Page 105 - Smart Thinking: Skills for Critical Understanding and Writing, 2nd Ed

92 SMART THINKING: SKILLS FOR CRITICAL UNDERSTANDING & WRITING

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