Contents:
1) Socratic Logic by Peter Kreeft
a. The Two Logics
b. All Logic in Two Pages: An Overview (B)
c. The Three Acts of the Mind (B)
d. The First Act of the Mind: Understanding
e. The Problem of Universals
2) Gene Odening Presentation on the Trivium
a. Discussion on Cognition
b. Discussion on Grammar
I would like to recapitulate some of the concepts that were discussed at the end of the first logic
saves lives podcast. The first hour was mainly Brett and I discussing historical topics to present
some context to the narratives we’ve come to study and understand, but the last half hour we
delved into the most important aspect of the essence of logic and the rules associated with it. I
had prepared for reviewing and applying the fallacies last week to the Steve Shives presentations
we’ll be going over in later episodes, but I felt as though I might’ve lost some people with some of
the concepts presented towards the end of the podcast as I hadn’t planned to present those in
particular, which created a sort of disharmonious blend of many different ideas that might be hard
to piece together. I would like to concisely clarify some of those concepts, as they are vitally
important to understanding what logic is, what the Trivium is, and how it’s a basic description of
the mind. This short introduction is necessary to understand what an informal fallacy is, as
concept formation applies directly to the improper usage of language which creates faulty
arguments. The above table of contents is for further reading into the concepts I’ll be divulging in
this brief, but substantive description.
The ideas of logic are built upon a foundation of how the mind processes information. From
observation, we have observed three types of responses to sense stimuli. The first type would be
called the primary level, that of a direct-sense experience involving one stimulus and one
automatic response, or reflex, with no attendant memory. An example would be a doctor testing
out your reflex by applying a mallet against your knee. Your knee automatically responds to the
stimulus, with no attendant conscious action on your part. The second level is called the
perceptual level. This involves the first level, but adds a brain to the nervous system and
subsequently a memory associated with discrete units of stimulus. This memory allows us to
connect stimulus together in a causal recognition. An example would be the behavioral
conditioning of animals, whereby which they can respond to a sound or a gesture through their
sense of hearing or sight, and because of their memory they can respond, automatically, to the
behavior that has been conditioned based on the stimulus. This is automatic as well, but has a
level of complexity due to the memory of the stimulus.
The last level is the conceptual level, and builds upon the first two. This allows us to abstract, from
memory, perceptual instances and differentiate the unique characteristics associated with a
sensed phenomenon or thing in reality. An example would be using our five senses to perceive an
apple, and then form a concept that extracts the unique characteristics that are universal to all
apples, and use a symbol or sound to communicate this abstract concept to others. This level is
not automatic – it has a degree of freedom often called free will. Free will is the ability to judge,
accurately or inaccurately, the unique characteristics of a concept.
Concept formation is the foundation upon which logic is built, and it’s the beginning of the first
stage of the Trivium, which we call the General Grammar stage. I mentioned concept formation
mixed in with a host of other concepts that might’ve presented some confusion to the listeners, so
let me briefly and basically explain why this idea is so important to logic and the Trivium, and why
this is necessary to understand before we dive into applying fallacies to the language people use.
Concepts are immaterial ideas. They have no extension in space and time – you can’t measure it.
They rest upon an interaction of electrochemical machinery and impulses, but that only allows for
the potential for this phenomenon we call conscious reason, it doesn’t state what thought we will
have or how our ideas match up with reality or other people’s thoughts. Concept can be loosely
traced back to the Medieval Latin word conceptum, “draft, abstract” or classical Latin “(a thing)
conceived”. It comes from the past participle of concipere, concept, which means “to take in”.
We humans take in stimulus through our five senses, and through our nervous system and
memory we can abstract, Latin for “to draw from, to drag out of”, in other words, to extricate or
extract properties, qualities, and characteristics that we observe from the thing perceived. This is
what means it to form a concept. An example would be the apple; we can sense certain
characteristics that are in common to many different apples like colors, shapes, sizes, and tastes.
From this, we can create a concept about what makes an apple. In order to do that, there are two
properties of concept formation that are critical to philosophy and classical, Aristotelian logic.
These properties are abstraction and universals.
As I mentioned, to abstract something is Latin for to lift out of, or to extract from something
characteristics from the thing being perceived. You can think of it as our mind’s ability to compare
and contrast information to find what makes things alike or different. From this property, we can
identify what I mentioned in the first podcast as key, differentiating factors; qualities and
properties that make something truly unique compared to the other things we perceive in reality.
Those unique characteristics, through abstraction, are called universals. Universals come from the
Latin uni, one, versal, with respect to many. In other words, universals are properties and qualities
that can be said about many things that exist. An apple is a round fruit with red, yellow, or green
skin and firm white flesh. A tree is a plant that has branches, bark, and a root system. The
following examples can be said about all apples and all trees. How did I identify those
characteristics? I perceived many different apples and trees, and I was able to abstract the unique
characteristics that all apples and trees have in common. This is what we call essence in
Aristotelian logic. We see many different types of apples and trees, but we don’t see the nature of
the apple or tree, its appleness or treeness. Through abstraction, we bring all apples and trees
under one concept “apple” or “tree”, held in our mind, and communicated through language.
