Concept Clarifier in
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There are many ways to divide up knowledge, and they all have problems.  This is the best I've come up with so far.  The word "know" is used to express two concepts:  ACQUAINTANCE and CERTITUDE.

1.  ACQUAINTANCE is of 2 types:  FAMILIARITY and OPERATIONAL acquaintance.
e.g.  to know Fred, your car, your face in the mirror
OPERATIONAL:  to know how to X, or how to do X
e.g.  to know how to swim, or solve math problems
These 2 types exist in a range of degrees.
Degrees of FAMILIARITY range from distinction to exaustive familiarity:
Distinction:  to know X from not-X
Exhaustive familiarity:  to know everything about X
Degrees of OPERATIONAL acquaintance range from:
First time encounter
Every day experience.

2.  CERTITUDE can be expressed verbally as propositions.
Propositional certitude exists in 2 types.
Certainty has no degrees.
Probability judgment has countless degrees.

Note the difference between probability and probability judgment.  Probability itself is based on mathematics, and is therefore objective.  But probability judgment is an opinion.  It happens every time a mind makes a guess.

CERTAINTY (not subject to error, 100% certitude)

A statement is said to be certain by impossibility of the contrary.  This is not quite correct.  Two contrary statements cannot both be true, but they can both be false.  A statement is certain by impossibility of the contradictory.  If two statements are contradictory, one of them is necessarily true, and the other necessarily false.


This could be called ONTOLOGICAL CERTAINTY

I know that I exist and experience (prior to understanding logic).
I know that I exist, think, perceive, and emote – have emotions.
I know I feel because it's part of sensory perception.
I know I desire and will to do things because those are parts of emotion.

But I don't know I exist as what I think I am.  I may be a brain in a vat.
I don't know my thoughts are correct.  I only know that I think.
I know I'm perceiving a sensation, but I don't know if that sensation is caused by what I think is causing it.
If I think I'm feeling an emotion, I can't possibly be wrong.  But I may be wrong about what is causing that emotion.

It appears to me that the reliability of logic should also be in the category of impossibility of the contradictory, but I can't prove it.  I cannot conceive of any possible state of affairs such that truth would violate logic.  But I can't prove it's impossible by logic.  Just because my mind can't conceive of something doesn't mean it's impossible.  Therefore I can only claim to know logic is reliable by inconceivability of the contradictory.


The truth of a proposition is known by inconceivability of the contradictory if a counter-proposition cannot be thought of which cannot be shown to be false, self stultifying, or meaningless.
This could be called EPISTEMOLOGICAL CERTAINTY or undeniability or rational knowledge.

Example of inconceivability:

I know there is no such thing as a square circle because I can't think the concept.

Examples of self stultification:

I know that knowledge exists, because to deny that I know is itself a knowledge claim.
I know that absolute truth exists, because denying it is an absolute statement.
I know that logic has truth value, because I can't deny it without affirming it.  Denial is a logical event.

AXIOMS:   All mathematical, logical, epistemological, and geometric axioms are in this category.  They can't be proven, but assuming them is necessary in order to prove anything else.  In fact, the idea that categorization is even possible is an epistemological axiom necessary in order to make, or even think, a declarative statement.

By the strictest definition of certainty, impossibility of the contradictory would be the only thing in the category.  But we all use the terms "certain" and "know" when talking about things in the category of inconceivability of the contradictory.  So because of language convention and practical necessity, we put inconceivability of the contradictory in the category of certainty.  And we keep getting sloppier...

(subject to error, less than 100% certitude)

        (a difference that makes no difference)

I know that the world apart from me exists because if it were imaginary, it would make no difference to me.
I know that my memory has recorded real, not imagined events for the same reason.  But I do not know that all events in my memory are real and not imagined.


i.e.  I am unable to perceive evidence of the contradictory.
e.g.  There is not a weightless invisible parrot on my shoulder.
Russell's teapot does not exist.


i.e.  I have never perceived evidence of the contradictory, and if there were such evidence I would have probably perceived it by now.
e.g.  Mermaids don't exist.
They may exist, but I have never perceived any evidence of it.
The Holocaust actually happened.
It may not have, but I have never perceived any evidence to the contradictory.


i.e.  I have perceived evidence of the contradictory, but not enough to dissuade me from claiming knowledge.
e.g.  I know my world view is correct.
I know there have been no alien spacemen land on Earth.
I know magic doesn't exist despite having seen tricks I can't explain.

e.g.  a coin flip
Anything less than 50% certitude can be dismissed on semantic grounds.
49% certitude of X is 51% certitude of not-X.

By whatever level of certitude you claim to know that X is true, you claim to know that any hypothesis contradictory to X is false.

Our language has a problem expressing probability in terms of a percentage.  We can legitimately say "1% probable" or "99% probable," but "100% probable" means certain.  Yet "100% certainty" is redundant, because certainty has no degrees, so "99% certain" is technically incorrect.  We could call it "99% certitude," unless someone wants to quibble that certitude means the same as certainty.  Note how disgustingly imprecise our language is for describing philosophical reality!  Earthly languages were not designed for correctness; they evolved to get people what they want.  And we must all condescend to erroneous conventions in order to communicate.

Any proposition which violates the laws of logic is necessarily untrue.
I sometimes have thoughts that violate the laws of logic.  Therefore, I know that my knowledge is limited, and my thoughts are not always correct.

If I'm not certain of the truth of premises A and/or B, but I am certain of logic, then if A & B logically imply conclusion C, then I am certain that A & B imply C.  But I have only the same level of certainty of conclusion C as I have of A & B.