Oxford Languages defines “logic” as “reasoning conducted or assessed according to strict principles of validity.” Logic is its own field of study.
However, logic is also simple and concrete. This is why the formal concepts of conjunction and disjunction have the common words of “and” and “or”. We use logic on a daily basis!
What most people do not do is to apply rigor. We will get to that part later.
The words “true” and “false” are seldom used in daily conversation. However, people do frequently use the more common words of “yes” and “no” many times in a day.
Let’s think about a simple inquiry that occurs many times in most households: “did you put the dishes in the dishwasher?” The following answers are considered equivalent:
In real-life, the word “true”, as an adjective, is used to indicate “consistent with fact”, and the word “false” means “not consistent with fact.”
The word “not” is the easiest of the three. In the sentence of “cockroaches are not cute,” it means that “cockroaches are cute” is false.
Consider the sentence, “my cat is agile and friendly.” This means the cat has both the attributes of “agile” as well as “friendly”.
The word “or” requires more attention because there is an option of exclusivity. For example, in the sentence, “the package will arrive today or tomorrow,” it is unspoken, but the package will not arrive today, and arrive again tomorrow.
There is where natural language lacks accuracy. The same word “or” is used for two different concepts. These two concepts are:
In daily life, the context often provides sufficient clue as to which meaning is applicable. However, in an abstract application, there is no context to differentiate which meaning is applicable.
Most natural languages make it easy to distinguish a declaration from an inquiry. However, the difference between a declaration and a statement is more subtle.
A statement is something that can be true or false. For example, “my cat is fluffy” can be a declaration, confirming that my cat is, indeed, fluffy. However, “my cat is fluffy” can also be just a statement where the truthfulness of the statement is not know.
A statement can be utilized to formulate longer statements. For example, “if my cat is fluffy, then it takes longer to brush its fur” utilizes “my cat is fluffy” as a statement that can be true or false. Note that the statement “if my cat is fluffy, then it takes longer to brush its fur” can also be a statement or a declaration.
Examples: “Everyone needs to wash hands before eating!”, “Some students budget their time according their course loads.”
These words are known as quantifiers. “Every” is somewhat related to “and”, while “some” is somewhat related to “or.”
In daily conversation, “enough to” is a phrase for “sufficient.”Needed to”, on the other hand, is used to convey “necessary.”
“Jim took one sip of the soup, and that was enough to make him feel sick for the rest of the evening.”
“Exercise is needed to maintain good health.”
The previous section shows that most of us already understand logic and utilize logic on a daily basis! But what makes a person described as “logical” different from others?
A “logical person” does not need to take college level classes in logic or reasoning. A logical person applies logic consistently and with rigor. In this context, according to the Merriam Webster Dictionary, “rigor” means “strict precision.”
In return, Oxford Languages define “precision” as “the quality, condition, or fact of being exact and accurate.” The same source defines “accurate” as “correct in all details, exact.” A dictionary has a finite number of words, at some point, definitions are bound to be cyclic!
To be exact is to be without confusion, and the potential there of. One can compare exactness to the resolution of a digital image. A high resolution image (photograph) does not necessarily mean it is correct in the sense that the image reflects fact.
On the other hand, a image taken by a poor camera is factual (hence “correct”), but has low resolution (hence not exact).
A high resolution image that is factual is precise because it is correct and detailed.
But how does rigor apply to logic?
This essentially means “whenever possible, use logic.” This can be using logic to deduce a fact that is not stated, this can be using logic to discover the inconsistency of statements (because they cause a contradiction).
There are a few reasons why rigor is absent.
The first reason is that rigor requires effort. There is an expense of time and mental energy. In other words, one reason of the absent of rigor is how people prioritize their use of time and energy, and this ultimately relates to the value system of an individual.
Related to the first reason is the consequences of rigor. What if rigor (in the application of logic) results in an outcome that opposes the norm, the convention, the tradition? It is one thing to say that knowing the truth is worth my own time and energy, it is a different thing to announce to others that they are incorrect.
Furthermore, if an individual has never been exposed to the rigor of logic, this individual may not even be aware of what rigor of logic is.
The rigor of logic is not about intelligence, it is about how one views the value of applying logic. There are useful skills that requires the rigor of logic. These skills will be explored in their own modules. Here is a list of the skills: