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Adam I. Gerard
ISU
NIU
CS MS TBD

On The Origins of the Concept of Contradiction

Just some quick thoughts on the origins of the concept of Contradiction.

Contradiction in Classical Logic

Brief summary/review.

  1. P and ~P are both asserted to be T.
  2. P and ¬P must be Lexiographically Identical with the exception of the first character in the WFF.
  3. Such notions are Syntactic and Semantics.
  4. These are strictly more stringent notions than the following.

Contradictions in Behavior and Action

We often encounter something like the following:

  1. P1 - He went to the store to buy this week's groceries.
  2. P2 - But he ended up only buying candy.
  3. P1 and P2 diverge in outcome alignment, goal-setting, or the achievement of specified objectives.

Hypocrisy

Recollect that many of the early discussions on Contradiction originated in discussions on learning, politics, and rhetoric:

  1. A person P may claim that something or someone X is wrong, evil, must abstained from, or condemned.
  2. But, P then engages in, partakes of, or performs X.
  3. This particular kind of Hypocrisy isn't just about misalignment in espoused Virtues, Truth, or Norms.
  4. It also involves concerns around Fairness ("Some rule applies to thee but not to me!").

Contradictions Between Words and Action

We often encounter something like the following:

  1. P1 - "He said he was going to the store."
  2. P2 - "But then he spent the day playing video games."
  3. What's implied is that P1 and P2 are inconsistent with respect to each other.
  4. We might even hear something like "That's contradictory." (say in a court of law after reading testimony).

We observe:

  1. P1 and P2 aren't Lexiographically Identical.
  2. There are suppressed (omitted) inferential relations between the two (that P2 implies the negation of P1) specific to the context and circumstance embedded into the speech.
  3. But P2 strictly speaking doesn't entail P1 (one could go to an online store).
  4. This involves Pragmatics and Semantics.

Considerations

  1. There are presumably many other legitimate occasions in which people naturally will call something a Contradiction.
  2. Contradictions (metaphorically) involve some kind of "tension", some "resistance" between the Truth Values of multiple Assertions, Expressions, Sentences, or Propositions.
  3. E.g. - one denies another, they are mutually exclusive, they are both self-denying and self-affirming, and so on.
  4. Above, we see stronger and weaker notions at play.

Origins of Such Concepts

There are at least two kinds of questions we can ask about such conceptions:

  1. What is common to them?
  2. Is there some deeper concept (or conceptual basis) from which they originate?

Commonalities:

  1. Alignment - agreement of Truth Values, consistency of outward behavior and professed imperative, uniformity in Norm Commitment or expectation, etc.
  2. Truth, Norm Commitment, Fact, Norms

Origins:

  1. Does that mean that the concept of Contradiction primarily arises from considerations about Truth (this is perhaps the default option that most academics would take)?
  2. Or does that mean that the concept of Contradiction primarily arises from considerations about Ethics or Fairness (that )
  3. If it's the latter, does Truth then have its origins in Ethics (the naturally tendancy in the 20th Century has been to see Ethics as being a Science of Norms which requires Truth as a precursor).
  4. Or alternatively, does this suggest that the concept of Contradiction primarily arises from Pattern Matching or Structural Alignment (sameness of Behavior, Truth Values, etc.)?

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