Deduction, Necessary Truth and the Real World

Consider this categorical syllogism:

Major premise: All bachelors are unmarried.

Minor premise: John is a bachelor

Conclusion: Therefore John is unmarried.

If valid and sound, the conclusion has necessary truth.

But that necessary truth is arguably de dicto necessity: a necessity that is a property of the argument being an analytic a priori system, where “John” is merely a hypothetical person who is a bachelor by definition. It follows that even the conclusion must be understood as analytic a priori.

But once we assert “John is a bachelor” of a real and specific person in the world, suddenly something important happens: the minor premise “John is a bachelor” becomes synthetic a posteriori, and can only be proved a posteriori, or by experience, empirical evidence and inductive arguments. The truth of the minor premise therefore becomes contingent, not necessary. It can never have apodictic truth, because there must always be some small doubt about its truth: for example, if John says he is unmarried, then he might be lying or delusional (e.g., perhaps he is mentally ill). If public records say John is unmarried, they may be in error or fraudulent. If John’s friends say he is unmarried, then they may also be mistaken or taken in by John’s lies, and so on.

There is no way to obtain absolute and apodictic truth in propositions known a posteriori.

The consequence of this is that the deduction above only has necessary truth when it is strictly understood as an analytic a priori argument and where the logical necessity is de dicto necessity.

When asserted of a real person, the minor premise and the argument can never be proved in the sense of being absolutely true, because we cannot have apodictic truth about a synthetic a posteriori proposition (the minor premise).

The belief that the syllogism has necessary and absolute truth about any concrete real world person is an illusion that arises by merely assuming the world conforms exactly to the assumptions and requirements of analytic a priori argument: we are using words to abolish uncertainty and effectively imposing an unempirical argument on the real world that can only be known a posteriori. In short, we are conflating (1) the analytic a priori with (2) the synthetic a posteriori, when they are strictly separate.

It has become fashionable in modern analytic philosophy to admit the existence of a second type of necessity: de re necessity. Here it is conceived that the possession of a property y by a certain thing x is logically necessity for it to be identified as a certain kind or type x (a type of essentialist argument).

For example, water is necessarily H₂O: for a thing to be the substance we call water, it must be by necessity have the property of being physically H₂O.

But one can wonder whether this new view that there are necessary a posteriori truths and metaphysical/ontological necessity has gone too far.

Consider the proposition:

Statement 1: water is necessarily H₂O.

Conceived as an analytic a priori statement, it has necessary truth.

But let us consider this statement:

Statement 2: This specific real world sample of water is necessarily H₂O.

Here we face the skeptical challenge and Hume’s problem of induction: how can you be absolutely certain that what you are looking at is water at all? You may have made some error. It might be something that looks like water but is not physically H₂O. Even a scientific analysis of the substance that seems to show that it is chemically H₂O could in theory be mistaken or fraudulent. Or a more elaborate sceptical challenge would be: how can you be absolutely certain that anything you have seen now or in the past that you call water really is H₂O and not some elaborate trick by Descartes’ demon?

Statement 2 above asserted of a real world thing must simply abolish uncertainty by begging the question and assuming all epistemological problems and challenges can be countered, in much the same way that the original syllogism above when asserted as absolutely and necessarily true of any concrete real world person simply abolishes uncertainty and renders the argument analytic a priori.

One could argue, then, that modern metaphysical (essentialist) necessity remains a property of analytic a priori systems.