What I show below is not some idea I found in a book about philosophy or logic. I developed this explanation from long years of contemplating the subject.
Bruce R. Bain's answer to What does “everything in between” mean?
Some of the writings on the subject may cause us to think
that it is very complicated. Well, it is a complete science.
However, there is a simple way to understand it.
Our science of Logic is based upon Aristotle's Three Laws.
So this is an explanation of The Three Laws.
These 3 Laws show us Two Extremes or "opposites" and a Mean Value
which is "something in the middle" between the two opposites.
I usually teach Logic by suggesting that a student print out an image
of the Gray Scale such as Artists use. Here is a link to a Gray Scale image.
There are basically, 3 parts. There are two complete opposites; White and Black.
There are the "Two Extremes". Opposites like this are referred to as antithetical.
There is a larger part of the image that is between in different degrees.
These are the various shades of gray.
These are the Middle or the Middling Values which are also called
The "Mean Value".
These 3 parts are called "Identities". It is just like you or I.
We each have our "identity". I am not you. You are not me.
Other people are neither you nor I.
So, the following uses a lot of repetition to emphasize each of these distinct Identities. When we set out to analyze by logic, we need to "identify"
2 Extremes and a Mean Value (or several Mean Values.
I can IDENTIFY the Three Laws of Logic
(as taught by the Greek philosopher Aristotle)
in the following manner:
(1) The Law of Identity
(2) The Law of Non-Contradiction
(3) The Law of the Excluded Middle
Allow me to present the several facets of the subject, as follows.
First, it is necessary to find the Identity.
Second, it is necessary to find the Opposite of the Identity. The Opposite of the Identity is that which “contradicts” the Identity
Third, it is necessary to find the Middling Value, or Mean Value,
between the two extremes. Any Middling Value is an Identity also, but just not the same thing as the set of Identities that it is “excluded” from.
The problem may be introduced for our consideration as follows.
(1) What is the claim for the Identity?
(2) What are the 2 Extremes, or Opposites?
(3) What is the Mean Value or Middling Value?
This is how we identify the basic facts about the subject of our research.
A Fundamental means to obtain all knowledge is the concept of OPPOSITES or the ..."dichotomy"
The image of the Dichotomy gives us Two Extremes.
One Extreme is the Contradiction of its opposite.
What is needed to complete our "thinking" process is something in the middle of the Two Extremes.
This is called a Mean or a "Middle Value" or "Middling Value" .
Thus, identifying two extremes or opposites
and a "mean" completes our knowledge.
In the study of Logic, one of the three Laws of Logic
is called the Law of the "Excluded Middle"
If the Identities (extremes) are
White and Black,
the Mean or "Middling Value" or
"Middle Value" between Black and White
would be obvious
as the color Gray.
See images for "Gray Scale" which shows
the "Middling values" or "mean values"
[Search images + gray scale]
This shows TWO EXTREMES and a MEAN.
In summary then, it can be seen that to "know" anything,
we need to identify Two Extreme Identities
and some Identity that is in the Middle between
the Two Extremes.
4 = 4
4 is not equal to 3.99999
3.99999 is a mean or "middling value"
Regarding the identity 4, the value 3.99999 is not 4.
4 is not equal to 4.11111
4.11111 is a mean or "middling value".
Regarding the identity 4, 4.11111 is not 4.
5 = 5
5 is not 5.1 or 5.2
5.1 or 5.2 is a mean or "middling value".
5 is not 5.01
5.01 is a mean or "middling value".
5 is not 4.99
4.99 is a mean or "middling value".
Remember, mean or "middling values" are
the Excluded Middle values.
"Middling Values" are excluded from the Identity.
Search out pairs of word opposites in books or the Internet.
Such opposites or "Dichotomies" give you the foundation
for speaking and writing English, and engaging in dialogue.
Two Extremes and a Mean are necessary
for all "value" or Identity determinations.
Black and White are Extremes.
Gray represents a Mean, or "middling" value
between the two Extremes.
If one cannot identify two Extremes of "value" it will be difficult to understand what a Mean value would be.
= is read "the same as" or "equals"
In philosophy, which derives from ancient Greek Math and Geometry, statements like "0.5 = 1/2" are demonstrative (or show)
THE IDENTITY STATEMENT, which is one of
the Three Laws of Aristotelian Logic.
Statements as to being, or anything written as
an EQUATION, are illustrative of IDENTITY STATEMENTS.
Statements of Identity are used for definitions.
Any statement, which says that SOMETHING IS,
shows itself to be an IDENTITY STATEMENT.
This is the First "law" of Logic
A = "A" is illustrative of an Identity Statement.
"The Phone Connection is poor."; is an Identity Statement.
It is a statement of Fact about something.
Bruce is happy, is like writing Bruce = (or is) happy
That is a statement about "identity" or What-------Bruce------Is.
