What is a number? Is it some Platonic entity floating outside of space and time that we somehow come into communion with? We'll be following up our foray into analytical philosophy with Frege with some Bertrand Russell: specifically his Introduction to Mathematical Philosophy (1919), which is the much shortened, non-technical version of his famous Principia Mathematica
We'll focus on chapters 1-3, where he recounts Frege's derivation of the concept of number (he says these pick out sets of things in the actual world: the number 3 is identical to the set of all trios, for instance, where "trios" are defined without explicit use of the number 3 or any other number), and then chapters 13-18, where he deals with some potential problems with this definition (e.g. ch. 13 asks what happens if there are a finite number of things in the world: then some high number would end up equaling the empty set), giving a crash course in symbolic logic (in ch. 14 and 15), giving a quick account of his theory of descriptions (as discussed in our Frege and Wittgenstein episodes) reducing (in ch. 17) the notion of a class or set itself to more fundamental logical notions (i.e. propositional functions), and (in ch. 18) giving a summary account on the relation between mathematics and logic (i.e. that there's no line to be drawn between the two).
Read along with us online (the page includes a variety of different pdfs for tablet/phone reading) or buy the book.
Burl says
April 16, 2011 at 3:20 pmBefore going off on Bertie, paradoxes, metaphysics, and fun logic stuff like that. I have been trying to get a grip on ANW’s (Bertie’s professor) take on space-time w/ little luck.
I keep running into people who claim it does not exist. I posted a link to one such person a few comboxes back, and here is another http://www.anti-relativity.com/twinsparadox.htm
I cannot find fault in the anti-relativism argument in the link above. When two reference frames are in relative motion, there is a paradox created in saying time dilation occurs in one of the frames…which one?
To hell w/ the madness of metaphysics, even physics looks to be illogical. Or can we say relativity IS metaphysics? Can someone help me with this? I mean, is relativity a settled matter in physics and I am just finding crackpots (including ANW) arguing with faulty logic?
Please advise.
Anh-vu Doan says
April 16, 2011 at 11:15 pmBurl- This person’s arguments go wrong right here:
“Unfortunately, you must stop your thinking there for it to make any semblance of logical sense. If you continue on to think about it and examine it from Blue’s view, you will conclude a completely opposite effect. From Blue’s view, time must be going by slower for Red. Both views connot be correct”.
In fact, both views are correct. Relativity is a settled matter. The twins measure time differently because they are in different reference frames relative to each other – one is moving closer to the speed of light than the other. Really, relativity is quite easy to understand if one understands the notion that the speed of light is the fastest one can go in the universe. If one cannot catch up to a light beam – if one will measure the speed of light to be the same no matter how fast one moves – then there is only one conclusion: that one’s own sense of distance and time must be changed as one accelerates closer to the speed of light.
The rest of this person’s argument is predicated on the presumption that both twins’ measurement of time cannot be correct, when in fact they are. This has been corroborated by experiments done with atomic clocks and satellites.
Burl says
April 17, 2011 at 2:47 amAnh0vu Doan
Read the whole website where the ‘myths’ created by those experiments and GPS etc. are elaborated.
Also refer to another site I discussed in the blog on scientism here http://partiallyexaminedlife.com/2011/04/07/the-pernicious-influence-of-scientism/#comment-29120
This guy points out that if you say space-time is 4 dimensional and you want to speak of movement within it, you discuss displacement along each axis per time, or d/dt. But the derivative of the time axis w/r time is a unitless constant of 1.
If that doesn’t raise any flags, how about the axiom of space-time that states that anything at rest is moving at the speed of light along the time axis…what is that supposed to mean?
Wes Alwan says
April 17, 2011 at 1:56 pmFor the solution to the twins paradox, see http://mentock.home.mindspring.com/twins.htm; http://en.wikipedia.org/wiki/Twin_paradox.
Burl says
April 17, 2011 at 2:47 pmI am unsure of both links, Wes. The wiki mentions the dubious plane and GPS ‘proofs’ of dilation. As for the 3 frames solution in your 1st link, why must the two come back to the same place to check their respective ages? Why can’t the moving twin and the one resting merely report their ages at a specific simultaneous point in the future? At which time, which is younger?
I am starting to be convinced that Whitehead’s intuition to argue for a theory of relativity that remains square with his philosophical radical empiricism offers a superior theory to Einstein’s ‘What you gonna believe, your lieing eyes, or my philosophical assumption of a non-geometrical receptacle for the contents of space?’
