Logic Class #1; Introduction

Welcome to Logic Class. There are some things I'd like you to know before we get started. This class will cover college level material, but it will be in a conversational language, at least as straightforward as I can manage to make it. Logic is not a difficult subject. Also, it might not be quite as complete and rigorous (no tests), but it will be more complete in some regards, which will become more apparent as we go along. Any material that is not normally included in textbooks will be annotated.

Logic is a natural function and is something we do frequently. We all already are logicians; but some have more skill than others. What this class will help with is to put a foundation and structure to what we already do. If I fail at this, please, please challenge me to do it better. The material will be derived primarily from college texts and from philosophers as appropriate; these will be credited. I will add my own comments as we go.

Don't worry about big, two-dollar words. They actually describe simple things; mostly they are just names. Besides, a dollar doesn't go that far these days.

I think that there are four main categories for this class to pursue:

1) Put a structure forward for analyzing arguments, propositions and assertions for values such as validity, correctness and truth;

2) Give examples for clarity;

3) Develop robust participation through discussion in the comments;

4) Use these principles for analyzing complete truth statements.

I hope that you will ask questions and make comments, and that everyone who is interested will engage in the conversation.

What is logic? The Definition.
There are a great many books that claim to be logical or to teach “critical thinking”, many of which are actually selling an ideology which is then supported with rationalization. There are many ideologies that claim logic as their focus; but these can be saturated with errors. But there are principles for logical thinking that we can access.

Logic has a specific history and is a "science" which is based upon specific principles. Logic is taught in college courses, and there are college texts available.

Here are some definitions from several college texts on Logic:

”To study logic is to study argument. Argument is the stuff of logic…" "The central problem which worries the logician is just this: how, in general, can we tell good arguments from bad ones?”
"Logic"; Paul Tomassi, Routledge, 2004; p2.

”The core of logic has always been the study of inference.”
"The Art of Reasoning"; David Kelley, W.W.Norton & C0, 1988; p2.

”Logic is the study of the methods and principles used to distinguish good (correct) from bad (incorrect) reasoning.”
"Introduction to Logic", 5th Ed.; Irving M. Copi, McMillan & Co, 1978, p3.

"The distinction between correct and incorrect reasoning is the central problem with which logic deals.
"Introduction to Logic", 5th Ed.; Irving M. Copi, McMillan & Co, 1978, p5.

”Every argument confronted raises this question: Does the conclusion reached follow from the premises used or assumed? There are objective criteria with which that question can be answered; in the study of logic we seek to discover and apply those criteria.”... ”But where judgments that must be relied upon are to be made, their most solid foundation will be correct reasoning. With the methods of and techniques of logic we can distinguish reliably between sound and faulty reasoning.”
"Introduction to Logic", 12th Ed; Irving M. Copi & Carl Cohen, p4, 5; p3.

Logic is not an unsupported, fluke invention of man, nor is it merely a pragmatic program for organizing mental objects. I have come across people who have stated just those opinions of logic. One person claimed that logic could be bent to prove anything whatsoever. That's not logic, it is illogic.

Logic is a reflection of the order that is visible in the immutable laws of the universe, and their effect on our ability comprehend. If there were no universal order there could be no order to thinking about it. It is the ordered functioning of the universe that allows ordered thinking.

Certain things about the orderly nature of the universe can be observed; there are rules for existence that never are violated, at least in the non-quantum, macro universe which is the one in which we live and think. These observations of characteristics of the universe can reveal that even though the most basic rules are not provable, they are indisputable within our limits of observation and they are useful in describing order.

These useful observations regarding order in the universe cover two separate arenas: the basic properties of existence, and the basic properties of validity and truth. They can then be developed into “principles” which guide our thinking in certain categories.

When these principles are violated, an incorrect view of the subject at hand is likely. So following these principles is necessary in order to achieve valid thinking.

Informal vs. Formal Logic
Formal logic assigns symbols to premises and then manipulates the symbols using a mathematics of logic. This allows the form of logic to be analyzed without any confusing interference from the meaning contained in the words of the premises. It allows for increased complexity to be reduced in order to be more easily managed without error.

Informal logic addresses premises directly, with a minimum of mathematical manipulation or symbols. We will use informal logic in this series of classes, so that much of the time the meaning is preserved and visible during the analysis.

