By Jaxson

Main Difference

The main difference between Dichotomy and Paradox is that the Dichotomy is a splitting of a whole into exactly two non-overlapping parts; dyadic relations and processes and Paradox is a statement that apparently contradicts itself and yet might be true

• Dichotomy

A dichotomy is a partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be

jointly exhaustive: everything must belong to one part or the other, and

mutually exclusive: nothing can belong simultaneously to both parts.Such a partition is also frequently called a bipartition.

The two parts thus formed are complements. In logic, the partitions are opposites if there exists a proposition such that it holds over one and not the other.

Treating continuous variables or multicategorical variables as binary variables is called dichotomization. The discretization error inherent in dichotomization is temporarily ignored for modeling purposes.

A paradox is a statement that, despite apparently valid reasoning from true premises, leads to an apparently-self-contradictory or logically unacceptable conclusion. A paradox involves contradictory-yet-interrelated elements that exist simultaneously and persist over time.Some logical paradoxes are known to be invalid arguments but are still valuable in promoting critical thinking.Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell’s paradox, which questions whether a “list of all lists that do not contain themselves” would include itself, and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry’s paradox, are not yet resolved.

Examples outside logic include the ship of Theseus from philosophy (questioning whether a ship repaired over time by replacing each and all of its wooden parts, one at a time, would remain the same ship). Paradoxes can also take the form of images or other media. For example, M.C. Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.In common usage, the word “paradox” often refers to statements that are ironic or unexpected, such as “the paradox that standing is more tiring than walking”.

Wikipedia
• Dichotomy (noun)

A separation or division into two; a distinction that results in such a division.

• Dichotomy (noun)

Such a division involving apparently incompatible or opposite principles; a duality.

• Dichotomy (noun)

The division of a class into two disjoint subclasses that are together comprehensive, as the division of man into white and not white.

• Dichotomy (noun)

The division of a genus into two species; a division into two subordinate parts.

• Dichotomy (noun)

A phase of the moon when it appears half lit and half dark, as at the quadratures.

• Dichotomy (noun)

Division and subdivision; bifurcation, as of a stem of a plant or a vein of the body into two parts as it proceeds from its origin; often successive.

An apparently self-contradictory statement, which can only be true if it is false, and vice versa.u

“”This sentence is false” is a paradox.”

A counterintuitive conclusion or outcome.s

“It is an interesting paradox that drinking a lot of water can often make you feel thirsty.”

A claim that two apparently contradictory ideas are true.t

“Not having a fashion is a fashion; that’s a paradox.”

A thing involving contradictory yet interrelated elements that exist simultaneously and persist over time.

A person or thing having properties.t

“He is a paradox; you would not expect him in that political party.”

An unanswerable question or difficult puzzle, particularly one which leads to a deeper truth. s

A statement which is difficult to believe, or which goes against general belief.

The use of counterintuitive or contradictory statements (paradoxes) in speech or writing.

A state in which one is logically compelled to contradict oneself.

The practice of giving instructions that are opposed to the therapist’s actual intent, with the intention that the client will disobey or be unable to obey.s

Wiktionary
• Dichotomy (noun)

a division or contrast between two things that are or are represented as being opposed or entirely different

“a rigid dichotomy between science and mysticism”

• Dichotomy (noun)

repeated branching into two equal parts.

a seemingly absurd or contradictory statement or proposition which when investigated may prove to be well founded or true

“the uncertainty principle leads to all sorts of paradoxes, like the particles being in two places at once”

a statement or proposition which, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems logically unacceptable or self-contradictory