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making some prediction or estimate of what the most likely conclusion would be given that evidence.

The lesson to learn here is: if you think about the kinds of complex arguments that you have been developing in earlier chapters of this book, what you will probably see is that, towards the end of a complex argument, the reasoning will become deductive, carefully delineating a logical set of relationships that, in the earlier parts of the complex argument have been established through inductive reasoning.

Categorical and propositional logic

Now we will look at the two common forms of deductive reasoning. For a long time, logic was primarily thought to consist in the formation of definitive relationships (such as the deductive examples above), normally expressed in the form:

Humans are mammals. All mammals breathe air. Therefore humans breathe air.

Such reasoning is called categorical precisely because it is not about actual events so much as the ideal categories by which we can define and discriminate the innumerable things in the world into a regular pattern or order. What is significant is that categorical logic is mostly associated with European thinking prior to the modern era of scientific investigation and the constant quest to discover what was new, rather than earlier attempts to precisely define a never-changing pattern of categories and attributes. It should also be noted that this form of reasoning depends absolutely on how we define terms such as air and breathe, and how precisely we use words in our claims. Technically fish also breathe—they breathe water and extract from it, if not 'air' then air's constituent elements. Yet fish are not mammals. Thus while useful to understand, categorical reasoning is more interesting for our purposes in that it models how dominant forms of reasoning are bound up in the social order of their time.

Propositional logic on the other hand depends upon propositions: statements that propose a relationship between two states of affairs. Technically these statements should be expressed as 'if..., then...' claims. However it is possible to write them in such a way as to imply, rather than explicitly state, the propositional nature of the claim. If the Ancient Greeks spent a lot of time philosophising about how specific items and general groups might be put together and thus developed categorical logic to a fine art, in the nineteenth century, European philosophers became fascinated by propositional logic. If/then statements are, probably, at the heart of most of our reasoning, even though we often do not realise it. They link together one event (the 'if part) and propose that if it happens, then something

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