Pragmatic Logic and Propositional Logic
I have defined an additional split in logic, Pragmatic Logic and Philosophical Logic. Pragmatic Logic is a procedure for producing a conclusion. The conclusion is based on accurate use of prior premises (assertions) which support the conclusion. This procedure is intended to produce conclusions that are necessarily valid, given that the premises are used in the prescribed fashion. Testing for this type of logic includes looking for informal fallacies.

However, Pragmatic Logic looks only at the process, and ignores the possibility that one or more of the premises might be wrong. If the process is correct, Pragmatic Logic is happy. Basic Propositional Logic, which exams statements that propose a conclusion, fall under Pragmatic Logic.

These terms and more will be defined as we proceed: proposition, argument, premise, valid, correct, truth.

Philosophical Logic and The First Principles
Philosophical Logic goes beyond Pragmatic Logic, and looks at each premise for its Truth Value – whether the premise is supportable through evidence or prior true sub-premises. This has produced another level of logic: the testing of premises for adherence to axioms including First Principles. First Principles are the most basic axioms that underlie all logic; they will be covered under Philosophical Logic.

The Source of Logic
Logical processes are attributed to Aristotle for having developed propositional logic, and the processes have been developed further by Gottlob Frege, who contributed quantificational logic. There have been a multitude of contributions from many others including Boole, De Morgan, Peirce, Russell, Tarski etc.

But the actual source of logic is not human derived. Logic has dual natural sources: first, the law-driven structure of the universe which have been observed for the eons of human existence; second the rational faculties that are found in the human mind, before (a priori) and independent of the mind being subjected to an educational environment.

According to John Locke, at birth the human mind, while not containing any naturally included factual information concerning the material universe, does contain the elements of rationality: the human mind comes with inborn faculties including these capabilities:

a) Apprehension (information gathering);

b) Comparison (relating new information to prior information as it is stored in the memory);

c) Differentiation (finding differences between new information input and stored information);

e) Judgment (determining whether the new information is similar to or the same as stored information);

f) Comprehension (deriving meaning).

These two rational structures, the law-ordered universe and the rational mind, allow us to perform the necessary intellectual functions to create a valid view of the universe and its constituents, and to determine the truth value of such an analysis.

Defining Evidence:
Whether a statement qualifies as proper evidence is a serious and somewhat complex subject; this is somewhat outside the realm of logic, which is more interested in valid formats and procedures. But since it is necessary for determining a truth value, evidence will be covered, and its several definitions will be provided.

Defining Truth
The basic materialist definition of truth is this:

A statement is true if it conforms to reality.
(Correspondence Theory of Truth)

This statement has a limited utility if one is uncertain of the definition of reality, and where its limits do or do not lie. Further, one’s view of reality might not correspond to another’s view of reality. This leads to a squishy understanding of truth, whether it exists, and whether it is merely dependent on one’s personal viewpoints.

Possibly the best definition of truth was provided by George Boole, a very simple mathematical statement which we will cover later. It will be shown that logic is a binary function (having only two states – True and False): any amount of falseness in an argument, even deeply embedded, renders the argument false (even if the argument has a valid structure). Conversely, true arguments contain only truth, no falseness.

Getting through the layers of premises and presuppositions to reach the axiomatic foundation will be covered.

Intellectual Integrity.
It is presupposed that honesty is an underlying characteristic of those who deal in logic. Yet that need not be the case. For every argument pro and con, one conclusion must be incorrect. While the incorrect use of logic might be intentional (in order to sell something, for example) it is not the intent behind the argument that concerns a logician. A logician is merely trying to find out if an argument is valid.

The analysis of process, taken by itself, is not enough to guarantee that truth is being generated by an argument. Also needed is a commitment to investigate the sub-premises and unstated presuppositions that underlay the premises. This is necessary in order to ferret out falseness which might not be visible within the stated argument but which nonetheless ultimately negates the argument when the fallacy is ultimately discovered. Such fallacies might exist several layers below the visible argument. This means that there is a requirement for analyzing more than just the visible argument. We will see some examples.

Perhaps this makes logic appear difficult. I hope not, because logic is a natural inclination of the human mind.

Please ask any and all questions you might have, and make any comments too.