16 ideas
| 13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
| Full Idea: The two best understood conceptions of set are the Iterative Conception and the Limitation of Size Conception. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) |
| 13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
| Full Idea: There are set theories that countenance exceptions to the Principle of Separation in exchange for a universal set. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) |
| 13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
| Full Idea: The possibility of unrestricted quantification does not immediately presuppose the existence of an all-inclusive domain. One could deny an all-inclusive domain but grant that some quantifications are sometimes unrestricted. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1) | |
| A reaction: Thus you can quantify over anything you like, but only from what is available. Eat what you like (in this restaurant). |
| 13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
| Full Idea: There are doubts about whether absolute generality is possible, if there are certain concepts which are indefinitely extensible, lacking definite extensions, and yielding an ever more inclusive hierarchy. Sets and ordinals are paradigm cases. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.1) |
| 13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
| Full Idea: If one thought of second-order quantification as quantification over first-level Fregean concepts [note: one under which only objects fall], talk of domains might be regimented as talk of first-level concepts, which are not objects. | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2) | |
| A reaction: That is (I take it), don't quantify over objects, but quantify over concepts, but only those under which known objects fall. One might thus achieve naïve comprehension without paradoxes. Sound like fun. |
| 21110 | An understanding of the most basic physics should explain all of the subject's mysteries [Krauss] |
| Full Idea: Once we understood the fundamental laws that govern forces of nature at its smallest scales, all of these current mysteries would be revealed as natural consequences of these laws. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 08) | |
| A reaction: This expresses the reductionist view within physics itself. Krauss says the discovery that empty space itself contains energy has led to a revision of this view (because that is not part of the forces and particles studied in basic physics). |
| 21105 | In 1676 it was discovered that water is teeming with life [Krauss] |
| Full Idea: Van Leeuwenhoek first stared at a drop of seemingly empty water with a microscope in 1676 and discovered in was teeming with life. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 04) | |
| A reaction: I am convinced that this had a huge influence on Leibniz's concept of monads. He immediately became convinced that it was some sort of life all the way down. He would be have been disappointed by the subsequent chemical reduction of life. |
| 13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
| Full Idea: We generally take an assertion's domain of discourse to be implicitly restricted by context. [Note: the standard approach is that this restriction is a semantic phenomenon, but Kent Bach (2000) argues that it is a pragmatic phenomenon] | |
| From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1) | |
| A reaction: I think Kent Bach is very very right about this. Follow any conversation, and ask what the domain is at any moment. The reference of a word like 'they' can drift across things, with no semantics to guide us, but only clues from context and common sense. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |
| 21109 | Space itself can expand (and separate its contents) at faster than light speeds [Krauss] |
| Full Idea: Special Relativity says nothing can travel 'through space' faster than the speed of light. But space itself can do whatever the heck it wants, at least in general relativity. And it can carry distant objects apart from one another at superluminal speeds | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 06) | |
| A reaction: Another of my misunderstandings corrected. I assumed that the event horizon (limit of observability) was defined by the stuff retreating at (max) light speed. But beyond that it retreats even faster! What about the photons in space? |
| 21104 | General Relativity: the density of energy and matter determines curvature and gravity [Krauss] |
| Full Idea: The left-hand side of the general relativity equations descrbe the curvature of the universe, and the strength of gravitational forces acting on matter and radiation. The right-hand sides reflect the total density of all kinds of energy and matter. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 04) | |
| A reaction: I had assumed that the equations just described the geometry. In fact the matter determines the nature of the universe in which it exists. Presumably only things with mass get a vote. |
| 21107 | Uncertainty says that energy can be very high over very short time periods [Krauss] |
| Full Idea: The Heisenberg Uncertainty Principle says that the uncertainty in the measured energy of a system is inversely proportional to the length of time over which you observe it. (This allow near infinite energy over very short times). | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 04) | |
| A reaction: Apparently this brief energy is 'borrowed', and must be quickly repaid. |
| 21106 | Most of the mass of a proton is the energy in virtual particles (rather than the quarks) [Krauss] |
| Full Idea: The quarks provide very little of the total mass of a proton, and the fields created by the virtual particles contribute most of the energy that goes into the proton's rest energy and, hence, its mass. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 04) | |
| A reaction: He gives an artist's impression of the interior of a proton, which looks like a ship's engine room. |
| 21112 | Empty space contains a continual flux of brief virtual particles [Krauss] |
| Full Idea: Empty space is complicated. It is a boiling brew of virtual particles that pop in and out of existence in a time so short we cannot see them directly. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 10) | |
| A reaction: Apparently the interior of a proton is also like this. This fact gives a foot in the door for explanations of how the Big Bang got started, from these virtual particles. And yet surely space itself only arrives with the Big Bang? |
| 21108 | The universe is precisely 13.72 billion years old [Krauss] |
| Full Idea: We now know the age of the universe to four significant figures. It is 13.72 billion years old! | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 05) | |
| A reaction: It amazes me how many people, especially in philosophy, would be reluctant to accept that this is a know fact. I'm not accepting its certainty, but an assertion like this from a leading figure is good enough for me, and it should be for you. |
| 21111 | It seems likely that cosmic inflation is eternal, and this would make a multiverse inevitable [Krauss] |
| Full Idea: A multiverse is inevitable if inflation is eternal, and eternal inflation is by far the most likely possibility in most, if not all, inflationary scenarios. | |
| From: Lawrence M. Krauss (A Universe from Nothing [2012], 08) |