The Divisions of Logic
What is Logic? Why Aristotelian Logic? What are the Parts of Logic?
Logic is the science of the “ideal laws of thought and the art of applying them correctly”. (CdF) Strictly speaking, logic is not part of philosophy. Whereas philosophy aims to study the first causes of reality, logic merely focuses on describing how to think correctly. Furthermore, logic can be applied to other fields, such as physics and chemistry, in order to elucidate the correct methodology to use to find truth. Logic is a pre-philosophy, used for finding the correct way to demonstrate philosophical truths.
Today, there exist two broad types of Logic: Aristotelian logic and symbolic logic. Aristotelian logic, based on Aristotle’s 4th century Organon, was taught universally in the West until the publication of Bertrand Russell’s and Alfred North Whitehead’s Principia Mathematica in 1913; the new symbolic logic was proposed primarily due to some “unfashionable … presuppositions” (SL) in the “old” logic. The exact presuppositions are a subject for metaphysics, but suffice it to say that, since most modern philosophers rejected Aristotle’s assumptions in favour of Hume’s, symbolic logic, outside the Catholic Church, became the most dominant form of logic.
Why should you study Aristotelian Logic, and Aristotelian philosophy more generally? Peter Kreeft gives a two main reasons, summarized below:
Aristotelian Logic is concise and concrete
Aristotelian Logic is logical
On the first one, I will quote Kreeft directly:
in a logic text book misleadingly entitled Practical Reasoning in Natural Language, the author takes a full six pages of symbolic logic to analyze a simple syllogism from Plato’s Republic that proves that justice is not rightly defined as “telling the truth and paying back what is owed” because returning a weapon to a madman is not justice but it is telling the truth and paying back what is owed.
The second one refers to the “problem of material implication” in symbolic logic where any proposition implies a true proposition, and any false proposition implies every proposition. The problem is quite technical and requires its own article, but suffice it to say that it should make you highly suspicious of the assumptions of symbolic logic.
What are the parts of Logic?
Jolivet distinguishes between two parts of logic: formal and material.
Formal refers to the “correct form of the intellectual operations … which assures the agreement of the thought with itself” (Cdf). The intellectual operations are connected with Aristotelian psychology and they represent “apprehension, judgement, and reason”.
Material concerns itself with the “special rules that derive from the nature of the object of investigation”. (CdF) One of the ways that it does this is by investigating the “conditions of certainty”, but distinguishes itself from Epistemology in that Epistemology aims to know whether human faculties can attain truth or not (CdF).
For the next article in the logic series, we are going to look at terms and concepts.