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I have read some of the philosophies on either side of the argument, but lack the historical overview to really get a picture of the main achievements chronologically. I'm taking nominalism to mean either rejection of universals or abstract objects, insight from either camp would be welcome.

Pseudonym
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  • You can see : [The Medieval Problem of Universals](http://plato.stanford.edu/entries/universals-medieval/), [Nominalism in Metaphysics](http://plato.stanford.edu/entries/nominalism-metaphysics/), [Nominalism in the Philosophy of Mathematics](http://plato.stanford.edu/entries/nominalism-mathematics/) and [Platonism in the Philosophy of Mathematics](http://plato.stanford.edu/entries/platonism-mathematics/) for historical overviews and recent debate. – Mauro ALLEGRANZA Nov 02 '16 at 07:56
  • @MauroALLEGRANZA Thanks, I had read the first two, but not the mathematics references so I will see if I can find any answers there. The problem I found with the first two is that whilst they gave an excellent historical account, I could not find in them an idea of what had been achieved in the field, as opposed to simply an account of what had been said. – Pseudonym Nov 02 '16 at 08:26
  • Achievements ? See [Plato](http://plato.stanford.edu/entries/plato/). – Mauro ALLEGRANZA Nov 02 '16 at 11:17
  • @MauroALLEGRANZA I'm sorry, I don't understand the reference, it's just taken me to a page about Plato, could you elaborate? – Pseudonym Nov 02 '16 at 13:35
  • You need to be more precise as to what you consider an achievement, if successive arguments alone do not qualify. –  Nov 02 '16 at 16:39
  • @Jobermark I'm not qualified to define achievement, however philosophers generally define it is fine for my purposes. Whatever purpose philosophers have for doing philosophy, when they've succeeded in that purpose is what I mean by an achievement, but I may be wrong. I just presume it's not the case that everything a philosopher writes achieves its purpose, hence my distinction between an account of what has been written and an account of the major achievements. By my definition the achievements would be the selection of all that philosophers have written that succeeded in their defined goal. – Pseudonym Nov 02 '16 at 16:48
  • You seem to come at philosophy with a standard inspired by science, and that does not work well. This is not a "field" as you see it, there is no definitive "purpose", and therefore no "major achievements" except in a loose sense of informing and clarifying other endeavors. What has been "achieved" is largely what has been said or rather understood. On universals, Wittgensteinian "family resemblance" interpretation of them is currently prominent http://philosophy.stackexchange.com/questions/31879/is-it-possible-to-use-wittgensteins-family-resemblance-to-separate-high-art-fro/31901#31901 – Conifold Nov 02 '16 at 17:56
  • @Conifold I seem to be missing something important here in my language. I'm presuming you're not trying to say that philosophy has no objective measure. There are philosophers who are considered great, there are those who become philosophy professors and those who do not make the grade. Whatever is measuring these people, that's what I'm trying to get at. If you are good at philosophy, what is it you're good at? On what basis do editors of philosophy journals publish or not publish? On what basis do people even vote on sites like this? Any help here on what I'm failing to grasp would be great. – Pseudonym Nov 03 '16 at 07:31
  • @Conifold By the way, thanks for the link, it's an approach I've not read yet, although I'm now not sure why I'm reading any of it! – Pseudonym Nov 03 '16 at 07:33
  • I like Friedman's optimistic expression of it in Dynamics of Reason:"*although we do not (and I believe should not) achieve a stable consensus on the results of distinctively philosophical debate, we do nonetheless achieve a relatively stable consensus on what are the important contributions to the debate, and accordingly on what moves and arguments must be taken seriously*". As far as "results" philosophy does not have any "objective" measure or even agreement, there is more agreement on comparative worth based on originality and novelty of ideas, intellectual depth and sophistication, etc. – Conifold Nov 03 '16 at 17:49
  • @Conifold That's interesting, thanks. I'm having great trouble with the move from science to philosophy (I'm thinking of posting this as a question but not sure it would be on topic, by the rules). Your comments here have helped greatly with my understanding, but the scientist in me has to ask - is there evidence of *agreement* on "intellectual depth" and "sophistication" as you suggest? Or do groups of philosophers actually disagree with each other even on who to take seriously, either contemporaneously, or over time? – Pseudonym Nov 04 '16 at 07:01
  • Not so much on "intellectual depth" and "sophistication" themselves, but on who has "more" of that. In the case of universals Ockham, Kant, and Wittgenstein are seen as initiating major shifts in the debate. Perhaps a "result" is that after Wittgenstein the original realism/conceptualism/nominalism trichotomy of ideal entities/thoughts in mind/made up labels is seen as employing inadequate (too primitive) terms, and a new context of semantics/epistemology is needed where the problem transforms. But analytic/continental philosophers may split sharply on some figures, like Hegel or Wittgenstein. – Conifold Nov 04 '16 at 23:36
  • Also take a look at this earlier thread which I think was similar in spirit [What standards exist for developing a philosophical model?](http://philosophy.stackexchange.com/questions/38062/what-standards-exist-for-developing-a-philosophical-model) On the analytic/continental divide over certain topics, criteria and people see D'Agostini's [From a Continental Point of View](http://www.tandfonline.com/doi/pdf/10.1080/09672550110058821) – Conifold Nov 04 '16 at 23:59
