To celebrate World Logic Day, I thought to write a public-facing explanation of why logic matters (and why I do research in it!). There are some instrumental reasons why logic matters: we quite directly owe, to research in logic, our computers and cell phones. In addition, I have often used a nice analogy with Aristotle’s theory of vision to explain why logic matters.
Aristotle held that one sees colors only when a transparent medium was activated by the present of light. This was natural enough, since we cannot see well in the dark. Philosophical insights are like colors, and logic is like light: symbolism in formal logic illuminates a whole array of philosophical ideas and novel suggestions that we otherwise would have been literally in the dark about.
This is the field of *philosophical logic*: the part of logic that is concerned with symbolizing various hypothesis, theories, experiments, and so on. Still, logic can often illuminate through a muddy medium: we can look at a philosophical problem through logic and see but a distorted picture of it, as when we look at something through water.
This is the field of *philosophy of logic*: the part of logic (and philosophy!) that is concerned with what logic is about, whether only one logic is in some unrestricted sense *correct*.
Both of these areas are part of my academic work, and both are naturally visible on analogy with Aristotle’s theory of vision. Happy Logic Day!
*Sources and further reading.* The philosophical logic versus philosophy of logic distinction is explained in Burgess’ *Philosophical Logic*, which is a fantastic book. Susan Haack’s book *Philosophy of Logics* treats philosophy of logic in greater detail and depth, and also belongs on your shelf. Aristotle’s theory of vision is presented in *De Anima* and the *Parva Naturalia*.