Sorry about the *, but no formatting in the title.
Reference the IEP.
Reference this paper
I am primarily an armchair philosopher, and by some accounts from some dopers a good one, and by other accounts from other dopers a shoddy one. And the lynchpin of philosophical systems of thought revolves around what I will call a class of claims (you may think of this is a formal class or not). The claim runs so: Every system requires certain assumptions which are taken as true.
In order to improve my own philosophical thought, then, I suppose if I were to start anywhere I should start with the motivation behind this claim, and claims like it.
Claims like it tend to discuss elements of knowledge that are named a priori, which is taken to represent a type of knowledge that, in principle, can be known before any experience. There are several accounts of a priori knowledge, though. Some consider math an element of the a priori by stating that, should all of my experiences be false (and I am merely a brain-in-a-vat subject to someone or something’s whim) I still know that, for example, 1+1=2.
In treading into a discussion of the a priori, we are also bound to discuss another topic, the analytic/synthetic distinction. I think this is best described as Hume’s Fork. Analytic truths are wholly analyzable by the structure of the propositions themselves. From tautologies only other tautologies are derivable. No new information is added. Mathematics could be seen to be analytic in this sense. Or predicate logic. Synthetic statements, on the other hand, are not analyzable solely by their constituents. The statements rely on information not strictly contained in the meaning of the proposition. In the terminology of Hume’s Fork, analytic statements are necessarily true and synthetic statements are contingently true (based on some information not contained solely within the proposition itself, but “out there” in the real world).
From these we gain the following four types of knowledge:
analytic synthetic
a priori
a posteriori
Consider that a table where the column headers go first, and the row headers go second.
Philosophers in some quarters have felt that two cases are impossible; to wit, the synthetic a priori and the analytic a posteriori. Others have disagreed for metaphysical reasons.
I reject any claim of the a priori as: a statement that is universally and necessarily true. A rejection of this involves the rejection of the axiomatic claim (which I consider to be the “one claim” around which all other axiomatic claims are sourced from) that all systems are founded on certain assumptions which are regarded as true.
My rejection runs thusly:
[list=1][li]Truth is a statement made from within a system; i.e.—this statement P is true iff it follows from {X} [some set of rules]. The truth of P normally comes from a rule-for-testing. in some cases the “system” is only a positive definition which allows for exlcusion based on the terms at hand.[/li][li]In order to examine {X} for truth we would need a system. But if we could have a system for {X} then this system would have its own {Y} rules which implies an endless heirarchy for truth-determination.[/li][li]We might be tempted to then assert the truth of {X} independently of a system; that is, we elevate them to the a priori state and assert them as elements of knowledge which we cannot test.[/li][li]This creates a system that has a foundation of truth which is not verifiable, and must be accepted or rejected on no basis whatsoever. To attempt to give it a basis then takes on the form of a system, already mentioned as a case of an infinite heirarchy above.[/li][li]So then we must create a method not found in a system per se which can distinguish unjustifiable/unverifiable axioms of the a priori from other unjusitifable/unverifiable claims.[/li][li]Any application of a method is an empirical investigation, and is thus subject to the uncertainty found from it.[/li][li]So then we cannot assert the truth of {X}.[/li][/list=1]
This forms one of my two reasons for rejecting axiomatic claims as true. And the emphasis there is crucial to my point. In another thread I am attempting to investigate, with some help from dopers, the phenomenological barrier which prevents anyone but ourselevs from “looking inside my head” or “seeing with my eyes” etc. In this I want to define and examine what I will term the transcendental barrier: this is the barrier that separates a metaphysical claim of truth from our understanding of it. In the other thread I shared the opinion of a philosopher (after much effort) that communication regarding “events” behind the phen. barrier were impossible. In this I would like to investigate a similar claim: that communication regarding “truth” on the other side of the transcendental barrier is also impossible, and thus nonsensical.
As a summary, I would like to say this: claims regarding truth independent of anyone that can say it is true are erroneous. Discussing that knowledge exists which is independent of any particular knower is nonsense. [please do not feel I am saying everything is subjective or some such: I am NOT]
As a summary of the summary: everything that is true is synthetically true, and only from a synthesis can the analytic truths be found.
I am prepared to defend or otherwise justify these statements as necessary. Discuss, anyone?