Saturday, August 08, 2015

Clark and Gödel

In my experience, Clarkians like to describe Scripturalism as an axiomatic system. For instance:
(A) There is an axiom, called “The Axiom of Revelation,” from which, by itself, there can be validly deduced an important set of theorems.
(B) These theorems belong to a number of fields, such as theology, history, logic, ethics, politics, etc., and they constitute the Christian doctrine on these subjects.
(C) This axiomatic set of propositions is available to human beings as certain knowledge.
(D) This set contains the only certain knowledge, as perhaps opposed to opinion, available to human beings. (This is to be contrasted with the failure of other methods of obtaining knowledge.)
(E) The Axiom of Revelation is “The Bible is the Word of God.” - See more at:

The general reason for this is that Scripturalism is a variant on modern classical foundationism, which lends itself to an axiomatic model. 
In addition, this has specific philosophical precedents. For instance:
Given Spinoza’s devaluation of sense perception as a means of acquiring knowledge, his description of a purely intellectual form of cognition, and his idealization of geometry as a model for philosophy… 
Upon opening Spinoza's masterpiece, the Ethics, one is immediately struck by its form. It is written in the style of a geometrical treatise, much like Euclid's Elements, with each book comprising a set of definitions, axioms, propositions, scholia, and other features that make up the formal apparatus of geometry.  
Some of this is explained by the fact that the seventeenth century was a time in which geometry was enjoying a resurgence of interest and was held in extraordinarily high esteem, especially within the intellectual circles in which Spinoza moved. We may add to this the fact that Spinoza, though not a Cartesian, was an avid student of Descartes's works. As is well known, Descartes was the leading advocate of the use of geometric method within philosophy, and his Meditations was written more geometrico, in the geometrical style. In this respect the Ethics can be said to be Cartesian in inspiration.
Axiomatization was carried forward by Hilbert: 

In the early 1920s, the German mathematician David Hilbert (1862–1943) put forward a new proposal for the foundation of classical mathematics which has come to be known as Hilbert's Program. It calls for a formalization of all of mathematics in axiomatic form, together with a proof that this axiomatization of mathematics is consistent.
But that proved to be a blind alley: 
The first incompleteness theorem states that in any consistent formal system F within which a certain amount of arithmetic can be carried out, there are statements of the language of F which can neither be proved nor disproved in F. According to the second incompleteness theorem, such a formal system cannot prove that the system itself is consistent (assuming it is indeed consistent).  
In order to understand Gödel's theorems, one must first explain the key concepts essential to it, such as “formal system”, “consistency”, and “completeness”. Roughly, a formal system is a system of axioms equipped with rules of inference, which allow one to generate new theorems. The set of axioms is required to be finite or at least decidable. 
A formal system is complete if for every statement of the language of the system, either the statement or its negation can be derived (i.e., proved) in the system. A formal system is consistent if there is no statement such that the statement itself and its negation are both derivable in the system. 
One can also give more general epistemological interpretations of Gödel's theorems. Quine and Ullian (1978), for example, consider the traditional philosophical picture that all truths could be proved by self-evident steps from self-evident truths and observation. They then point out that even the truths of elementary number theory are presumably not in general derivable by self-evident steps from self-evident truths.
This, however, generates a dilemma for Scripturalism:
If, on the one hand, Scripturalism is an axiomatic system, then it cannot be shown to be consistent, or proven true, within the system itself. To prove it, you would have to go outside the system. But inasmuch as Scripture is said to be the only source and standard of truth, that would mean referring the validation of Scripturalism to an authority over and above Scripture. 
If, on the other hand, Scripturalists elude the problem by admitting that the comparison with an axiomatic system is just a vague metaphor, then Scripturalism relinquishes the claim to be a logically tight-knit epistemology or belief-system.  

1 comment:

  1. "But inasmuch as Scripture is said to be the only source and standard of truth, that would mean referring the validation of Scripturalism to an authority over and above Scripture."

    I never understood why some Scripturalists overstate Scripture as having a "systematic monopoly on truth." How do they expect to know when the second coming occurs? How do you derive that truth from Scripture when Jesus explicitly said it hasn't been revealed?