propositions that seem to contradict themselves but are nevertheless true

Paradoxes, like this one, are propositions that seem to contradict themselves but are nevertheless true.

circumstances in mathematics, philosophy, or other domains that present a seeming contradiction

Paradoxes are circumstances in mathematics, philosophy, or other domains that present a seeming contradiction, which may be difficult to resolve.

apparent contradictions

Paradoxes are apparent contradictions, with emphasis on apparent because on further investigation they do not contradict each other.

a class of phenomena which arise when, although starting from premises known as true, we derive some sort of logically unreasonable result

Paradoxes are a class of phenomena which arise when, although starting from premises known as true, we derive some sort of logically unreasonable result.

logical possibilities which create apparent contradictions towards already known facts

Paradoxes are logical possibilities which create apparent contradictions towards already known facts.

the interdependent oppositions that lurk beneath our dilemmas and persist over time

Paradoxes are the interdependent oppositions that lurk beneath dilemmas and persist over time.

interesting puzzles in philosophy and mathematics

Paradoxes are interesting puzzles in philosophy and mathematics, and they can be even more fascinating when turned into proofs and theorems.

apparent contradictions, not real ones

Paradoxes, you might recall, are only apparent contradictions, not real ones.

conflicting choices or conditions that demand equal attentions

Paradoxes are conflicting choices or conditions that demand equal attentions.

the types of truths, which at first seem incredulous, but on deeper inspection, prove themselves to be intractably true, and therefore impossible to ignore.

Paradoxes are the types of truths, which at first seem incredulous, but on deeper inspection, prove themselves to be intractably true, and therefore impossible to ignore.

which are true but whose truth is intuitively surprising to people who are not familiar with them

The paradoxes are logical statements which are true but whose truth is intuitively surprising to people who are not familiar with them.

two ideas that seem contradictory or mutually exclusive

We all know that paradoxes are two ideas that seem contradictory or mutually exclusive, yet are actually both true in a way that does not yield completely to our either/or logic.

the mad scientists, the sorcerers, and those who break the rules of reality

Paradoxes are the mad scientists, the sorcerers, and those who break the rules of reality.

a strategic marketing organization that helps technology companies collect, analyze, and use data to make smarter sales, marketing, and product decisions

Paradoxes is a strategic marketing organization that helps technology companies collect, analyze, and use data to make smarter sales, marketing, and product decisions.

entire phrases, sentences or quotes

Paradoxes, however, are entire phrases, sentences or quotes.

without solution

The paradoxes are recurrent subjects, without solution, that, contradictorily and at the same time, are also a form of resistance and a form of deepening of the mind during the observation process.

recurrent subjects

The paradoxes are recurrent subjects, without solution, that, contradictorily and at the same time, are also a form of resistance and a form of deepening of the mind during the observation process.