PHI 112:  LANGUAGE, LOGIC AND MATH, aka, Intro to Logic

Waggle Section

History of Philosophy and the Place of Logic therein

Philosophy is an English word derived from the Greek filosofia or the love of wisdom.  In the most general of terms, the tradition holds that there are three objects of study in philosophy: the True, the Good, and the Beautiful

The True	The Good	The Beautiful
Logic	Ethics	Aesthetics
Metaphysics	Politics	Poetry
Epistemology	Theology	Rhetoric

Ancient, Medieval, Modern, and Post-Modern philosophy has focused on these objects.  Under the sciences or studies of the True, are metaphysics, epistemology, and logic.  These sciences are typically referred to as the theoretical sciences.  Simply, metaphysics is the study of things, or that science that attempts to answer the question: "What is it?"  Epistemology is the study of knowledge, or that science that attempts to answer the question: "How do you know it?"  Logic is the method or a method of inquiry that is governed by strict rules in order to determine the validity of positions.   I will have more to say about logic below.  The goal or end of the theoretical sciences is knowledge.  Often Cosmology, or the study of the arrangement of things, or that science that attempts to answer the question of the order of things, is added to the theoretical sciences.

Under the sciences of the Good, are ethics, politics, and theology.  These sciences are typically referred to as the practical sciences.  The practical sciences attempt to answer the general question "What is the good life?" with ethics focusing on the good life of the individual and politics focusing on the good life for the collective.  Often theology is added to the practical sciences, as the study of divinity and humanity's relationship to the divinity.  The goal or end of the practical sciences is action.

Under the sciences of the Beautiful are aesthetics, poetry, music, and rhetoric.  These sciences are typically referred to as the productive sciences.  Understood quite generally, aesthetics is the science of feeling, or sensation; poetry is the science of verbal communication appealing to sensation; music is the science of non-verbal communication appealing to sensation; and rhetoric is the science of crafted discourse.  The goal or end of the productive sciences is making of something, i.e., a product.

Philosophy differs from other sciences in several ways.  There are a range of methods used, accounts given are systematic - explaining the whole sum of natural events in the same terms and by the same method used throughout.  Unlike other sciences, philosophy attempts to uncover the arch (arche) or first principles underlying phenomena to account for similar phenomena.  Philosophers also attempt to provide accounts in an economical use of language - involving few terms and only the essential distinctions necessary for clarity.  Finally, philosophers appeal to reason, and to argumentation to support positions held.  When I refer to a science, what I mean here is a body of knowledge governed by a specific object of inquiry, deploying the same method of inquiry throughout.

Philosophy, in the West, is the product of Greek speculative thought.  Thales of Milesia  (cir. 585 BCE) is credited by the tradition as being the first philosopher.  There is some disagreement amongst the ancients as to exactly who was the first philosopher.  Some, Aristotle for one, say that Anaximander (cir. 500 - 428 BCE) was the first philosopher.  He, being a generation later than Thales, was the first philosopher who actually wrote down his discoveries.  What makes matters more difficult for us in determining the exact beginning of philosophy , is that most of these ancient writings have not come down to us intact.  We have to rely on a variety of source materials, which are often contradictory and are sometimes of a hostile nature.  Contemporary scholars refer to Thales and Anaximander, and company, as the Milesian "school".  The Milesian "school" focused on the study of Nature and the attempt to give a rational account for change in material nature by appeal to a principle of a set of principles to explain change in material things and to explain the order of things.  By nature, here, is meant fusia and the order of things, here, is meant kosmoV.  Hence, the primary focus of pre-Socratic philosophy was cosmology and metaphysics.  Briefly, these philosophers posit a single substance underlying the appearances and the changes in that substance account for differing phenomena. 

Without going into great detail on the various schools of ancient pre-Socratic philosophy, the central thread of what anchors our perception of philosophy is the emergence of Socrates.  The following are dates for Socrates and his most famous followers:

Socrates                       470 BCE - 399 BCE

Plato                            427 BCE - 347 BCE

Aristotle                       384 BCE - 322 BCE

Alexander the Great      (not a philosopher)

Logic was developed by Aristotle as the method of inquiry that is governed by strict rules in order to determine the validity of positions.  Precursors to Aristotle's method are the methods of the following philosophers and thinkers: Plato's Dialectic, Parmenides Logos (LogoV), and Sophistic Eristics.  To some extend, there is some "cross-fertilization" between Aristotle's Logic and Euclidean Geometry, especially in the form of proofs and the notions of definition and proposition in Euclid's Geometry.

The three core concepts in logic are: Truth, Validity, and Soundness.  Truth is a feature of propositions, or, in our case, to sentences.  Validity and Soundness are criteria used for the evaluation of arguments.  Logic is first concerned with the Form of an argument, or a structured piece of reasoning.  Validity is mainly concerned with the form of an argument, where as soundness is mainly concerned with the form and the content of an argument making soundness a stricter concept than validity.

The word 'Logic' has its origin in the Greek word logoV (logos) which means collectively: reason, account, cause, word, explanation.  Because of the connection between discourse and reasoning, Aristotlean logic trades off of the grammatical features (i.e., noun or name, verb, predicate, etc.) of discourse and the rules for preserving truth through reasoned discourse. Many of the structures in Ancient logic and Ancient mathematics are rather similar.  Not surprising, then, is it to learn that the Greek word for understanding and learning is the root for our word mathematics.  This linkage between logic and mathematics is still present in contemporary thinking.  In fact, for most of the history of philosophy, grammar and logic are linked until the end of the 19th century, when a formalized, symbolic logic is created by Frege, Russell, Whitehead, and Wittgenstein, who contributed greatly to our contemporary understanding of logic as a symbolic calculus.  This symbolic calculus is now though of as the foundations for mathematics.

The upshot of this is that logic should be understood as a method of inquiry, primarily used to make positions clear, and to critique positions.  For our purposes, we will be using the formal features of logic to examine or investigate critical thinking.  This class will trade off both critical thinking skills and informal logic principles.  Many of the terms we will use are technical and need to be assimilated quickly.

Some terms, such as argument, premise, critical attitude, etc., will have a common or non-technical meaning.  Don't confuse the common meaning of these terms with the technical meaning.  You should learn the definitions of these terms by heart.  With regards to definitions, these should be learned word for word.  Because of Logic’s rule governed nature, there is no room for interpretation of these definitions.  There are only a handful of such definitions, and it is critical that you get them precise.

It is my position that given logic's rule governed nature, all of you, by the end of this course, ought to be able to handle any of these problems in our text as well as I can.  To facilitate your understanding, my approach  to logic is along the following lines.  Think of logic as if it were a strategy game.  Critical thinking is playing the game.  In order to play the game, you need to learn the rules and know how to apply them.  As there are different things that one needs to do in a game, there are different types of reasoning that we will be studying, and different ways of analyzing these.  Different maneuvers in the game will be called by specific, clearly understood names.  To play the game well, you need to memorize the rules and the maneuvers of the game.  If you allow yourself to think if this course along these lines, then you'll be surprised how easy it can be to learn this subject matter.

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