Logic for apologetics

Dr Greg Restall

I am a logician by trade. I spend time teaching and researching in the areas of formal and philosophical logic. I think that logic has important connections with reasoning and rationality, and that reasoning and rationality in turn have something important to do with understanding, communicating and shaping our beliefs and the beliefs of those around us.

However, these connections are not immediate and they are not obvious. In this article, I would like to look at some of these connections: to critically examine some of the connections that many take for granted, and to make some connections that have not been so well understood.

The heart of logic (at least as I have learnt it, and as far as I teach it) is the question of deductive validity. An argument is deductively valid if its form (or structure) is such that if the premises are true, the conclusion must be true too. Deductively valid arguments show us how to step from premises to conclusions, in such a way that anything needed to make the transition is made explicit. The following (famous) argument is not deductively valid, as it stands.

1. Nothing causes itself.
2. There are no infinite regresses of causes.
3. Therefore, there is a cause which has no cause of its own.

The premises are not enough to ensure the truth of the conclusion, because they would be true were there just two things (call them Fred and Martha) such that Fred causes Martha (and nothing else), and Martha causes Fred (and nothing else). In this case, no object is uncaused, nothing is self-caused, and there is no infinite regression of causes. (“Wait!” you say, “we cannot allow a cycle of causes!” “Well,” I reply, “add that to your list of premises, and we’ll check the argument again”.)

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Looking for valid arguments in our reasoning (what we might call articulating that reasoning) is a good way to make explicit the connections between premises to the conclusions. I think that this is a good thing, when it comes to developing theories, for a number of reasons. If an argument is totally explicit it is easier to evaluate. In particular, if all of the premises of an argument are fully explicit, then they are available for critical evaluation on their own. An explicit premise can be questioned in a way that a merely implicit one cannot (namely, it can be questioned explicitly).

Once the argument is articulated, the premises and conclusion can be modified. Once you see all of the premises of the reasoning laid out, you can try substituting some concepts for alternative concepts, and the result is still a valid argument. (Given a valid version of the cosmological argument, given above, try replacing “is a cause of ‘ by “is a reason for,’ and you get an equally valid argument.)

This is not only fun and interesting. It is also useful, especially when we do not have a confident grasp of our own concepts. The argument itself then makes explicit the properties of the concept required. For example, suppose you strengthen the cosmological argument in such a way as to make it valid. This would tell you, then, the kinds of properties of the relation of is a cause of which would ensure that there is a first cause.

This result stands even if we are not confident of exactly what might cause what. Similar considerations arise when it comes to reasoning in physics (we are not confident that we have the concepts “wave’ or “particle’ nailed down) or theology (try “person’ or “substance’ or “nature,’ etc.)

Now, let’s look at how the discipline of looking for valid arguments (in this tight, logician’s sense) relates to apologetics, and in particular to that sub-discipline of apologetics (which is simultaneously revered and reviled) of finding “proofs for the existence of God.’ There are many proofs for the existence of God. If we take proof to mean “valid argument’ we can agree that there are many proofs for the existence of God.

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Logic for apologetics – Dr Greg Restall


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