EXAMPLE: Jane Chen is a Businesswoman.
That is a statement of Identity, which says What Jane Chen is.
There are three Ancient Laws of Logic taken from Aristotle, and they are more than 2,000 years old.
All of Science, and indeed, all of Western Civilization is based upon the acceptance of these as demonstrations of what is True, and what is False, and how the mind works..
What is an "identity statement"?
The mind operates "logically" whether we know it or not.
The ancient Greeks figured that out.
Any statement as to BEING, or any statement that says
...is an Identity Statement.
"Hot Soup is Good!" is an identity statement. Soup = Good
"I am a woman"; is illustrative of an identity statement
COMPARISON and CONTRAST are the essential components of
the Three Laws of Logic.
Most books on reasoning, employ the reference to COMPARISON and CONTRAST
as the common means for analyzing ideas.
To compare one identity to another, to see SIMILARITIES and DIFFERENCES between identities is how the mind "thinks". The mind compares LIKES and UNLIKES, and things that are ALMOST LIKE.
Here again, are The Three Laws of Logic as taught by the Greek Philosopher Aristotle
(1) The Aristotelian LAW OF IDENTITY. (A = A)
(2) The Aristotelian LAW OF NON-CONTRADICTION.
(A is not equal to Z)
(3) The Aristotelian LAW OF The EXCLUDED MIDDLE.
(A is not equal to "almost A")
The way it can be explained most simply is this way.
(1) The Aristotelian LAW OF IDENTITY. (White is White)
(2) The Aristotelian LAW OF NON-CONTRADICTION. (White is not Black)
(3) The Aristotelian LAW OF The EXCLUDED MIDDLE. (Gray is not White and Gray is not Black)
The Mind works by comparing one identity to another, to see SIMILARITIES and DIFFERENCES
These are the foundation of knowledge in Science, in Law, in Philosophy and in Theology.
Being familiar with them is the key to skill in critical thinking.
Gray as a color is a MIDDLING value between Black and White
The Gray Scale offers the comparison with the two "extremes":
So seeing Black and White as the Two Extremes and Gray as a "Middling Value" or "Middle" between the Two Extremes, establishes what is called a DICHOTOMY or DUAD or what can be seen as a basic Duality of Opposing identities. This duality is symbolized by the Chinese Tai Chi Symbol. In Western Civilization, it can be found in other ways, such as "Post and Lintel" Architecture, the "posts" representing the two extremes, and the "lintel" representing the spectrum of Mean Values or Middling Values..
Gray is a MIDDLING or MIDDLE and Middles are "excluded" from the “opposites” if f the Identity statements refer to values that are not in the Middle.
The Excluded Middle can always be thought of as something that is "almost the same" as an identity, but "not quite the same" as the identity. That is why it is "excluded" from being the identity.
If one wishes to refer to a "middle" as the identity discussed,
then one is discussing the "middle" and changing it into one of the identities that compose one part of a Dichotomy, which of itself, has an "opposite".
By the way, one of the reasons that modern people have so much difficulty sorting out and analyzing what they read, is that modern authors have learned a cunning trick. They do not identify two extremes or two opposites in their compositions. They allow to wallow around in their rhetorical compositions as though nothing existed but "middles" or a never ending sequence of "gray" generalities.
It is a very clever trick..
So we may ask, WHAT IS THINKING?
Thinking is a process of comparing any identity to the Likes or Similars in our memory.
Thinking is a process of comparing any identity to its Unlikes or Dissimilar identities in our memory.
This is why books that write about study of written material come somewhat close to teaching us, when they encourage us to Compare----And---Contrast.
They come close, but they never actually teach people what "thinking" actually is.
. Now you know, what you probably will not find written in a book.
By the way, I spotted an error in logic immediately in your question.
It is a common error that I have come to recognize, because English is a language based upon logic.
Your question began "Will we....etc." You are not a plurality, or a "we" and neither am I. You are an individual. Your question, to be consistent with logic, should begin; "Will I.....ever be able....etc."
If you are an agent or representative for a group of persons or an organization,
then you can write as the plurality, "we".
So take caution not to write of yourself, as though you are part of some kind of a herd of humanity. You are a unique individual.
The answer is; Yes, of course you will, because I will teach you.
What are the rules that make philosophy work? If philosophy is about "how to think" and not "what to think", what are the rules underlying this "how"?
What Are the Three Laws of Logic?
The Ten Rules of Pragma Dialectics:
#1 The Freedom Rule
#2 The Burden of Proof Rule
#3 The Stand Point Rule
#4 The Relevance Rule
#5 The Unexpressed Premise Rule
#6 The Starting Point Rule
#7 The Argumentative Scheme Rule
#8 The Validity Rule
#9 The Closure Rule
#10 The Usage Rule
See also: Analysis of any proposition in the context of the 3 Laws of Logic is representative of
"magic triangle" + "rearrangement of fractions"
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