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Related, I suppose, to this question.

In mathematics most theorems are of the form:

If we have a [type of object] with [property 1] then it also has [property 2]

That is, they are conditional statements on classes of objects. Traditionally analytic philosophy, in its description of the objective world, has (in spite of its similarity, as being composed of arguments, with mathematics) dealt in absolutes rather than conditionals.

I am interested in whether there has been any move toward the conditional in analytic philosophy. Particularly intriguing, and most conceivable to me, is the prospect of a systematized relativism in which beliefs follow conditionally- has this been done? Or anything in this vein, for that matter?

Edit

I am well aware that in a strict logical sense any proposition is equivalent to a conditional, however it is in the latter sense alluded to in Joel's answer, that is:

in any situation in which the axioms are true (or in which the background assumptions are correct), then p

that I am referring to conditionals. I am however not alluding to the strict axiomatic method, so much as the application of analytic reasoning to non-trivial background assumptions. As I said above, most interesting to me would be if the background assumptions in question concerened the beliefs of an entity, together with certain assumptions relating to the entity's rationality, but anything of the broader putative genre would intrigue me greatly.

  • 2
    Your wikipedia citations does not support your claim tat Gödel's Incompleteness Theorems caused a problem for Platonism. This is as it should be as the theorems did not serve to undermine Platonism. Indeed, Gödel's own reaction to them was to move towards a more platonistic position. – vanden Jul 4 '11 at 13:12
  • Battle? Retreat? I really don't follow your metaphor for the historical trends and events in Foundations of Mathemtics. Can you elaborate? – Mitch Jul 4 '11 at 14:20
  • I have done some fairly dramatic editing. My motivation, with its inevitable controversy, seemed to be detracting from the question itself. – Tom Boardman Jul 4 '11 at 14:58
  • ...And I've removed it. Joel's answer certainly addresses the letter of my question, but a logical answer isn't really what I'm after. – Tom Boardman Jul 4 '11 at 22:23
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    @Joseph, apologies, still getting used to the 'house style'- people seem to really dig short questions here, but it's rather difficult to explain where you're coming from in that short a space. Better now...? – Tom Boardman Jul 5 '11 at 11:49
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I have two remarks.

First, I observe that every statement is logically equivalent to a conditional statement. Specifically, any proposition p is logically equivalent to the conditional proposition ¬p → p, among numerous other conditional propositions, such as (p ↔ p) → p, which the reader may easily verify. In this sense, if one allows propositions to qualify as "conditionals" when they are merely logically equivalent to conditionals, then the notion is simply too generous, since every statement will qualify. And otherwise, if one insists literally on an explicit conditional form, then the notion seems to be concerned with presentational style over substance. Thus, the class of statements-expressible-as-conditionals is not so robust logically.

Another way to make this point is that in principle, any philosophical work can be put explicitly into the desired conditional-only form, without changing the meaning of the work, by replacing every assertion p in the work with a conditional propositional equivalent to it, such as ¬p → p. However, because this would clearly be silly, it is not clear what the substance of the property of "expressed in conditionals" really carries.

Second, I would like to mention that whenever one argues in an axiomatic system, such as in mathematics and perhaps other contexts as well, and even when one argues in a context of background assumptions, then there is an implicit intention that asserting p really means "in any situation in which the axioms are true (or in which the background assumptions are correct), then p "

  • +1 and any arguement worth making can be done using mathmatical notation good job sir. – Chad Jul 5 '11 at 14:06
  • just wanted to let you know the question has been updated for clarity in response to your first point (if you happen to wish to reformulate) – Joseph Weissman Jul 5 '11 at 17:32
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    Thanks, Joseph; unless there is some reason to do otherwise, I'll just leave this answer here, since it addresses the literal interpretation of the title question, even though I realize I haven't satisfied the OP's intent. I'll hope that Tom doesn't mind. – JDH Jul 5 '11 at 20:37
  • @JDH not at all! may apologies for somewhat pulling the rug out from under you here, moreover in my originally direly-worded god-brain question: right on the money If not what I was failing to get at! – Tom Boardman Jul 5 '11 at 23:43

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