Wednesday, October 10, 2007

An Update On Advances In Biblical Logic: The Roles of Set Theory and Propositional Logic in the Development of Systematic Theology

Okay, but you have to start somewhere. There is a fine saying I have heard among dentists: "You don't have to brush EVERY tooth, just the ones you want to keep." Biblical theology proceeds in a similar fashion. You have to use it, and sharpen your tools now and again to retain what you have gained therein so far.

I continue my studies into the relationship between various logical relations and the light of nature, as compared to the teachings (taken as a whole) of the Word of God written, often simply the "Holy Bible."

I have come to the following conclusions thus far (though I cannot promise some reformulation will proceed from additional progress -- such is the nature of reformation) -- I hope they help:

First, all the propositions constituting the light of nature (as a single unit or web of beliefs) must be in the nature of the case LOGICALLY NECESSARY truths.

Second, each proposition constituting (with the others) this web are by logical necessity related TO EACH OTHER in just the same way -- by logical necessity also. That is, any two logically necessary propositions -- no matter how disparate they may seem -- can be linked together by other such propositions to imply the first. You simply have to imagine what the propositional gaps between them might look like and work from one to the other, using propositions from your developed general and special revelatory sets.

Third, like the Word of God written, the light of nature also necessarily contains ONLY mutually affirming propositions (it has the consent of all the parts, with each part cheering the others on. Go team).

Fourth, here is an implicate that follows from 1-3. Each proposition of the light of nature entails all others of that kind.

Fifth, the Bible confirms the use of "sets," the grouping of propositions which specify like content into individual "bundles," for comparison with all others -- both from general AND special revelation.

This happens many places in the Word, including the very outset, where God groups each kind of animal with its proper sphere (birds with the heavens, fish with the oceans, and land creatures with the earth, etc., as well by special liturgical terms and groupings -- the seven lampstands, and the phrases "Set in order," and "each according to its own kind."

This means that set theory has the "green light," from the Word, so long as the categories used come from the Word itself, or as logical implicates from the light of nature, for the nonverbal Word in nature cannot reprove but must sweetly comport with all that special revelation God has given to his people.

Sixth, Special revelation contains all of natural revelations propositions "in miniature," or representatively -- for representation is an inherent feature of all covenants, and both the Word in nature and in Scripture are innately covenantal. Thus, in all matters of religious and logical controversies, none other final judge may have the last say-so other than the Holy Spirit speaking in the Scriptures, in whose sentence we must finally rest.

Thus, the way to really power-up a systematic theology (given the above doctrines) goes like this:

1. Identify the most central biblical concepts -- those at the heart (not the outskirts) of the Biblical worldview, and glean everything you might from all the canon (from Genesis forward), grouping all such propositions in the appropriate set. For instance, this procedure would require the "covenants set," "prophets set," "priests set," and "kings set." Next one would necessarily need the "Melchizedek proposition set," etc.

2. One would need to do similarly with the propositions determined from general revelation, by implication one from another, individually and in combination with other like propositions.

3. In sets from both 1 and 2 immediately preceeding, one would need to number each proposition in the set as they come to notice. This would render each proposition determinable from either GenRev or SpRev, with a number -- say "SpRev 45." This way one could cross-reference each proposition with others in an identifiable fashion, which would enable a kind of "shorthand" made of symbols -- just as with symbolic logics. This will speed things up considerable.

4. SpRev could be reduced simply to SR (in capital letters only). Then one might add the subset -- say from the 15th proposition in the Melchizedek proposition set (mel15) with each subset in lower case letters only. This would be SRmel15. To cross-reference this with the next proposition in the set, you could simply put the two in brackets:

(SRmel15) (SRmel16) = New proposition (list any implicate that follows).

This way each propositional combination, and its determined consequents could proceed in order fashion, and provide the basis for a biblical symbolic logic, the first of its kind, so far as I know. Then one could use the operations common in other logics (for modus ponens, modus tollens and the like). For these are demonstrably from the light of nature.

Other operations and combinations (biblically-authorized forms of argument) could easily be determined from the argument structures used by the prophets, apostles and the Lord Jesus Himself. This is the role of exegesis in the development of logic, which is used in turn for the development of a systematic theology -- which we can prove -- is actually the case by the impossibility of the contrary in each and every case, or which (if not) we must discard as falsfied either by self-elimination (as with necessarily false claims), or by contradiction of any one implicate of the Holy Scripture.

There is in principle, should one proceed upon these insights, no limit to the extent to which such a team could elaborate with precision and demonstrable accuracy the biblical worldview -- dare I say it -- to "boldly go where no one has gone before," but which many have implied without realizing it.

This is the self-conscious paradigm extrapolation from the Word written and nonverbal. This is the goal of systematic theology -- to explain, expound and clarify, to verify, confirm or falsify and accuse.

With some attentuation and modification (to be sure), this is the future of biblical study. This is inescapable with the rigor of biblical logic itself. For, "the way of life winds upward for the wise," and the Lord said, "I will build my Church."

The contrary is impossible.

And now for a completely unscientific, and non-Cartesian postscript.

Sooner or later one will have to figure into this equation (when distinguishing general and special revelation) necessary truths from contingent ones. By "contingent" truths we mean to specify truths describing the choices and actions of secondary agents like people and animals. These could have been otherwise, given their reality as a direct consequences of choices people did not have to make (in other words, choices in which they sometimes choose otherwise when presented with similar circumstances).

Necessary truths, on the other hand, cannot logically be otherwise than what they are because their denials lead inescapably to absurdity. This is not the case with contingent truths, such as "my dog is golden in color." Denying this proposition may be false, but it does not imply absurdities.

Now the propositions making up general and special revelation can (strangely) be said to be BOTH contingent and logically necessary, but in different senses. Hold off on the twilight zone music. Please allow a brief explanation.

All the propositions of the Bible are logically necessary as a product of the canon, since the canon as a whole (and all its parts) form the One meta-transcendental. But prior to its inclusion in the canon, the statement, "Johnathan tasted the honey, and his eyes brightened," was merely a CONTINGENT in terms of what we could justify.

But because God's eternal counsel proceeds from all eternity (in His unfathomable Wisdom), the truth of that proposition was a CONSEQUENT absolute necessity, given the divine choice to foreordain whatsoever has or will come to pass. So here we have a historical necessity -- the consequent absolute necessity of the truth of A (where A represents a proposition which later is to appear in the canon), then there is the historical contingency of A (we cannot justify the claim that "A is historically necessary" unless and until God prophesies it), and then there is the logical contingency of A (since we cannot say that A is logically necessary until we SEE its inclusion in the canon) and consequent upon such an inclusion we can say justifiably that "A is logically necessary."

Logically necessary claims do exist outside of the Bible, but the Bible either implies them, or else warrants them in a way other than implication by secondary authorities which it authorizes - as in the general reliability of your senses ("The seeing eye and the hearing ear, the Lord has made them both." Combine this passage with the teaching that God made all things "very good" for mutually affirmation and correspondence, then we may infer that your senses (in ordinary circumstances) generally do not belie the facts. Their sensations "match" the real world.

Thus do I refute Kant's (epistemic) chasm between the noumenal and phenomenal realms he postulates.

The Non-Euclideans go wild for these distinctions. If they do not now seem of particular help or interest, open a bottle of Heineken and sip away. They will soon become downright fascinating. How do you think logic students REALLY get through this stuff -- with truth tables? Oh please. I am told that reading Tarski on defining logical consequences requires a veritable liquor license.

(But never drink and derive). And remember Modus Ponens. It's the law.

But more on that later.

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