What use is formal logic to philosophy?

Stephen asked:

Greetings Philosopher-Kings! My question to you is of a practical nature but I feel would fall outside of the Problem Removal Service. I am only beginning my self studies in the field of philosophy and have been groping around to find the most efficient path to becoming relatively well-versed in philosophy. What I respect the most about the study of philosophy is the ability of the philosophers I have met or read to quickly and clearly identify the flaws in the premise or structure of an argument. I have assumed this was due to their background in formal logic.

My question then is ‘How integral is Logic or Advanced Logic to the study of philosophy as a whole, and is it simply useful in some fields such as philosophy of language or mathematics, and not in others, such as ethics or political philosophy where perhaps only a basic understanding of argumentation theory would be necessary. Moving forward in the study of philosophy (and any of the other common fields in academia for that matter) would the study of Logic be very beneficial?

(If you are feeling generous, some names of a few good books to get started in the field would be a great help.)

Answer by Craig Skinner

I’m no philosopher-king, actual or potential, but having reached the end of the beginning (recent distance-learning BA Philosophy with Pathways support), maybe I can help you as an acknowledged beginner.

You say you are ‘groping around to find the most efficient path’. In my view, there is no substitute for hard work, and it needs to be focussed, interactive and challenged. Best is to sign up for some qualification (diploma, degree, Pathways modules all suitable). Self-study alone, although educational and fun, tends to be diffuse and unrigorous. You need to be writing essays which are critically appraised by somebody further along the road, and aiming to pass exams or submit a dissertation within a definite time frame.

What about formal logic?

There is no need for fluency in the formal languages of logic in order to study and understand philosophy. The 2010 study guide for the London BA (Phil) says in its blurb about the compulsory Philosophical Logic module ‘Formal logic does not figure as such in the examination…., but some knowledge of elementary formal logic is necessary for the subject as a whole’. It then goes on to recommend a book offering a ‘gentle introduction’ to formal logic (more from me below).

I got excellent marks in my Philosophy of Mathematics, Philosophy of Science and Philosophical Logic modules with no more knowledge of formal logic than a ‘gentle introduction’.

As a student of philosophy your focus will be analysis of and reflection on concepts arising out of/built into logic and reasoning – deduction, induction, abduction, validity, identity, necessity, truth, reference, definite descriptions, conditionals. In addition you may wish to reflect on the reasons for the existence and the value of non-standard logics which deny bivalence or deny Aristotle’s laws such as LEM or even LNC. Also a basic understanding of nonbivalent, including fuzzy, logic, is needed to understand the concept of vagueness.

In addition you will be familiar with notions that long predate formal logic, such as circular argument, begging the question, equivocation, reductio ad absurdum.

I think too much 20th Century analytic philosophy writing was infected by logical symbolism, but the heyday of this has passed and philosophical logic is re-emerging with new vigour after decades of debility due to that infection. The love affair between analytic philosophy and logical symbolism blossomed with publication in 1905 of the Theory of Descriptions in Russell’s ‘On Denoting’ (that ‘paradigm of philosophy’ as Ramsey called it in 1931). Russell was seen as ushering in a new age of rigour – many old philosophical problems would simply be shown up as confusions of thought; woolly Continental metaphysics was exposed; Meinong’s alleged nonsense about nonexistent objects was supposedly rebutted. And indeed it was a shot in the arm to philosophy, although our view of it is more nuanced these days, and logical analysis of language delivered less than was hoped for. But, at any rate, Russell couched his theory in the symbolism of his (and Whitehead’s) Principia Mathematica, starting the trend of discussing such matters in terms of symbolism when they can be understood without it (of course it is true that some people find it easier to grasp ideas symbolically).

As for the gentle introductory text, I have the main contenders on my bookshelves, including Hodges, Newton-Smith and Guttenplan, and have read them. They are all more than adequate. I think the best is Guttenplan:

Guttenplan S (1997) The Languages of Logic; an introduction to formal logic, 2nd ed., Blackwell

All the best with your studies.


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