Formal Logic
The Instrument of Logic
The discipline of traditional logic can be divided into two main categories of study: that of “Formal Logic” and that of “Informal (or ‘material’) Logic.” Formal logic is primarily interested in the “structure” or “form” of an argument. Even though the premises of an argument may not be true, if the “structure” of the argument follows an acceptable form, it is considered a “valid” argument. A commonly used example of this is the following syllogism:
The moon is made of blue cheese.
I like to eat blue cheese.
Therefore, I would like to eat the moon.
In formal logic, this would be regarded as a “valid” argument, because it conforms to the rules of a properly constructed syllogism.
The second category is what is known as Informal Logic; and it is the home of the logical fallacies discussed previously. It also uses the form of syllogism to make rational decisions. Contrary to formal logic, informal logic places a great deal of attention upon the “truth of its premises” and its content, in order to arrive at a “sound” consequent. An example often used is:
All men are mortal.
Socrates was a man.
Therefore, Socrates was mortal.
In this example, each premise is true, the syllogism construction is valid; so the conclusion is considered a “sound argument.”
A bit needs to be said about certain terminology used in the study of logic, because some terms are used with slightly different meanings than we are accustomed to hearing them in common usage. Frequently in casual use, the words true, valid, and sound are used interchangeably as conveying the same general concept of reliable content. However, in logic, each have a separate and distinct meaning.
Statements of fact are referred to as True or False (not logical or illogical). True means that the statement corresponds to reality.
If statements, whether they be true or false, follow a logical progression, the argument is called a “Valid” argument. It is called valid, only because it conforms to the rules of syllogism or categorical logic in its “structure.”
An argument that contains both all true statements, or premises, and is valid in structure or form, is referred to as a “sound argument.” All syllogistic arguments must contain at least two premises and one conclusion. So, in the above example:
All men are mortal. (true premise)
Socrates was a man. (true premise)
Therefore, Socrates was mortal. (valid form)
SOUND ARGUMENT
Decision-making, or arriving at a sound argument with a true conclusion, is a process of how each individual perceives and manages information. A syllogism is simply a mechanism of verbal expression signifying how that occurs.
Premises are formed by our minds conceiving of a mental image or concept and labeling that concept or mental picture in a clearly defined term. Words like “all,” “man,” “mortal,” and “Socrates” have certain unique or particular content of meaning universally within our culture. As such they are unambiguous. When these terms are arranged in a way to state a truth (or false) claim, we are expressing a proposition, or if arranged within a syllogism, a premise. (e.g., “All men are mortal.”) But random propositions make no sense in reasoning. To fully arrive at a new idea or conceptual truth, propositions require being arranged in a manner of progressive insight.
All men are mortal.
All cows are mortal.
All birds are mortal.
Though each statement may be true, there is no additional insight gained. It is not an argument at all; only three propositions with the same idea.
The rational linkage of propositions in a manner to obtain additional insight is called “deductive reasoning” and is often expressed in the form of syllogism as demonstrated above. Deductive inference or reasoning is the process of gaining new information by using the information it has already. Furthermore, it is the process whereby antecedent information is arranged in such a way that a consequential truth can be inferred by necessity. The form of syllogism is one way of doing so. However, in order to arrive at a “sound conclusion,” the essential components and structure of the antecedent propositions need to be properly presented as a means to insure both the truth of the premises and the validity of structure’s inference. The Essential Law of Argumentation states that: “If the antecedent [series of propositions] is true, the consequent must also be true.”
Propositions are truth claims and are constructed in sentence form with a subject (S), a predicate (P), and a connecting term, usually “is” or “are” known as a copula. This is the form in which a premise must be stated in order to be treated logically and is referred to as its “logical form.”
As an example, the sentence, “Johnny is a fighter,” can be used in a syllogism because it is in its logical form. But how about the sentence, “Johnny often fights,”? This sentence is not in its logical form, and as such, cannot be used meaningfully in a logical syllogism. The reason why will become apparent as we study the use of syllogisms further.
Propositions can be presented one of four kinds of statements:
All S is P
Some S is P
No S is P
Some S is not P
As such, each form of statement has two characteristics: quantity and quality. Quantity is represented in the terms: “all,” “no,” “some;” and has to do whether the statement is universal or particular. Quality represents whether the statement is affirmative or negative.
