A ‘solid’ statement is one of the form ‘there exists an x such that for each y, P(x, y)’. A ‘fluid’ statement is one of the form ‘for each x, and for each y, P(x, y)’. Notice that the negation of a fluid statement is a solid statement. That is, the negation of ‘for each x, and for each y, P(x, y)’ is ‘there exists an x such that for each y, not-P(x, y)’. Taking Q(x, y) to be not-P(x, y), we have ‘there exists an x such that for each y, Q(x, y)’, which is the exact pattern of a solid statement.

keywords:

[logic]

[logical quantification]

[mathematics]

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