Biblical Hebrew Forum

["Matthew Anstey" <manstey AT portal.ca>]

Gday B-Haverim

Happy new year and all that jazz! We are obviously off to a productive start
regarding BH debates, judging by recent posts. I wanted to comment on Rolf's
"logic" stuff, eg:

>In OT studies we can from this learn two things: (1) When we are doing
>research or arguing about passages we should always try to connect our
>conclusions with a theoretic framwork which is logically valid, and
>calibrate our conclusions by way of it,

Rolf, you have presented many arguments on the list using "syllogistic
logic," which ensures "logical validity." There are many issues however
surrounding the use of logic.

Firstly, you (not just Rolf, but a generic "you") need to specify which
system of predicate logic you are using. Logical arguments are valid
_within_ the logical system they are framed in, and sententially invalid
arguments may prove to be valid in more powerful systems (egs 2+2=5 in some
second-order logics; in intuitionistic logic the rule of double-negation is
rejected, so not(notP) is not equivalent to P, etc). So before one ought to
accept your hard-and-fast logic as universally true, you first need to
define your logical system (ie lexicon and syntax, sequents, theorems etc).
It will then be true in the "universe" you define by logic.

Secondly, you need to specify what sort of "validity" you are using. Is it
semantic or deductive? Semantic consequence means that the conclusion of an
argument follows from its premises when no interpretation of the argument's
form makes the premisses true and the conclusions false. Deductive
consequence means the conclusion follows from its premises using the rules
of inference of the logical system. The first says nothing about rules of
inference, and the second nothing about truth. That is, you have not
specified the completeness or the soundness of your logical system.

Thirdly, you need to specify the relationship between your logical system
and the "real world," which for simplicity (;->) we can define as the
"mind-independent world." What I mean is that we may all agree (without too
much angst) that critical thinking is necessary, but you are assuming a
priori that (as it seems from your posts, correct me if I'm wrong) that
first-order monadic predicate logic (MPL) is the way to prove an argument is
correct, and this we will certainly not all agree on. And furthermore, this
_itself_ is an argument that depends upon MPL to be valid. So you cannot
easily prove that MPL guarantees truth. You can easily present us a sound
(and usually complete) version of MPL, but the relationship between MPL and
"truth" cannot be proved by MPL itself. You are forced into metaphysics (or
deconstructed into language games, or reduced to phenomena, etc).

Fourthly, many people use the term "predicate," as in the predicate "P is
God." But a logical predicate is quite a different creature than a
linguistic one. Linguistically we all know how Greek and Hebrew and English
form predicate sentences. But in logic predicates are said to "satisfy
objects," or that the object possesses the corresponding property of the
predicate, etc. So we need a theory of predication before we can proceed,
and this must consider sense, reference, etc, and the relationship between
the predicate and the real world. So it is no good proceeding by finding a
series of linguistic predicates in the Bible, like "Jesus is the first and
the last" and "God is the first and the last" and adding some other bits to
get "Jesus is God." This relates to the second criticism above, since while
it may be deductively valid, it may not be semantically valid.

These are I think four major issues involved with the application of logic
in reasoning, but there are more and I may have missed some other biggies.

The solution to these have puzzled philosophers and others for all time so I
don't think we'll make any breakthroughs here. But some clearer
understanding of the tools, presuppositions, and issues involved may help.

With regards

Matthew Anstey

PS I'm going away tomorrow for three weeks so I can't respond to this
personally till I get back. If it still has steam then, or it emerges again
sometime, I'll be in boots and all on this discussion!