Therefore, the previous statements can be envisioned in this way:
All S is P Affirmative – Universal
Some S is P Affirmative – Particular
No S is P Negative – Universal
Some S is not P Negative – Particular
Formal logic goes into much greater detail than this in the composition and arrangement of propositions, but for now this will give one some sense of the necessary components of true premises. But a word needs to be said about the terms within propositions and their characteristics.
Ambiguity within propositions can occur due to the various meanings and contexts in which words or terms can be utilized. Univocal (Latin: unus + vox meaning “one voice”) terms are words or terms which have the same meaning regardless of the context in which they are used. Equivocal (“equal voice”) terms are those which are spelled and pronounced exactly alike, but mean much different things depending upon how they are used in context (e.g., “plane,” “jar”). Analogous terms are likewise spelled and pronounced alike and have different meanings, but the meanings are similarly related. When using the phrase “a set of wheels,” is the meaning “my car” or “a set of tires?” The “wings” of a bird and the “wings” of an airplane are analogous because they have a similar function.
The reason these distinctions are so important is that logic relies upon a clear and precise use of terms for meaning. In his book, Traditional Logic, Martin Cothran uses this example to demonstrate how our terms in propositions have to be precise in meaning:
All NBA basketball players are man.
Dennis Rodman is a good NBA basketball player.
Therefore, Dennis Rodman is a good man.
Then he asks the question, does “good” mean “proficient” or “morally upstanding?”
Another characteristic of terms, or rather the concepts behind the terms, is that of extension of meaning. This is a somewhat abstract notion, but a very important one to be aware of in the context of argumentation. This has primarily to do with the specificity of terms definition. It contrasts the term’s comprehension with that of extension…comprehension being the sum total of all that a term “is;” and extension being the “concept” to which that term refers. Furthermore, these are complementary concepts. The greater the comprehension (specific definition) of a substance or concept, the less extension (various modes of expression) it will possess. In like manner, the less comprehension (specific definition), the more extension (various modes of expression) it will have.
Man can be comprehended (specifically defined) as a SUBSTANCE which has a MATERIAL BODY that is a LIVING ORGANISM as a SENTIENT ANIMAL who possesses the capabilities of RATIONAL THOUGHT. As such, the concept of “man” has little further extension (that is,other various modes of expression or concepts to which it belongs).
On the contrary, if one were to consider the comprehension of BODY, that which has MATERIAL FORM, there is little specific definition in the concept of “body;” but a great deal of extension. It could include living or non-living, sentient or non-sentient, rational or non-rational “BODY.”
Why is this such an important concept to understand? Not only is it essential for clear and precise rational deliberation; but it has great impact in the realm of language and communicating meaningfully with one another. This concept of comprehension and extension finds its relevance there as well. It is a major subtle but powerful process in which social propaganda and social engineering strive to alter culture to its own ideologies by presenting ambiguous terms of meaning.
This is accomplished by means of language and conceptual deconstruction. Seemingly innocent at first, it alters the well-defined and uniformly understood content of a term and substitutes a less well-defined one. Comprehension now is limited and extension is gained. For example, intentionally expressing a falsity was once described by all as a “lie.” The word, “lie” had the negative connotation of an immoral act that should not be emulated or tolerated by any person of ethical character. Today the concept of “lie” has been deconstructed (thereby with less comprehension or specificity) to possess the extension (broader conceptual range) to encompass concepts including “short circuit,” “excessive carelessness,” or “inadequate disclosure” – all in the interests of lessening the comprehended concept of “lie” to something less morally offensive. Furthermore, as distinctives are removed from society’s use, an opportunity is created to promote alternative moral positions as acceptable. (e.g., changing the use of the word “winner” to “participant” in children’s sports). As one changes language, one changes culture. Words form ideas and ideas have consequences.
The spine of moral responsibility, that which one’s conduct is built upon, is shaped by many factors. The corrective of critical thinking, by use of logic, helps one arrive at sound conclusions based upon truthful and well-reasoned propositions. Critical thinking teaches one how to think well and responsibly; but what are the moral components of this endeavor?
Without the corrective of critical thinking, ideological persuasion is left to its own devices. Unfortunately, most persons do not take the effort or have the skills to think clearly. Without this effort and skill, one is left unanchored upon the shifting sea of the prevailing winds of morality. Reason anchors us to a natural moral law which is universal, timeless, and unchanging. Reason, as such, serves to create a framework for valid analysis and judgments with which to take beneficial actions. All “natural law” is predicated on this fact: that reason is a fundamental faculty of humankind with which to guide individual and societal behaviors in a manner beneficial to both.