What is the value & meaning of the null set?

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"The ideas are either right or they are wrong: true or false; but is there another way?"


Hidden assumptions

unexamined biases

Bacon's idols

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Critical thinking requires four steps:

  • analysis
  • explanations
  • discovery of evidence
  • reflection on the meaning


analysis, from analyze means to break into smaller parts and define terms, explain the meaning, and identify any unstated assumptions.

explanations, frequently when explaining the meaning of any statement, concept, artifact, or experience, further explanation is desired to convey clearly the depth of what you want to examine

etymological description looks to the origin and meaning of words used in the argument's premises, to uncover vague or loaded terms, that sound good rhetorically, but mean little.

chronological exposition traces the historical development and meaning of the argument's premises and when the collateral evidence was first associated with the case you are examining.

dialectical narrative is the deliberate search for the opposite, or the antagonistic material, that is then laid side by side with the argument's assumptions and collateral evidence to sharpen the contrasts in order to discover unexamined references in this context of explaining what is meant.


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discovery of evidence, this is a recall, research and investigative stage of getting more deeply into the material to explore the reliability of what you have analyzed and explained. It consists of three sub steps or sub-routines

      1. investigate the available data, by tracing what the author has looked at and evaluate how her conclusions were drawn.
      2. evaluate the argument in light of any new or data that he or she ignored in presenting their case.
      3. exposition requires that you discuss what the argument's proponent have done, how they arrived at their conclusion and the degree of uncertainty in their conclusions, or the tenuous quality of the findings in this research field.


reflection on the meaning of what you have explained, researched and argued requires time and some focused thinking. DO not hurry this process because it is designed to allow you to state the argument from your point of view, especially revealing the evidence that neither confirms nor supports the prevailing contention with respect to the argument's unexamined beliefs.

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Affirm, to find comparative data that supports, sustains, or agrees with the concept because it upholds the premise.

Negate, to find evidence or contrasting data that undermines or disagrees with a concept, because it denies the premise.

Null set, the findings of evidence that can neither deny nor sustain the premise, or uphold the assumption under investigation.

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refers to specific examples of facts about what is known

should include identification of where disagreements arise

may be an inventory of related data

should always be summarized in relation to the investigation.

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is always laid out by specifying what is certain, or known from what is less certain, and marginally known to what is unknown, and ultimately what may be unknowable.

these are facts, the specific findings that no one on any side may dispute

confirmed by more than one source, and not merely copied from one printed or digital source to another.

this does not usually include opinions unless there is something factual about the use of an unconfirmed belief.

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It may be assumed that by using analogies we can make reliable statements about the world we inhabit. We live, for example during the course of twenty four hours in a period of light and in a period of light's absence, that we call darkness. "Night and day," day and night are dialectically different experiences of life on earth. Some stories of creation, the Judeo-Christian for instance speaks of darkness from which everything arises by the grace of God a creator. Other stories may, in contrast, emphasize the loss of light when accounting for the darkness.

In everyday expression we speak of the coming of darkness as nightfall where dusk brings to a close the light of day with the apparent movement of the sun below the Earth's western-most horizons. The opposite experience occurs long after twilight and darkness absorb the nocturnal hours when faint shadows emerge and the dawn treads subtly at first and then breaks over the shaded portions of another day. Light and dark we imagine are opposites because we are reinforced in that assumption by the passage of days in a chain of time.


For centuries writers have used darkness as a metaphor in that the concept of "shedding light" on a subject is to "enlighten" or otherwise dispel doubt about related ideas or set of assumptions. Darkness is the metaphor that reveals the hidden, the superstitious, the occult, and the unseen, even lost world of our experience. Current astronomers have delineated a class of physical substance they term "dark matter" because we can sense its presence, but can not visibly discern what it is. Like some black hole that is known by how it perturbs surrounding bright objects, dark matter is a mysterious and yet to be explained important facet of our cosmic experience.


What if we argue that light and its absence are opposites and they by analogy can be understood dialectically as the inverse of one another. That is to say, dark negates light and light contradicts the dark; they are opposite qualities. This is one reinforcement for the belief that we understand new experiences better when we contrast one thing with another.

Many writers have noted the above symbolic representation of opposition, referred to in ancient Taoist texts as the yin and the yang of Chinese intellectual tradition. In the west, night on the right side an day on the left side may be misinterpreted as these opposite categories are used to classify all other sorts of experiences, encounters and artifacts in our lives. Aristotle used a dialectic to understand the world we experience, sense and contemplate as the union of wet as opposed to dry, and hot as opposed to cold. The branch of argumentation in the Middle Ages was one of the five foundations of the seven liberal arts and it was called the dialectic.

dialectical approaches when explaining reality.
Realm of knowledge:    
Socratic tradition
Zero, zed

But what if there are more than two alternative categories into which we may fit, ideas or concepts and experiences or sensations? What if there --instead of two ways-- there is another way? What, then, is this third way?

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Aristotle's argument

Any of a set of statements that rests on evidence from information and data.


dialectical, to assume that one concept may be set against its opposite concept: affirm, or ratify set beside negate or nullify.

The use of opposite concepts to explain matter:
as opposed to
  wet dry

Here we have Aristotle's dialectical rendition of what is called the

"Doctrine of the four elements."


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Periodic table of the elements

There are more than just two or four factors when discovering the relationship among all the different experiences and imaginative ways we have of telling one another about us, our world and the reality we share with our audiences, readers, or listeners.

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Among any competing means of examining and explaining something there always lies another way to comprehend differences.

For Galileo, the rejection of Ptolemy and Aristotle as a dialectical exercise provoked his curiosity, triggering his experimentation, and led yo the publication of a book El Dialogo that provoked a fire storm among philosophical and theological authorities.

In the debate there emerged a third alternative to the matter of determining if the sun or the earth were the center of the heavens, and that was championed by Tycho Brahe, the diligent observer and recorder of events that occurred in the night sky.

1. Geocentric -- Earth centered

2. Heliocentric -- Solar system has the sun at its core

3. Polycentric -- Brahe's reconciliation of sun and earth




meaning the earth is the center of the heavens with the sun and planets moving about the earth, as the moon appears to move.

Dante's view

meaning the Sun, our nearest star, is the center of the heavens with the earth and planets moving about the sun, as the moon appears to move, revolving about the earth as one of six known planets.

Solar system


meaning dual centers with the earth moving about the sun and other planetary things revolving about the earth.

Tycho Brahe


Galileo's meaning

What is the value of the null set in a world beset by dichotomous thinking?
Protons and electrons: animation
We learn to understand that there are not just:
protons proton and
electrons, electrons
neutrons proton  
    as well;

that makes all the difference in understanding the world's smallest composite parts!


From the decay of neutrons there emerges the protons and electrons that comprise us, all the living things, and other objects in this world.

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