Dr Greg Restall is Associate Professor in Philosophy at the University of Melbourne.

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".)

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. Here is one.

1. Jesus was raised from the dead.
2. The only way that you can be raised from the dead is if God raises you.
3. If God raises someone from the dead then God exists.
4. Therefore, God exists.

There are many more valid arguments for God's existence. Perhaps this next one is salient at the moment:

1. My train (in Sydney) was running on time this morning.
2. The only way that you can get your train on time (in Sydney) is if God helps you.
3. If God helps you then God exists.
4. Therefore, God exists.

As far as structure goes, there is precious little difference between these two arguments. They are both deductively valid. As far as logic is concerned, these arguments are on a par. (On the other hand, these arguments have quite different apologetic payoffs.) In fact, I can supply you with a little formula you can use for constructing your own valid proofs for the existence of God. Take a proposition at random. Replace the letter "p' in the following schema by that proposition.

1. p.
2. If p then God exists.
3. Therefore, God exists.

This argument is perfectly valid: if the premises are true, the conclusion is guaranteed to follow. So, there are many different valid arguments for the existence of God.

Of course, there are just as many valid arguments for the non-existence of God as for God's existence. Replace "God exists' by "God does not exist' in the schema above to find some of them. More interesting and useful arguments for God's non-existence are available too, of course. One of the most important such arguments is a form of the problem of evil. For shorthand, let X be some horrendous evil, an evil event or state of affairs so bad as to seem to serve no overarching good purpose.

1. A good being would prevent a horrendous evil if it could.
2. A powerful being could have prevented horrendous evil X.
3. If God exists, God is both good and powerful.
4. Horrendous evil X was not prevented.
5. Therefore, God does not (or at least did not) exist.

This argument is valid as it stands, and it is an argument for God's non-existence. Clearly some valid arguments are apologetically worthwhile (both positively and negatively) but some are not. These arguments are not all equally apologetically worthwhile, but in a sense they are equally logically worthwhile.

We can safely conclude, I think, that logic is not the only criterion one must use to evaluate what is good for apologetics. What, then, is logic good for? If it's too crude to draw a distinction between good arguments for God's existence and bad ones, what hope is there for any useful application of logic for apologetics? To answer this, I think we need to take a look at some misconceptions about what logic does.

Is logic an instrument of repression?

A common complaint about logic is that it represses. It is supposed to encourage "linear' thinking, force or coerce belief in its conclusions, leave no alternatives open, and generally be a Very Bad Thing in Western Culture. Now, perhaps logic has been used in this kind of repressive or coercive way. However, this says no more about logic than the coercive way that styles of speech are imposed/restricted in certain subcultures means that speaking is a Bad Idea. I think, however, that this is not merely an error in understanding the nature of logic: it is a fundamental misconception. Logic cannot coerce belief. Given a valid argument, you can believe the conclusion or you can reject one of the premises. Neither of these options is forced: you have a choice. (Furthermore, you can even accept the premises and reject the conclusion! Logic alone cannot force someone to be reasonable.)

However, the right way to think of logic is not as repressive, but rather, as liberating. The search for valid arguments actually opens up options more than it restricts. Once we find a valid argument, we have the options of accepting or rejecting any of the premises.
The more you practise logic, the wider you recognise the field of logical possibilities to be. We logicians recognise that there are very many different coherent possibilities. Perhaps not all of these possibilities are on a par epistemologically, or apologetically, but as far as logic goes, they are all coherent.

Logic is not restrictive. On its own it provides a very large field of play.

The virtues of the practice of logic Now, here is one consequence of this kind of conception of logic for apologetics. When it comes to the reasoned articulation and defence of Christian faith, and the persuasion of non-believers, logic, and what we might call a "logical temperament' has its uses. This use is not so much in finding good "arguments for the existence of God,' for the reasons we have seen. Any appeal that the conclusion might have on the basis of the premises will, in turn, rest on the appeal of the premises of these arguments. Experience tells us that this is a contingent matter: varying from person to person. Some will find principles about cause and effect appealing (and will accept the cosmological argument as an articulation of their sense that there must be something to which this universe is responsible) and others will not. Some people find the evidence for the resurrection convincing, and others do not. I leave it to the epistemologist to tell us the conditions under which we are warranted in accepting the premises of our reasoning.

The logician has a different story to tell. Regardless of this contingent and variable state of affairs, there is a constant virtue in deductive reasoning. Irrespective of what we might think of the premises of our reasoning, logic is ideal when it comes to articulating the kinds of reasons there might be, both for and against contested claims. Once the structure of a chain of reasoning is spelled out, one can more easily judge the costs and benefits of the options of accepting or rejecting the premises and the conclusions.
For example, with the argument articulating the problem of evil, we have a kind of map of options: we can reject one of the premises or endorse the conclusion. Different options will involve different commitments. Articulating these options is like drawing a map of conceptual space. The map does not tell us where we ought to be, but it does tell us something of the features of the different points on the landscape around us.

Taking this attitude will mean adopting a kind of humility. We will almost certainly be moved to conclude that, as far as logic is concerned, many different positions on matters of fundamental importance to us are coherent. (Logic is not going to prove to be a silver bullet that will show that this or that position is itself inconsistent.)1 Those of us who are confident that Christian faith is not only coherent but appealing will have reason to pursue this kind of project, for it provides a technique for making clear the appeal it has.

Furthermore, in taking seriously the kinds of reasons that our opponents or interlocutors bring to the table, we will gain an understanding of how their positions differ from ours, and they will hopefully learn that we can treat their views seriously and with respect, without necessarily endorsing them. This kind of reasoning practice (one which gives logic a central place) is most certainly a Good Thing, and this is one important, and perhaps not well recognised, place where logic can find its role as an aide to apologetics.

E N D N O T E
1 This humility isn't a kind of epistemological relativism. I take seriously the claim in Romans 1:290 that knowledge of God is available to all.