1 of 1- Johannes
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Modal logic and the Christian doctrine of the Trinity
Of the truths comprising the Christian doctrine of the Most Holy Trinity, there is one which might be the least often taken into account. Focusing on the fundamental dogma of this doctrine, that of the generation of the Son:
X = God begets eternally a consubstantial Son.
the related seldom considered dogma is:
Y = X is necessary, by nature.
Though Y has not been solemnly defined by an Ecumenical Council or a Pope, it is part of the Universal Ordinary Magisterium, having been stated in the symbols "Fides Damasi" (DS 71 / Dz 15) and that of the XI Council of Toledo, 675 (DS 526 / Dz 276).
Fides Damasi: "The Father generates the Son not by will [i.e. freely, contingently], not by necessity [i.e. as compelled from outside (?) or by indigence] but by nature."
St. Thomas Aquinas states this in ST I q.41 a.2:
resp: But we, on the contrary, must assert that the Father begot the Son, not by will, but by nature.
ad 5: But a thing is said to be necessary "of itself" which cannot but be: in this sense it is necessary for God to be; and in the same sense it is necessary that the Father beget the Son.
Relating the above to the systems of modal logic described in
By faith, and only by faith, we know:
T
□T
From reason we can demonstrate that the above propositions are possible, i.e. that:
◊T
◊□T
In S5, the last proposition amounts to □T. But this is a truth that can be demonstrated only by faith. Therefore S5 is not valid when dealing with the doctrine of the Trinity.
As an aside, IMV St. Bonaventure's "necessary reasons" for the Trinity can be interpreted in a doctrinally orthodox way as the second case of acceptable rational demonstrations, i.e. demonstrations that it is possible, or even plausible, that it is necessary that God begets a consubstantial Son.
- DanielCC
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Re: Modal logic and the Christian doctrine of the Trinity
Johannes wrote:
By faith, and only by faith, we know:
T
□T
From reason we can demonstrate that the above propositions are possible, i.e. that:
◊T
◊□T
In S5, the last proposition amounts to □T. But this is a truth that can be demonstrated only by faith. Therefore S5 is not valid when dealing with the doctrine of the Trinity.
Why should we S5 to be questionable in this situation as opposed to ◊T itself? Without the data of Relation we (allegedly) have no ground for assuming T to be possible - might not, if we are taking the Relational account of Persons, claim that from what we do know about this theory by reason that epistemically any number of Persons in God is 'possible' (sans Revelation we have no more reason to assume Three Persons than Four), albeit whichever is the case is so necessarily?
(We know a Relational account is coherent and we also know that the truth of one necessarily rules out the truth of others yet by reason we do not know which is true)
EDIT: Also, about knowability by Faith alone. Presumably there is a perfectly good rational reason for the Trinity albeit one which is beyond the grasp of our finite, creaturely intellects. An infinite intellect could carry out a full S5 proof from the possibility of the Trinity to its actuality.
Last edited by DanielCC (5/10/2016 3:34 am)
- Johannes
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Re: Modal logic and the Christian doctrine of the Trinity
Why should we S5 to be questionable in this situation as opposed to ◊T itself? Without the data of Revelation we (allegedly) have no ground for assuming T to be possible - might not, if we are taking the Relational account of Persons, claim that from what we do know about this theory by reason that epistemically any number of Persons in God is 'possible' (sans Revelation we have no more reason to assume Three Persons than Four), albeit whichever is the case is so necessarily?
I am not talking about knowing the possibility of T before Revelation, but about demonstrating its possibility after Revelation.
EDIT: Also, about knowability by Faith alone. Presumably there is a perfectly good rational reason for the Trinity albeit one which is beyond the grasp of our finite, creaturely intellects. An infinite intellect could carry out a full S5 proof from the possibility of the Trinity to its actuality.
I fully agree with the first statement. The second, however, is unrelated to the first and to the issue I am raising, which is not about any possible S5 proof but right with S5 axiom that the possibility of the necessity of X implies the necessity of X.
As with Plantinga's ontological argument, I feel like the distinction between "for all I know, T" and "possibly, T" is being blurred. Christian orthodoxy entails that reason can show that the objections against T fail, but not that reason can show T to be possible.
I cannot see the difference between showing that the objections against T fail and showing that T is possible.
Last edited by Johannes (5/10/2016 4:19 pm)
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Thread Starter- Johannes
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Re: Modal logic and the Christian doctrine of the Trinity
If you show that the objections against T fail, all you demonstrate is that T might be true, given our knowledge of the world (i.e. we cannot show that T is impossible). To say that T is really possible in the way your argument seems to require, is to say that T might be true, given the way the world actually is.
That is the sort of thing I mean by saying that T could be true for all we know without being really possible.
Now I see, you are contrasting epistemic possibility with subjunctive possibility in any of its types, of which logical and metaphysical possibilities seem to be those applicable to this matter.
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