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To know something correctly requires describing a context that places that something, but to describe that context we would need to describe a wider context that places it and so on.

We have an infinite regression. So to obtain knowledge we must truncate this at some point, but then we do not have real knowledge of that something. Does this mean epistemology is not possible?

4

No, but it leads to things like Coherentist Epistemology, for example.

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Your use of the term “context” is not entirely clear. If you’re referring to the material content of an object (its contingent actuality), then the context is defined by its substantial being; i.e., its immediate qualitative and quantitative measurement. However, if you’re also referring to the formal conditions of predication of an object (its absolute possibilities), then the context is defined by its essential being; i.e., its necessary and universal qualities. The former kind of knowledge is scientific and conditional (empirical/a posteriori); it's finite in the sense that the content expressed by an object is particular to itself. The latter kind of knowledge, by contrast, is philosophical and unconditional (non-empirical/a priori); it's only infinite in the sense that its formal characteristics are predicable of an indefinite number of particulars; this is different than saying that its essential being is ungrounded or without limit. In either case, there is no infinite regress. For us to know something correctly (i.e., objectively) we need only understand the determinate content of an object in the context of its ontology. The ontology itself is a finite conceptual totality (a lifeless abstraction) capable of marking out the categorial structure of reality. Only when this scheme is properly mediated by the inductive details of experience do we constitute the truth of the object.

  • I think I understand the first part of this, but I have trouble with the second. Who introduced the term 'contingent actuality'? I can't agree that the content of an object is particular to itself. As you've said that this knowledge is scientific, I'll discuss it in scientific terms. The properties of a kind of particle, say an electron, is already tied in with that of spacetime. The two are intimately tied together. – Mozibur Ullah Sep 25 '12 at 18:27
  • “Contingent actuality” is a philosophical term of art (introduced by Aristotle as energeia and entelecheia) denoting the brute state of completion or particular realization of substance. It’s meant to be contrasted with the absolute possibility (i.e., the potency, force, logos, or essential being) of the very same substance. Both aspects are presupposed and required to demonstrate knowledge of an object. The content expressed by an object is therefore particular to itself because it lacks the determinate mediation afforded by a universal and necessary form of judgment. – Apollo_is_Dead Sep 25 '12 at 21:53
  • The properties of an electron, as you’ve indicated, are “kind” terms; i.e., it already contains the ontological concept of spacetime. The contingent actuality of an electron expresses only the qualitative and quantitative configuration or measurement of its properties, not the kind of properties that it possesses; e.g., its specific magnitudes or qualitative ratios. And so I agree that the two are intimately tied together. My comment was intended more to disentangle the different aspects of the knowledge context. I’m basically claiming that the context is finite, not infinite. – Apollo_is_Dead Sep 25 '12 at 21:55
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Disclaimer: I have no idea what Epistemology is but I may be able to contribute some logical reasoning.

Assertion: You say "Correctness" requires this notion of "Context" in order to say that something is correct w.r.t. this context?

Answer: Not necessarily. I can define something from nothing (axiom) and then everything upon this something (inductive definition). Then I can check the correctness of any expression w.r.t. these rules.

For instance:

  • (Axiom): I define number 0 to be "nothing", the empty set {}
  • (Inductive Definition of succ(x)): I define the successor of a number to be a number and specify the successor function of an element x to be the set of x combined with x:
    • succ(x) = {x,{x}}.
  • (Inductive Definition of add(x,y)): I define the result of adding two numbers to be a number and specify:
    • add(0,y) = y and
    • add(succ(x),y) = succ(add(x,y)).

Now we can check whether the statement "1+2 is a number" is correct. 1+2 is merely syntactic sugar for add(succ(0),succ(succ(0)) which resolves to succ(add(0,succ(succ(0))) and then to succ(succ(succ(0))) which is syntactic sugar for {{},{{}},{{},{{}}}.

The other part of the answer is: Perhaps yes, because Goedel shows in such effectively generated axiomatization of number theory will be true statements which cannot be proven in that system.

  • 1
    That's a nice bit of sleight-of-hand; you haven't actually defined anything from nothing, but from "nothing." You are also defining "successor"; upon what does this definition rest? – Michael Dorfman Sep 25 '12 at 11:04
  • Well, if I am allowed to define truth by creating a context, then I shall define the empty set as a fact, and the set of a set to be a set, too. Then, I can establish all kinds of knowledge "inductively". This context bases only on the existence of "empty set" as "higher-level context" which itself does not require further (regressing) context. – Marcel Sep 25 '12 at 11:34
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    You're still depending on notions like "set" and "empty set." It's turtles all the way down; there's no fixed foundation for you to build upon. Put another way: you can look up words in a dictionary, but they are always defined in terms of other words. – Michael Dorfman Sep 25 '12 at 11:45
  • Axiomatic systems are also a coding of mathematical knowledge. They're ahistorical. They're an efficient way of organising a certain kind of knowledge. Though there is always excess. If you actually look at the history of set theory/logical & formal systems, you see people reasoning in ways that are extra-set theory and moving and testing boundaries. Set theory is still a work-in-progress, and will always be until mathematicians tire of it. They may move even away from it. or discard it altogether, and then it will be a historical curio. Which would show its 'foundational character' – Mozibur Ullah Sep 25 '12 at 16:45
  • as a certain kind of myth. Or you could say they've gone a further 'turtle' down, or maybe sideways onto a larger sturdier one... – Mozibur Ullah Sep 25 '12 at 16:47

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