【Abstract】 , 【ideal】 , 【transcendent】 and 【transcendental】 all are closely analogous rather than synonymous terms.

The difference in meaning between 【abstract】 and 【ideal】 is not apparent when they are applied to things which are admirable in actuality as well as in idea, as a virtue or a desirable quality or attribute.

• 【abstract】 (or 【ideal】 ) justice
• 【ideal】 (or 【abstract】 ) morality

When, however, they are applied to the name of a category known through actually existing representatives, they reveal their fundamental differences in meaning; for 【abstract】 implies the formulation of the idea by abstraction, a logical process in which the mind selects the characters common to every known member of a species or every known instance of a quality and builds up a conception (technically, a concept) which describes no one actually existing thing or instance, but covers all things of the same kind or marked by the given quality.

• Man in the 【abstract】 .
• To shed tears over 【abstract】 justice and generosity, beauty, etc., and never to know these qualities when you meet them.
  —James
• Poetic theory is almost invariably an abstraction from poetic practice.
  —Day Lewis

【Ideal】 may or may not imply abstraction; very often it suggests the exercise of imagination or the adding and the elimination of characteristics as the mind seeks a conception of a thing in its perfection.

• 【ideal】 man
• Plato, in the construction of his 【ideal】 republic, is thinking . . . of the symmetry and beauty of the whole
  — Dickinson

In general, therefore, 【abstract】 connotes apartness from reality and often lack of specific application to actual things.

• algebra . . . is more 【abstract】 than geometry
  —Russell

On the other hand, 【ideal】 very frequently connotes superiority to reality or, less often, fancifulness, and, at times, untruth.

• that lofty order of minds who pant after the 【ideal】 . . . [whose] emotions are of too exquisite a character to find fit objects among their everyday fellowmen
  —George Eliot)

【Transcendent】 and 【transcendental】 , though often used as equivalents of 【ideal】 , actually imply existence beyond experience and lack of correspondence to reality as known through the senses. Thus in careful use 【transcendent】 (or 【transcendental】 ) beauty is not the perfection of the beauty that is known, but a supersensual beauty which has no parallel in experience and which cannot be apprehended through any likeness in actuality.

• the idea that God is 【transcendent】 . . . exalted above the world . . . is yielding to the idea of God as immanent in his creation
  —A Hen

In Kant’s philosophy they are distinguished. What is 【transcendent】 is both beyond experience and beyond human knowledge; what is 【transcendental】 is beybnd experience yet knowable, because the mind possesses knowledge not derived from experience but inherent in its own constitution and essential to its understanding of experience. Thus space and time, in Kant’s philosophy, are 【transcendental】 ideas.