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else will also occur. It is, perhaps, the philosopher's version of Newton's third law of thermodynamics, which stated that all actions have an opposite and equal reaction. Let us have a look at an example which uses a series of if/then statements to prove that Australia's economic health depends, not on low wages, but on high

1. If Australia's wages are reduced, then people will have less to spend.

2. If people have less to spend, then consumption will fall.

5. Therefore, if we want to avoid a loss in profit, we must not reduce

The power and flexibility of propositional logic is demonstrated by this example, not because these premises guarantee the conclusion is true, but rather because they create a series of logical relationships between two otherwise apparently unconnected events—the need to avoid a loss in profit and the desire not to reduce wages. If we were then to set about convincing someone of this ultimate conclusion, we would, by having set up the chain of propositions in this manner, have identified the key sub-conclusions that would each need to be supported by sub-arguments. Thus, we would have to establish that it was indeed reasonable to believe that 'If consumption falls, then the economy will slow down', and we might do this by reference to real-world examples such as previous economic conditions in which a fall in consumption has indeed caused an

The lesson to learn here is: while categorical logic concerns itself with the structural relationship of the categories we use, defining the inclusions and exclusions so that we can be sure what does or does not belong together as a group, propositional logic prompts us to ask the right questions about what we need to establish, inductively, to then make our overall argument convincing.

It is important to recognise that these five types are not mutually exclusive. We will consider causal reasoning but, for example, we also see that when looking at causes we are also asserting analogies between the cause of one event and another. Equally, when we look at analogies, there are ways in which analogical reasoning is the same as reasoning from generalisations or might involve causal relationships. Thus, the five types presented here are not done so in the same manner as the discussion of deduction/induction which showed how arguments of one type (in each case) could not be of the other type. Rather, I present these five types to assist you in thinking more broadly about the kinds of questions you might ask in your reasoning and (as we will see in chapter 8) to guide your

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