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.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ From August 2021, I will be the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.