Abstraction (the second of twelve things I love about philosophical logic)

September 6, 2017

As I mentioned in the previous entry, philosophical logic uses the tools and techniques from formal logic, and formal logic is nothing if it is not abstract. It gets its power — as well as its weaknesses, to be sure — by abstracting away from specifics and moving to generalities. We explain the virtues of a particular argument (in part) by looking at its form, the structure which is in common to other arguments of the same shape. This goes back, at least, to Aristotle, who taught us that it isn’t a coincidence that both syllogisms

All footballers are bipeds. All bipeds have feet. Therefore all footballers have feet.

All wombats are cute. All cute things are popular. Therefore all wombats are popular.

have similar virtues. At the very least, they’re both valid. They both have the form:

All Fs are Gs. All Gs are Hs. Therefore all Fs are Hs.

and any syllogisms with that form are valid. Attending to the shape of the reasoning, and “tuning out” concern about whether the premises are true (are all wombats cute? Are all footballers bipeds? — most likely not) and focussing on the form, we see how the premises and conclusions are connected.

To study form or structure is to learn how to attend to one thing and to ignore others, to look for a new level of generality. I love to take the opportunity to stand back, to look at a problem again from a different angle, to reframe it in a different way, to attend to it again, perhaps to see something new, to notice the parallels between one thing and another.

Thinking of the role of abstraction involved in formal logic brings to the fore the aspect of logic that is a design task. Logic is a kind of conceptual engineering. It is always a choice to attend to focus on some features of a problem and to ignore others. Being formal and abstract, logic allows us to stand back and look for structure, to look for patterns — and the result is the delight in recognising a unifying pattern that helps us see something that we didn’t see before.

Abstraction is the second of twelve things that I love about philosophical logic.

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