"Universal generalization " concludes the propositional function must be universally true if it is true for any arbitrary element of the Universe of Discourse.
2.
He also studied geometry and astronomy, using mathematics as " a means of discarding allegory and myth and advancing universal generalizations . " Thus, mathematics gave rise to philosophical speculation.
3.
Falsificationism would allow hypotheses expressed as universal generalizations, such as " all swans are white ", to be provisionally true until falsified by evidence, in contrast to verificationism under which they would be disqualified immediately as meaningless.
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The reason is partly technical ( it is difficult to construct and prove universal generalizations about criticism as a human behavior ) and partly practical ( it is more useful to understand particular behaviors which are of direct practical concern ).
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For example, by the problem of induction, no number of confirming observations can verify a universal generalization, such as " All swans are white ", since it is logically possible to falsify it by observing a single black swan.
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Duns Scotus however argued that inductive inference from a finite number of particulars to a universal generalization was justified by " a proposition reposing in the soul,'Whatever occurs in a great many instances by a cause that is not free, is the natural effect of that cause.
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A universal quantification of an open formula & phi; is true in a model iff every element in the domain satisfies that formula . ( Note that in the metalanguage, " everything that is such that X is such that Y " is interpreted as a universal generalization of the material conditional " if anything is such that X then it is such that Y ".
8.
"' No true Scotsman "'is a kind of informal fallacy in which one attempts to protect a universal generalization from rhetoric, without reference to any specific objective rule ( " no Scotsman would do such a thing "; i . e ., those who perform that action are not part of our group and thus criticism of that action is not criticism of the group ).
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