  • @Conifold Thank you for sticking with this, I'm sorry if I'm sounding a bit "slow", but this is very much what I was unable to grasp with the platonism/nominalism debate which I started my philosophical reading on. I'm afraid the question you've kindly dug out for me has left me no less confused. The accepted answer talks about logical coherence and gives Kant's ethics as an example. This is also an area in which I've been doing some cursory reading and I can't seem to escape to notion that all positions that could exist, do exist, which makes the exposition of them seem a bit pointless. – Pseudonym Nov 05 '16 at 07:44
  • By the above I mean no disrespect to the subject, I just mean - if no positions have actually been ruled out apart from those which no sane person would hold anyway then what has been the motive, the purpose of the exercise, regardless of how endeavours are judged, they must surely have purpose? – Pseudonym Nov 05 '16 at 07:47
  • Think of art: literature, music, painting. Is there a purpose other than the pieces of art themselves? It is not easy to pin down what function it serves in society. Logical positivists even likened the "non-scientific" side of philosophy to expressive art. One service is as an intellectual playground of ideas, an incubator for social and cultural engineering and "housekeeping" arrangements (including sciences). I also think you are underestimating the difficulty of forging "grand" positions that can withstand pointed criticisms from every which way, no luxury of limiting scope as in science. – Conifold Nov 08 '16 at 21:27
  • @Conifold I like your description of philosophy, but I'm doubtful that it is seen or treated that way in the real world. The difference between art and philosophy in that sense is that art is judged by non-artists, if no-one likes your painting you are no an artist (or at least not a good one). Philosophy, it seems, is only allowed to be judged by other philosophers, this suggests some kind of measure of quality complex enough that non-experts couldn't grasp it sufficiently to judge, but I have yet to hear what that quality is. I still feel like I'm missing something major here. – Pseudonym Nov 09 '16 at 08:15
  • Here is another quote, from Burge, "*Philosophy, both as product and as activity, lies in the detailed posing of questions, the clarification of meaning, the development and criticism of argument, the working out of ideas and points of view. It resides in the angles, nuances, styles, struggles, and revisions of individual authors*". I also doubt that complex art can be adequately judged by non-experts, but experts need not be artists. To use a sports analogy, both are more like figure skating than hockey, "measures" are vague, and you need an expert panel to judge it beyond like/dislike. – Conifold Nov 09 '16 at 20:04
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    @Conifold Thank you for your perseverance. I think I understand what you're saying. I'm not sure I like it as I think a lot of philosophers act as if it were something more than that, but your description explains the complication with my question perfectly. – Pseudonym Nov 10 '16 at 10:10
  • @Conifold I don't know what the protocol is for resurrecting old comment strings so I apologize if this is not the right thing to do, but reading through a few articles on this very subject has raised a question which relates precisely to your "sports" analogy which I hoped I might gain some insight from putting directly to you. – Pseudonym Jan 03 '17 at 11:19
  • The answer [here](http://philosophy.stackexchange.com/questions/40036/writing-and-publishing-a-philosophical-book-without-ma-phd-in-philosophy-and-no) seems very much to suggest that something complex, but universally agreed upon, is in the minds of the academics doing the judging. It is this factor that I'm interested in establishing. Is this a different approach to the one you've so patiently outlined above, or is it the same and I'm missing the similarity? – Pseudonym Jan 03 '17 at 11:27
  • Long comment threads are generally discouraged even for new posts, and just practically, it is easier to get more attention from different users by asking a new question. As for judging, even science is ultimately in the minds of people looking at the meter ("*only theory decides what can be measured*", Einstein), they just tend to have more agreement on what they see there. The more "eyes" something gets the more individual idiosyncrasies of "judges", or even communities of "judges", tend to wash out, it just takes a very long time in philosophy. But then we still read Plato and Aristotle. – Conifold Jan 04 '17 at 04:47

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Mark Balguer's Platonism and Anti-Platonism in the Philosophy of Mathematics is considered a critical text arguing that the ontology of mathematical objects is an open question such that there are perhaps equally good arguments on both sides for mutually exclusive positions.

Lothrop Stoddard
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  • If I understand correctly, this would make the answer to my my question "there have been none whatsoever", at least with regards to mathematics. If in 2001 it can be argued still that both sides could be equally well argued for, then neither side has managed to produce a conclusive argument in two and a half thousand years. Has anyone considered it might be time to give up? – Pseudonym Jan 03 '17 at 11:12
  • @Pseudonym fictionalists take it that we should drop ontological commitment as a criterion of the utility of a theory. Basically we have the structure of realism, minus the realism – Lothrop Stoddard Jan 03 '17 at 13:34