Einstein’s theory gives causal powers (gravity) to a non-actual entity – space. Thus for E, space-time has become an ANW-style supersized eternal object.
Check it out. http://www.religion-online.org/showarticle.asp?title=2390
Burl says
April 17, 2011 at 5:16 pmForget republican v democrat: are you a whole or a bunch of parts? http://departments.bloomu.edu/philosophy/pages/content/hales/articlepdf/endurantism.pdf
Burl says
April 18, 2011 at 6:36 amI would honestly like to ask all members of the PEL community what they think constitute space and time – not what some professor or philosopher thinks, but what you personally think
Burl says
April 19, 2011 at 9:31 amNobody has formulated a concept of space and time? Seriously?
Wes Alwan says
April 20, 2011 at 12:15 amI’ve formulated a very elaborate theory of not-having-the-time.
Josh says
April 19, 2011 at 11:24 amFor me, they’re not constituted by anything, they are the absence of constitution; “spacetime” is just the distance between matter.
Burl: insofar as the twins “paradox,” it’s not a paradox. Relativity isn’t intuitive to us because we don’t travel at speeds where it matters, just like the massive amounts of empty space in atoms isn’t intuitive, or quantum physics, or anything else that occurs at scales that we don’t interact with. Experimentation confirms things that we can’t grasp intuitively; this doesn’t somehow make the universe “wrong.” To answer your questions in order: Yes, relativity has been experimentally confirmed, and yes, you are finding crackpots who are disputing it on the basis of it not being intuitive, with faulty logic. An object at “rest” relative to another object experiences no time dilation with respect to that object. The twins have to communicate with each other to compare their ages.
I’m really looking forward to this episode!
Mark Linsenmayer says
April 19, 2011 at 9:24 pmGuess we’re due for another physics episode! (Maybe in the fall?)
Burl says
April 20, 2011 at 5:59 amIt was the recent PEL exchanges over scientism that set my mind to wandering into questions I had become aware of in the recent past concerning space and time. I provided some old and new links that strongly suggest it is not a settled matter even in science.
When I asked you PELers what space/time concepts your considerable learning had afforded you, I jotted down mine as simply:
If no thing existed, there would be nothingness; however, given that they do, the nothingness serves as an empty space in which all existents are. We lay a geometry on space to help us understand the relatedness of things.
Experience of the activities of things (flux) is felt as ‘in time’. (Analogously to how we sense things being located in space). We conceptually mark sequences of changes between things as time.
I went-a-searching and saw where physicists Stapp and Epperson were discussing Whitehead’s theory of extensive abstraction in _ Concept of Nature _. This work predates his metaphysical writings and is associated with his relativity interests.
For those of you wishing to find time to think, I would direct you to a nice summary chapter http://www.gutenberg.org/files/18835/18835-h/18835-h.htm#CHAPTER_VIII
As to the state of affairs in which well read people in the 21st century are so uncertain of reality, I would only comment that Bertie is not your go-to source for enlightenment.
There is a massive entity in the philosopher’s lounge that has been ignored throughout the 20th century: While it is not a literal white elephant, it is figuratively so, and it is white, as in Whitehead’s work in natural philosophy.
Burl says
April 21, 2011 at 10:14 amLike I said, Bertie is DEFINITELY not your go-to man for enlightenment.
I hope his treatment of logic is not as superficially vapid as his work in metaphysics
http://www.readbookonline.net/readOnLine/22893/
Perhaps had he spent more time engaged in serious thought instead of assassinating his superiors in thought, smiling at cameras, bed-hopping, and foisting his deficient memes upon the world in the form of Wittgensnide, he might have amounted to something approaching the calibre of Alfie.
On the subject of caliber (as in diameter, now), it is good that Bert was a pacifist, because anyone who thinks space is six-dimensional should not handle a gun!
Anh-vu Doan says
April 22, 2011 at 10:43 amWell, actually, according to the latest developments in string theory, science would seem to suggest that the universe has eleven dimensions of space!
The reason why I didn’t respond to your question of what I think of space and time, is because I don’t think it’s a proper philosophical question to ask what space and time are. It’s a physical question and an unanswerable one at that. Space and time are given, they are basic fundamental entities in the universe. One could just as easily ask someone to define “energy”, “mass” or “charge”. Moreover, they are not separate, as your links would seem to suggest, but one — this is the essential concept around which relativity dwells.
As to “anti-relativity”, what I would simply ask is which you find more credible: the data of physicists for over a hundred years, or the writings of a layman nonspecialist on the internet?