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.

apparent contradictions

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

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

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

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.

quirks in logic that demonstrate how our thinking sometimes goes haywire, even when we use perfectly logical reasoning to get there

Paradoxes are quirks in logic that demonstrate how our thinking sometimes goes haywire, even when we use perfectly logical reasoning to get there.

truths that we have yet to comprehend

Sometimes paradoxes are only truths that we have yet to comprehend.

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.

part of life

Paradoxes are part of life — and they are part of this pandemic.

conflicting choices or conditions that demand equal attentions

Paradoxes are conflicting choices or conditions that demand equal attentions.

apparent contradictions, not real ones

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

truths in a crooked form

paradoxes, when examined, are truths in a crooked form, and so they best suit the deformed.

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 key to psychological ones

Logic is the key to scientific truths, but paradoxes are the key to psychological ones.

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.

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.

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.

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.