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There is a sharp distinction to be drawn between arguments of the former kind and arguments of the latter. Assuming a satisfactory account of logical form, in order to know that the conclusion follows from the premises in arguments of the former kind one only needs to consider their structure or form; no other kind of knowledge is required. In the latter argument however in order to infer from the premise to the conclusion, one must know more than its form. One also needs to understand the signification of ‘man’ and ‘rational’ since in order to know that Caius is rational one also needs to know in addition to the fact that Caius is a man that all men are rational. There is good evidence that Bolzano was aware of some such distinction between arguments that preserve truth and arguments that do so in virtue of their “form.” Unfortunately, Bolzano’s definition of deducibility does not systematically uphold the distinction. Since deducibility applies across the board to all inferences that preserve truth from premises to conclusion with respect to a given set of ideas, it does not of itself guarantee that an argument be formally valid and the notion of deducibility turns out to be flawed: it makes it impossible to extend our knowledge in the way we would expect it. If we know, for instance, that all instances of modus ponens are logically valid, we can infer from two propositions whose truth we’ve recognized:

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