Magma2
Puritan Board Sophomore
Don writes:
While most of your post in my view was merely gainsaying and not argument, I thought I would touch on this last objection since it seems to be the most substantive and, besides, I think the other objections have already been dealt with.
First, it is quite impossible to say or write anything without presupposing the laws of logic. However, I think the question why not make logic another axiom in addition to the Scriptures is a good one, even if it wasn´t specifically the one you asked.
Clark answered this question as follows:
While I think the above answers what I think is the better question, I do think it possible to deduce the laws of logic, specifically LC and LEM from Scripture. On the Scripturalist list, George Coghill gave me permission to reprint his argument for LC and LEM here. His argument is pretty involved, but I think most (including myself) certainly can get the gist. Besides, I think his argument has a certain elegance to it:
Oh and please deduce the laws of logic from scripture as well without *PRESUPPOSING* them either before or while you are deducing them!
While most of your post in my view was merely gainsaying and not argument, I thought I would touch on this last objection since it seems to be the most substantive and, besides, I think the other objections have already been dealt with.
First, it is quite impossible to say or write anything without presupposing the laws of logic. However, I think the question why not make logic another axiom in addition to the Scriptures is a good one, even if it wasn´t specifically the one you asked.
Clark answered this question as follows:
The law of contradiction is not to betaken as an axiom prior to or independent of God. The law is God thinking.
For this reason also the law of contradiction is not subsequent to God. If one should say that logic is dependent on God´s thinking, it is dependent only in the sense that it is the characteristic of God´s thinking. It is not subsequent temporally, for God is eternal and there was never a time when God existed without thinking logically. One must not suppose that God´s will existed as an inert substance before he willed to think.
As there is no temporal priority, so also there is no logical or analytical priority. Not only was Logic the beginning, but Logic was God. If this unusual translation of John´s Prologue still disturbs someone, he might yet allow that God is his thinking. God is not a passive or potential substratum; he is actuality or activity. This is the philosophical terminology to express the Biblical idea that God is a living God. Hence logic is to be considered as the activity of God´s willing.
While I think the above answers what I think is the better question, I do think it possible to deduce the laws of logic, specifically LC and LEM from Scripture. On the Scripturalist list, George Coghill gave me permission to reprint his argument for LC and LEM here. His argument is pretty involved, but I think most (including myself) certainly can get the gist. Besides, I think his argument has a certain elegance to it:
That lc and lem are deliverances of scripture comes from 1 John 2:21:
No falsehood (pseudos) is of the truth.
That as it stands is a pretty good declaration of the law of contradiction. It says that there is no proposition (x) that is both a falsehood and of the truth (ie a member of the class of true propositions).
Note that this is a universal negative. That is, it applies to every member of the class, which in this case is propositions. Now, that it applies to all propositions not just those in scripture should be obvious from the fact that there are no falsehoods in scripture.
Let Tx stand for 'x is of the truth', and Fx stand for x is a falsehood.
Then we can put it into symbolic logic as:
~3x(Fx & Tx) ---(1)
where '~' means 'not' and '3x' means 'there exists an x'
By de Morgans laws this is equivalent to:
~3x~(~Fx + ~Tx) ---(2)
Now in scripture there are (as far as I can see) only two types of proposition spoken of: true ones and false ones. (If you disagree then please show where scripture indicates differently.) Also as far as I can see these two are in contradiction to one another (see the references Sean gave the other day). Again if you disagree then please show the error from scripture. If this is the case
That being the case (2) can be rewritten as:
~3x~(Tx + Fx)
Then by quantifier conversion this becomes:
(x)(Tx + Fx)
(where '(x)' means 'for all x')
Restating this in longhand it becomes:
For every proposition, x, it is the case that either x is of the truth or x is a falsehood.
And that is the law of the excluded middle.
[I used predicate logic first because it is easier to see what is going on and since when talking about contradictions predicate logic and aristotilian logic give the same results.]
For completeness, I shall do the same with Aristotilian logic:
No falsehood is of the truth can be written formally as:
E(F,T)
which by conversion can also be written as:
E(T,F)
As I said that is as good a statement as any of lc.
Then by obversion this becomes:
A(T,F')
and since T is equivalent to F' (as stated previously) we get
A(T, T) ---(3)
which is the law of identity.
Now recall from Clark's "Logic" that the universal affirmative can be written in symbolic terms as:
A(a, b) = (a < b)[(b < a) + (a < b')'(b' < a)']
So substituting from (3) into this gives:
(T < T)[(T < T) + (T < T')'(T' < T)]
Expanding gives:
(T < T)(T < T) + (T < T)(T < T')'(T' < T)
I am not going to go through this step by step (you can check it for yourself) but it should be pretty obvious that the left hand side of this disjunction reduces to 'T" and the right hand side reduces to 'F'
So we have:
T + F
Which is the law of the excluded middle, and states that every proposition is either of the truth or is a falsehood.
As a final note. This should be taken as a demonstration that lc and lem are deliverances of scripture. Since one has to assume them in order to proceed it constitutes proof only in the sense of implicit self reference along the lines of 2 Tim 3:16 or God swearing by himself.
Hope this helps
Cheers
George