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Logical Preconceptions

February 3, 2013

Some interesting conversations recently have brought up some issues that are worth thinking about in detail. The first is this: what preconceptions do we bring to an argument, either in discussions with others or when engaging with a book/article?

The context in which I started thinking about this was an argument over atheism. I was told that I only sought out arguments that agreed with my preconceptions, in this case that there is no god or gods. This is a serious accusation, and the closed-mindedness that it implies is something that many religious communities are accused of on a regular basis.

Luckily the book I had in my hand at the time was a prime example of why this doesn’t apply – it was arguing for religious agnosticism, a position that I find very unsatisfying. That said, the book was giving me food for thought and making me reassess the grounds on which my own beliefs are formed. There’s also the fact I spent a term reading a lot of theology – not exactly a close-minded reading list for me.

Having said all that, I wanted to add what preconceptions I do bring to arguments, or at least those preconceptions I’m conscious of. At the time, I could only think of a short list:

  1. An argument must be logical; and
  2. Any proposition must be backed up by evidence, which I take to mean the broad claim that there must be sufficient reasons to think that the proposition is true (this could be physical evidence, scientific consensus, a decent argument, and probably a number of other evidences).

This seems like a decent list to me. There are some minimal requirements for an argument to precede, and I think this list embodies them. Other ideas I take into an argument, such as the idea that there are no gods, are not fixed premises, but propositions which are very secure given my background beliefs and as such have a higher burden of proof for someone wishing to persuade me of their falsity. The important difference between my fixed preconceptions and these beliefs is that without the preconceptions I do not think rational discourse is possible.

All of which leads me to a question I was asked in an argument recently: what do I mean that at argument must be logical? A gut reaction to this question is to reject it – we all know what it means to make a logical argument, and to call this into question is to open up our discourse to a form of relativism that I don’t really want to imagine, with people deploying different “logics” when needs must.

But on reflection there are some interesting thoughts to have here. In what follows I draw on a Rationally Speaking podcast that I happened to have listened to recently.

A logical argument is, to my mind, an argument that we can express in the form of a valid deductive argument, with a conclusion following from a set of premises. The deductive argument may be modified slightly to proportion the probability of the conclusion according to the probability of one or more premises being true, but the general form remains.

An important tool in my armoury of “logical” arguments would be that a proposition p cannot be true at the same time as it’s negation, ¬p. We cannot contradict ourselves. This seems clear… but it isn’t necessarily the case that a logical system requires this. There is a view in logic called dialetheism, which says that it is possible for p and ¬p to be true at the same time.

Consider the liars paradox, the sentence “this statement is false”. If the statement is true then it is false. If it is false then it is true. Intuitively the response to this statement is to say that it is nonsense – the contradiction that is implicit in it renders in meaningless. Meaningless could be seen here to be in opposition to notions of truth – a statement is true, fales or meaningless. Another response is dialetheism. We say that the liars paradox is both true and false. There are a number of other responses, which I won’t go into here…

Having said this we have a problem. In classical logic it is a well-known fact that if we are given two propositions p and ¬p we can use them to prove any arbitrary statement q. q could be the statement 1+1=3, which is provable based on the premises “the sun is made of cheese” and “the sun is not made of cheese”. The truth of any statement, no matter how obviously false, can be established based on a paradox. This is a problem known as explosion – everything, including contradictions, becomes true. This leads to the problem that, while the dialetheist might want a particular p and ¬p to both be true, they don’t want every contradiction to be true – they want to control the explosion of truth.

To deal with this problem we would need a paraconsistent logic. This is a logic system that in some way says that contradictions don’t explode. For example. we could have a requirement of relevance of premises to the conclusion. As the substance making up the sun is not relevant to the nature of mathematics, the example given above would not hold.

What all this calls into questions is the idea that an argument must be logical in an intuitive way – there are forms of logic in which contradiction is accepted, and a carefree bandying around of such technical terms as used above calls into question the very foundation on which our discourse is built.

The solution to this problem now seems obvious – we should avoid these technical terms. The answer to the question “what do you mean by logic” is this: informal logic. Informal logic analyses how we argue in “natural language”. It doesn’t deploy technical concepts from logic except to clarify the logic that we actually use when arguing in everyday settings. If we rely on informal logic we have the full classification of logic fallacies to deploy when encountering bad arguments and, importantly, the principle of non-contradiction!

This may seems circular. An argument is logical if it is logical. But this is not the case. The argument is that and argument is logical if it follows a certain set of rules,those laid out in informal logic. We are not allowed to use logical fallacies in an argument for the reason that classical logic, as it applies to the language in which we argue, says that they do not imply the truth of a conclusion given the premises.

There are important settings for formal logical systems, but our everyday discourse and argument is not one of them. We should deny people the ability to muddy the waters with the dirt of relativism. A statement about god, about homeopathy or about history cannot be both true and false. There are standards of conversation, and that is one of them.

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