Comments

1. 

   Alex

   October 22, 2014 at 12:51

   With all due respect, Frege did not publish "The Foundations of Arithmetic" in 1879. It was published in 1884 I believe. And this book started the linguistic turn in philosophy. But in any case, please be cautious about the fact and fact-checking.
2. 

   whiskeylove

   October 22, 2014 at 14:51

   Thank you for the interview, Mr. Derbyshire and Dr. Goldstein. I greatly admire Dr. Goldstein's work. One thing: Foundations of Arithmetic was published in 1884, Begriffsschrift in 1879. So did Dr. Goldstein once believe philosophy started in 1879, or with the Foundations? : )
3. 

   Arnold Trehub

   October 22, 2014 at 16:06

   The question: Is mathematics a human invention or a human discovery, stimulated, by far, more responses than any other question on the web forum Research Gate.
4. 

   Ted Schrey Montreal

   October 22, 2014 at 16:56

   Invention or discovery? Fascinating question. I suspect Plato would have said 'discovery'? But I think 'invention' would be right.
   1. 

      pkbrando

      October 24, 2014 at 01:10

      Neither. Mathematics is a language that is very effective in describing the way things happen. As such, it is an action, not an entity.
      1. 

         Mark Titus

         October 25, 2014 at 23:18

         I think you are right. When human beings looked at their fingers and toes, and gave them a little thought, mathematics was invented and discovered.
5. 

   Arnold Trehub

   October 22, 2014 at 20:04

   Rebecca Goldstein: "What I’d like to think [Plato is saying] is that we can’t do it [philosophy] alone, it really has to happen in the clash of points of view. The things we really have to examine are so constitutive of our thinking that we’re not aware them, and so you need these other points of view. And I like to think that Plato is also telling us the more diverse the points of view the better." Isn't the same cautionary note also true of science? Science, as well as philosophy, needs an open clash of points of view. Today, with the communication facilities of the internet, we have an unprecedented opportunity to hash out the the major arguments at the frontiers of science. Active participation in open, moderated, internet forums is surely to be encouraged.
6. 

   Mark Titus

   October 23, 2014 at 00:20

   Not true I think. The major "clashes of points of view at the frontiers of science" are played out in Science and Nature and other scientific journals. For example, the recent debate over detection of gravity waves from the Big Bang. I think Goldstein is after something else--more connected to Dr. Phil and Oprah than philosophy.
   1. 

      Arnold Trehub

      October 23, 2014 at 15:32

      The scientific journals are essential, but they do not provide the opportunity for the nearly realtime exchanges among active investigators in focussed discussions on the dedicated internet forums.
      1. 

         Mark Titus

         October 24, 2014 at 00:02

         I looked up ResearchGate and appreciate your comment. However, the basic structure of science is in place and "clashes at the frontiers"--basically cosmology and sub-atomic physics-- occur; but I don't see how they can be responsibly addressed in the forums you mention. With philosophy it is quite different. Nothing is in place, and people like Rebecca Goldstein feed off that.
7. 

   Cliff Styles

   October 23, 2014 at 00:39

   An answer to your Plato on a bumper sticker question, which Goldstein didn't even attempt: 'The ideal is not real, what now?'
8. 

   Ted Schrey Montreal

   October 26, 2014 at 14:22

   "Mathematics was invented and discovered", is what I learn here. I shall sit back and ponder this a while...about as long as it takes me to have my cake and eat it too.
   1. 

      Mark Titus

      October 26, 2014 at 19:54

      It seems to me many things are mixtures of discovery and invention. Take the steam engine for example.
9. 

   Ted Schrey Montreal

   October 26, 2014 at 14:34

   "Math is a language...and "as such...an action, not an entity". Action, entity, description, discovery, invention, what else? For something as concise and clear as math, it's all rather convoluted.
10. 

    Ted Schrey Montreal

    October 27, 2014 at 00:41

    I took the steam engine, looked at it and concluded someone invented it, long before I discovered it parked in the old shed out back. Math is a system of abstractions of one kind or another; these (are made to) refer to aspects of reality. Abstractions do not occur in (physical) reality. However, one can imagine/assume they deal with aspects of reality---but only if one invents such connections.
    1. 

       Mark Titus

       October 27, 2014 at 02:12

       My point was that you have to discover something about water and its phase changes before you can invent steam engines, just as you have to discover something about fingers and toes (that they are "digits") before you can invent arithmetic. Granted, it's a little more complicated in the second case.
11. 

    Jack B.

    August 5, 2015 at 20:58

    Mark Titus has it right. Reason's principles and techniques are easily found-uncoupled from any putative creators or discoverers--in maths and science, logic and even the law when it ratiocinates unencumbered by fees or precedents. Reason's techniques are embedded in many fields, suggesting that when philosophy tries to apply them to specific areas, it treads not only on oft-trodden soil but soil alien to it. Hence, it is a meaningless discipline.