Goodman's problem of projectibility shows that any two objects share infinitely many predicates, so no determination rule can non-arbitrarily privilege the relevant similarity dimensions.

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Goodman(the statement opens with his name): Nelson Goodman was a 20th-century philosopher who created a famous puzzle about how we learn from experience and make predictions based on patterns we've observed.
Predicates(in logic and philosophy of language): Words or phrases that describe properties or characteristics of something—like 'is red' or 'is tall' in the sentence 'The ball is red.'
Problem of projectibility(as the core concept being explained): A puzzle about why some observed patterns seem reasonable to use for predictions (like 'all emeralds are green') while others seem silly (like 'all emeralds are grue'—a made-up color meaning 'green before 2050, then blue').
Similarity dimensions(as the different aspects we could use to say objects are similar): The different ways or angles from which two things can be compared as alike—for example, color, size, weight, or purpose.

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