On Feb 18, 5:43 am, Jason Resch <[email protected]> wrote: > On Thu, Feb 17, 2011 at 7:49 PM, Stephen Paul King > <[email protected]>wrote: > > > Hi All, > > > Question: Why must Platonia exist? > > How many ways are there to arrange 4 people in a line? If you think the > answer 24 is true, regardless of any assumptions of axioms or set theory, > etc. then truth has an objective, eternal, causeless existence of its own. > These truths and falsehoods define or depend on the existence of other > abstract objects, propositions, theoreticals, etc.
That mathematical truth is eternal, fixed etc, does not mean it ha any existence at all, and can be explained by mathematics being non- referential Platonism gets its force from noting the robustness and fixity of mathematical truths, which are often described as "eternal". The reasoning seems to be that if the truth of a statement is fixed, it must be fixed by something external to itself. In other words, mathematical truths msut be discovered, because if they were made they could have be made differently, and so would not be fixed and eternal. But there is no reason to think that these two metaphors --"discovering" and "making"-- are the only options. Perhaps the modus operandi of mathematics is unique; perhaps it combines the fixed objectivity of discovering a physical fact about the external world whilst being nonetheless an internal, non-empirical activity. The Platonic thesis seems more obvious than it should because of an ambiguity in the word "objective". Objective truths may be defined ontologically as truths about real-world objects. Objective truths may also be defined epistemically as truths that do not depend on the whims or preferences of the speaker (unlike statements about the best movie of flavour of ice-cream). Statements that are objective in the ontological sense tend to be objective in the epistemic sense, but that does not mean that all statements that are objective in the epistemic sense need be objective in the ontological sense. They may fail to depend on individual whims and preferences without depending on anything external to the mind. We are able to answer questions about mathematical objects in a clear and unambiguous way, but that does not mean mathematical objects are clear and unambiguous things. Being able to answer questions is essentially epistemic. It doesn't imply any ontology in itself. The epistemic fact that we can , in principle, answer questions about real people may be explained by the existence and perceptual accessibility of real people: but our ability to answer questions about mathematical objects is explained by the existence of clear definitions and rules doen't need to posit of existing immaterial numbers (plus some mode of quasi-perceptual access to them). by the -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
