Finite Evidence and Universal Propositions :: Ampliative Logic

Finite Evidence and Universal Propositions There is a lot of empirical evidence supporting the proposition '‘All metals expand when heated’. For example on many, many occasions we have observed metals expanding when heated. Because of this large amount of evidence we take the proposition to be true (or highly likely to be true). The proposition '‘All metals expand when heated’ is caled a universal proposition. A universal proposition mentions al things of a certain kind. The proposition '‘Al metals expand when heated’ is about al metals, not just some of them; it is about al pieces of metal, not just some pieces. Any piece of metal, any kind of metal, according to this proposition, wil expand when heated. Now as we have said there is a great deal of evidence supporting this universal proposition; it is not a proposition that many would doubt. But however large the body of evidence supporting this proposition, and whatever the variety, this body of evidence is finite. Our experience is finite, even our colective experience. But the proposition is universal: it refers to al metals, not just this bit or that bit, nor this kind or that kind. Any bit of metal at al, whatever kind, wil expand when heated. This is what the proposition says. The proposition does not just say, only those bits of metal that we have observed, expand when heated. Those bits we have observed, they expand when heated; but the proposition also says, even those bits that we have not observed expand when heated. This is what the '‘al’ means; this is why we cal the proposition universal. The evidence which supports ‘Al metals expand when heated’ is finite. The proposition which draws support from this evidence is universal. How can finite evidence support a universal proposition? A universal proposition, even when supported by evidence, goes wel beyond evidence. There are infinitely many bits of metal. Compared to the many bits of metal in the universe the bits we have observed is only a tiny fraction. How can a tiny fraction support such a large number? When we have no evidence for a proposition we would not take the proposition to be true. When we have only a litle evidence for a proposition we stil would not take it to be true. If we are to take a proposition to be true, or likely to be true, we require a large amount of evidence.