What definition does is to take concept formation one step further and ask you to use multiple
concepts to define new ones. It asks you to define a term, which is a word or group of words or
phrase that identifies a concept, and asks you to define it using other concepts. Man is a rational
animal. So we understand the concept man, rational, and animal all separately. But, when you
combine them together you use multiple concepts to define what is implied in the concept of
man. In other words, you’re breaking the art of abstraction into its component parts, like a
physicist reducing a force down to its component parts, to help identify the characteristics that
make something truly unique and universal. You can think of it, loosely, as the formula logicians
use to help identify the universal essence to a concept. The way this is done is by identifying the
genus, or the general characteristics that are in common to man, in contrast to the specific
difference, or the properties that make man different. In this case, the genus would be animal,
and the specific difference would be rational. Man is a rational animal. From this, you can glean
what question this answers, thereby relating it to what category, in existence, this belongs.
So now we have a very basic understanding of what a concept is, and how it relies on two
properties to create a concept; abstraction and universals, which identify the essence of a
concept, and the “formula” used to define concepts (definition of concept = genus + specific
difference). Once we identify the essence of a concept, the universal, we tend to group them into
categories based on the unique characteristics of the concept. In the general grammar stage,
Gene Odening presented a definition of existence, which is every substance, action, attribute, and
relationship that is, was, or ever will be. This definition relates to the concepts of existence;
substance is every noun and pronoun, actions are verbs, attributes are adjectives and adverbs, and
relationships are prepositions and conjunctions. An apple is a round fruit with red, yellow, or
green skin and firm white flesh. Now, as you continue to break concepts down, by definition, to
include all of the real, perceivable aspects a thing or entity might have in existence, you end up
with Aristotle’s ten categories of being. An example would be the concept of an apple. The apple
is a fruit, but what’s a fruit? A fruit is a seed-bearing structure that develops from the ovary of a
flowering plant. But what’s a plant? Plants are multicellular eukaryotes. As you continue to ask
more questions about what something is, you lose comprehension but gain extension; in other
words the terms have less meaning but apply to more and more things in reality. Aristotle was the
first to abstract to the most general categories that represent all real things that exist – abstracted
from sense perception and understood and communicated through language.
If we go back to the apple example, we can apply the definition of an apple to the general
categories of being, or the definition of existence. An apple is a fruit-(substance) with-
(relationship) red-(attribute), yellow-(attribute), or-(relationship) green-(attribute) skin-
(substance) and-(relationship) firm-(attribute) white-(attribute) flesh-(substance). This simple
example can be extrapolated to all types of definitions and be shown to relate to the categories of
reality and the definition of existence.
We have a clear line from how our minds interpret stimulus, to developing concepts using
abstractions to identify universal essences in things, to formulating definitions and relating the
most general categories of reality to which all real things belong and showing how language
relates to those basic categories. This is the total subject of general grammar. The long, arduous
terminology can be summed up by saying our mind compares and contrasts information it has
perceived from our five senses, and makes a judgment, through language, as to what something is
or not. Now, in the general grammar stage your listeners will be familiar with the 5 W’s + How.
Who, what, where, when, why, and how. These questions effectively answer to the concepts of
existence by identifying one of the main constituent categories implied in existence. Similar to the
physicist metaphor, we’re doing the same thing here with logic. I broke down what the general
grammar stage is based on how we develop and define a concept, which leads up to the five
simple questions we ask to start gathering and categorizing data. This is how the mind works.
As a last note, the history of philosophy is basically a history of man’s ability to abstract and create
universal concepts. There is a philosophic war about the reality of universals that has been going
on since the beginnings of philosophy. This is effectually what was destroyed towards the end of
the 19 th
and the beginning of the 20 th
centuries with the new psychology and radical empiricism
that denied metaphysics for a mechanized viewpoint of the human being, which continues today
through philosophies and scientific endeavors such as cybernetics, and transhumanism. If people
are interested in understanding the “war on universals” I will refer them to the contents in the
beginning of this document and follow the link to “The Problem of Universals”.
Section 3. The two logics (P) (This section can be omitted without losing anything you will need later on in the
book. It's here both to satisfy the advanced student's curiosity and to sell the
approach of this book to prospective teachers who may question its emphasis on
Aristotelian rather than symbolic logic, by justifying this choice philosophically.)
16 INTRODUCTION
Almost four hundred years before Christ, Aristotle wrote the world's first logic
textbook. Actually it was six short books, which collectively came to be
known as the Organon, or "instrument." From then until 1913, when Bertrand
Russell and Alfred North Whitehead published Principia Mathematica, the
firstclassic of mathematical or symbolic logic, all students learned Aristotelian
logic, the logic taught in this book.
The only other "new logic" for twenty-four centuries was an improvement on
the principles of inductive logic by Francis Bacon's Novum Organum ("New Or-
ganon"), in the 17th century, and another by John Stuart Mill, in the 19th century.
(Inductive reasoning could be very roughly and inadequately defined as
reasoning from concrete particular instances, known by experience, while
deduction reasons from general principles. Induction yields only probability,
while deduction yields certainty. "Socrates, Plato and Aristotle are mortal, there•
fore probably all men are mortal" is an example of inductive reasoning; "All
men are mortal, and Socrates is a man, therefore Socrates is mortal" is an exam•
ple of deductive reasoning.)
Today nearly all logic textbooks use the new mathematical, or symbolic,
logic as a kind of new language system for deductive logic. (It is not a new logic;
logical principles are unchangeable, like the principles of algebra. It is more like
changing from Roman numerals to Arabic numerals.) There are at least three
reasons for this change:
(1) The first and most important one is that the new logic really is superior
to the old in efficiency for expressing many long and complex arguments, as Arabic
numerals are to Roman numerals, or a digital computer to an analog computer, or writing in
shorthand to writing in longhand.