Are there any examples of deductive arguments used to defend a doctrine?

Question

Does anyone know an example of a doctrine, from any denomination, that is defended via a deductive argument, where the doctrine is logically deduced from an initial set of premises? If so, what about the argument's validity? What about its soundness?

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As a reminder of what a deductive argument looks like, the following is an example taken from the Wikipedia article:

1. All men are mortal. (First premise)
2. Socrates is a man. (Second premise)
3. Therefore, Socrates is mortal. (Conclusion)

Another illustrative example of a deductive argument is The Kalam Cosmological Argument:

1. Whatever begins to exist has a cause of its beginning.
2. The universe began to exist.
3. Therefore, the universe has a cause of its beginning.

Answer 1

I'll give the following "syllogism" to deduce the Trinity doctrine. But first I will define what is a syllogism? A syllogism in logic is a form of reasoning in which a conclusion is drawn from two given premises, one major premise and minor premise.

Here is a complex syllogism that "deduces" the Trinity.

If the Bible teaches that there is one God

and

If in the Bible The Father is identified as God

and

If in the Bible His Son is identified as God

and

If in the Bible their Spirit is identified as God

THEN the doctrine of the Trinity is valid

OR

The Bible is wrong.

So what is the definition of the Trinity? The doctrine of the trinity is not an "assumption." It is the normative systematic theology of God in Christianity and is BASED on the fact that the Bible is explicit in telling us that there is, was and forever will be only ONE God and the fact that the Bible "identifies three (and only three) persons as God.

So by what means does the Bible identify this ONE God?

1. His names
2. His titles
3. His unique attributes
4. His unique actions
5. His worship

I am not aware of any other literary, contextual means by which the Bible clearly identifies God. I could be wrong, but I think this list is comprehensive.

I will give two examples of of how this works. For example "His names." Called by the NAMES of God, (YHWH and its variants) either directly or indirectly, usually both.

Recognized with the TITLES of God, (Lord, king, savior, Alpha and Omega, first and last etc.) I think you get the idea. Enjoy!

Answer 2

An Example

One example (out of many, I am sure):

In the Summa Theologiae, Thomas Aquinas argues for the Filioque clause, as follows; I have added some formatting and numbering to bring out the analytic structure of the argument:

It must be said that the Holy Ghost is from the Son. For if He were not from Him, He could in no wise be personally distinguished from Him; as appears from what has been said above [i.e. elsewhere: see here, and here].

1. ...
   • it cannot be said that the divine Persons are distinguished from each other in any absolute sense;
   • for it would follow that there would not be one essence of the three persons: since everything that is spoken of God in an absolute sense, belongs to the unity of essence. Therefore

• it must be said that the divine persons are distinguished from each other only by the relations.

2. Now the relations cannot distinguish the persons except forasmuch as they are opposite relations;
3. • which appears from the fact that the Father has two relations, by one of which He is related to the Son, and by the other to the Holy Ghost; but these are not opposite relations, and therefore they do not make two persons, but belong only to the one person of the Father.

• If therefore in the Son and the Holy Ghost there were two relations only, whereby each of them were related to the Father [e.g. if the Filioque was rejected], these relations would not be opposite to each other, as neither would be the two relations whereby the Father is related to them.

4. Hence, as the person of the Father is one, it would follow that the person of the Son and of the Holy Ghost would be one, having two relations opposed to the two relations of the Father.
5. But this [the identification of the Son with the Spirit] is heretical since it destroys the Faith in the Trinity.
6. Therefore the Son and the Holy Ghost must be related to each other by opposite relations.
7. Now there cannot be in God any relations opposed to each other, except relations of origin, as proved above [i.e. elsewhere].
8. And opposite relations of origin are to be understood as of a "principle," and of what is "from the principle."
9. Therefore we must conclude that it is necessary to say that either the Son is from the Holy Ghost; which no one says; or that the Holy Ghost is from the Son, as we confess.

Let's look at the structure of the argument in brief:

1. (Premise A.i) It must be said that the divine persons are distinguished from each other only by the inter-personal relations,
2. (Premise A.ii) moreover they can be distinguished only by relations which are opposite.
3. (Premise B) The Spirit and the Son are only individually related to the Father, if and only if the Holy Spirit and the Son are not related with opposite relations.
4. (Conclusion W) If the Spirit and the Son were only individually related to the Father, the Holy Spirit and the Son would not be distinguished.
5. (Premise C) But the Holy Spirit and the Son are distinguished [because of the Trinity], so
6. (Conclusion X) The Holy Spirit and the Son are related with opposite relations.
7. (Premise D) All opposite relations in God are relations of origin.
8. (Premise E) Relations of origin involve both a 'to' and a 'from'.
9. (Conclusion Y) Among Holy Spirit and the Son are to be identified one as a 'to' and the other a 'from'. That is to say, either the Holy Ghost is from the Son, or the Son is from the Holy Ghost.
10. (Premise F) The Son is not from the the Holy Ghost [since nobody says that].
11. (Conclusion Z) The Holy Ghost is from the Son.

A, B gives W. Then, B, C, and W gives X. Next X, D, and E gives Y. Finally, Y and F gives Z.

Although Aquinas did not present the argument in this precise Premise-Conclusion format, it should be fairly clearly from the original text that his line of argument is deductive in nature. In fact, this is his style for the most of the Summa.

Validity, Soundness

The argument is valid, because the conclusions follow from the premises.

The argument is only sound if you accept the premises. That's going to be more controversial. Premises B, C, E and F are probably less controversial compared to Premises A and D, which is why Aquinas attempts to defend those two elsewhere: see the links in the original quoted text above.

General Remarks

Christian theology is not much different from other disciplines: deductive reasoning is a tool to clarify thinking and to persuade. Different schools of thought rely on this tool more than others.

The Scholastics, such as Aquinas, were characteristically fond of deductive reasoning (albeit sometimes based on controversial or speculative premises), but this is by no means exclusive to them. In fact, except for some of the theology of the 19th and 20th century, historically deductive reasoning was arguably the norm for settling doctrinal disputes. In more modern times, a trend toward deductive reasoning lies in Analytic Theology, following trends in its namesake: Analytic Philosophy.

It should be noted that deductive reasoning does not always take the form of Premise-Conclusion tabulated propositions, or formal logic. Indeed, this is usually overkill and fairly uncommon in ordinary theological discourse for reasons of brevity. However, the reasoning employed may still be deductive.