INTRODUCTION TO LOGIC
Contents:
The primacy of existence…
Existence exists and that which exists is what it is, independent of consciousness. In other terms, facts have primacy and are independent of consciousness.
Human consciousness is volitional, i.e. capable of selective focus of awareness of its contents. Beyond the basic sensations and perceptions, the contents–the conceptual contents–of such a consciousness do not automatically conform to reality. Therefore, human cognition needs a valid method of cognition to ensure that its contents correspond to reality.
Logic is the validating standard of cognition, i.e. the method by which a volitional, non-automatic consciousness can ensure that its contents correspond to reality.
The purpose of a validating standard–logic–is to enable us to determine when our conclusions do or do not represent facts. Only a standard derived from facts, i.e. from reality can enable us to perform this function; an arbitrary standard detached from facts is detached from reality, and thus, deals with the non-existent.
In particular, since we need a standard that is applicable to any and every fact, i.e. a standard that is universally applicable to facts, we need principles inherent in the nature of facts, i.e. inherent in the nature of existence as such. In other terms, we need principles that are true of being qua being.
(Credits to: Aristotle)
| Symbol | Meaning |
|---|---|
| A, B, C… | any part of reality |
| ¬ | “not” |
Logic has but one law, which is the basic metaphysical axiom inherent in being qua being, namely the law of identity:
A is A
The subsequent laws of logic are, in essence, restatements of the law of identity. However, they are restatements for epistemological use, i.e. for the purpose of finding out whether the law of identity has been violated or not.
A cannot be ¬A in the same respect.
The term “respect” means, “in relation to certain facts,” i.e. “in a certain context.” Note that with time, A can become ¬A in the same respect– but at that point, it is A anymore. Hence, to specify “at the same time” is redundant here.
Note that A and ¬A here can be anything; an entity, an attribute, an action, a unit, a concept, etc. Also, A and ¬A need not be the same kind of existent. With this in mind, we can apply the law of noncontradiction to the attribution of information.
if
A is B at a given time and in a given respect,
then
A cannot be ¬B at the same time & in the same respect.
To combine the above into one statement:
A cannot be B and ¬B at the same time & in the same respect
Note that time is emphasised because though it is implied in the term “respect”, it is the most important factor to consider.
Anything that exists is either A or ¬A at a given time & in a given respect
This is validated by the law of noncontradiction. Note that the law of excluded middle does not state that A is either B or ¬B, where B is some particular. Assuming A and B are not identical, ¬A includes B but extends beyond it to include everything except A.
The laws of logic, i.e. the law of identity and its corollaries, are presupposed by any and every thought and action. To deny these laws presupposes their validity, i.e. any supposed refutation of these laws is forced to count on their validity, thereby becoming self-refuting. For example, the concept of “proof” rests on the validity of logic; you cannot “prove” the validity of logic, as logic is what makes proof possible. However, this very fact validates logic, i.e. shows that logic corresponds to reality.
Validation is the process of showing that an idea corresponds to reality. Proof is a kind of validation that uses logic.
A logical argument is composed of 3 broad parts:
For a conclusion to be true, (1) the premises must be true, and (2) the inference must be valid, i.e. must be based only on the laws of logic. Premises are validated by valid concept-formation, which in turn is validated by a hierarchy of valid abstractions based on the material provided by sense-perception. Showing that a conclusion follows logically from true premises is proof. Note that the opposite of proof is arbitrary, which is baseless and disintegrated from knowledge.
Hence, the application of logic presupposes a valid method of concept-formation. The elaboration of such a method belongs to the broader domain of epistemology, and shall not be discussed in-depth here (it is discussed to some extent in the chapter “Definitions”).
A fallacy is an invalid form of reasoning, i.e. a form of reasoning that does not in fact prove the conclusion it claims to be proving. Common or informal fallacies are fallacies that apply to any form of reasoning, be it deductive or inductive. Being aware of key fallacies enables you to
In other words, being aware of fallacies is a means of intellectual self-defence.
Now for some definitions…
Truth:
A cognitive element that identifies a part of reality.
Context:
The sum of cognitive elements in relation to which any item of human knowledge is acquired, validated or applied.
Note, hence, that distorting the truth involves distorting the context, and vice versa. The classification, however, is based on what distortion was primary: the explicit elements of the argument or the implicit elements not stated yet underlying the argument.
A logical argument falls short either due to the inclusion of irrelevant elements or due to the exclusion of relevant ones. Hence, in essence, any fallacy is a combination of one or both of the following fallacies:
In practice, due to the overarching nature of these fallacies, apply them only when none of the other more specific kinds apply.