5 'Cosmological' | |
| A reaction: I wish physicists would tell us a bit more about the ontological status of the 'laws of nature'. Presumably they are not supernatural, so there is an aspect of nature which is constant in all frames of reference. Explanation please. |
| 20636 | Newton is a special case of Einstein's general theory, with an infinite speed of light [Einstein, by Close] |
| Full Idea: Einstein's general relativity included Newton's theory as a special case: Newton's theory corresponds to the speed of light being infinite relative to the speed of the interacting bodies. | |
| From: report of Albert Einstein (works [1915]) by Frank Close - Theories of Everything 5 'Gravity' | |
| A reaction: So Newton's theory was NOT wrong, but he made the false assumption that the speed of light was infinite. |
| 21230 | The theory is 'special' because it sticks to observers moving straight, at constant speeds [Einstein, by Farmelo] |
| Full Idea: Einstein's first theory is 'special' because it only deals with observers who move in a straight line at constant speeds with respect to one another. | |
| From: report of Albert Einstein (works [1915]) by Graham Farmelo - The Strangest Man 03 | |
| A reaction: Most theories of this period seem to have focused on the simplest cases, for obvious reasons. |
| 21231 | Assume the speed of light is constant for all observers, and the laws of physics are the same [Einstein, by Farmelo] |
| Full Idea: Einstein assumed that when each observer measures the speed of light in a vacuum, they find the same value, regardless of their speed; and that measurements will lead to agreement on the laws of physics. | |
| From: report of Albert Einstein (works [1915]) by Graham Farmelo - The Strangest Man 03 | |
| A reaction: So are the laws of physics constant for all observers, irrespective of their speed? |
| 20634 | General Relativity says there is no absolute force or acceleration [Einstein, by Close] |
| Full Idea: Einstein's General Theory arose from the idea that there is no absolute measure of force and acceleration. | |
| From: report of Albert Einstein (works [1915]) by Frank Close - Theories of Everything 5 'Gravity' | |
| A reaction: If absolutely everything is only true relative to something else you wonder what the point of measuring anything is. How big can a 'frame of reference' or 'inertial frame' be. Is the multiverse a frame of reference? |
| 20648 | Mass is a measure of energy content [Einstein] |
| Full Idea: The mass of a body is the measure of its energy content. | |
| From: Albert Einstein (works [1915]), quoted by Peter Watson - Convergence 04 'Intro' | |
| A reaction: If I knew what energy was, this would be very illuminating. This idea is e=mc^2 in words. We now have the Higgs field to consider when trying to understand mass. |
| 21232 | Space-time arises from the connection between measurements of space and of time [Einstein, by Farmelo] |
| Full Idea: Einstein noted that the measurements of space and time are not independent but inextricably linked, leading to the idea of unified space-time (introduced by his former teacher Minkowski). | |
| From: report of Albert Einstein (works [1915]) by Graham Farmelo - The Strangest Man 03 | |
| A reaction: Notice the instrumentalist assumptions behind this. |
| 7626 | I do not believe in a personal God [Einstein] |
| Full Idea: I do not believe in a personal God and I have never denied this but have expressed it clearly. | |
| From: Albert Einstein (works [1915]), quoted by Richard Dawkins - The God Delusion Ch.1.15 | |
| A reaction: This is an important corrective to those who claim Einstein as religious, on the basis of remarks about God not playing dice etc. See the whole of Dawkins's chapter on Einstein for full discussion. |