Properties: Paper Burns, but Is It Flammable?

The advances made in mathematics at end of the nineteenth century overlapped with advances in formal logic, leading to the birth of symbolic logic in the form of Frege’s Begriffschrift. In the twentieth century, logic was employed by philosophers, especially by those engaging in what is often called ‘contemporary analytic’ philosophy.

The rigor of formal logic can have a clarifying effect, especially in matters related to philosophy of language and in matters related to metaphysics. Ordinary organic human language, with its idioms and ambiguities, can muddle what should be precise discussions. Natural language contains metaphors which are ossified and used unconsciously, to the point that those using the language do not recognize them as metaphors. By contrast, systems of logic, according to Howard Kahane,

have been very useful tools for philosophers, logicians, scientists, and mathematicians. In particular, they have been used by some twentieth century philosophers in their attempt to get a clearer grasp on several of the central problems in philosophy.

But the application of modern symbolic logic to philosophy proper has yielded another, perhaps bitter, kind of fruit. For once the notation and proof technique of predicate logic is employed, important problems come into sharp focus, to which insufficient attention was paid previously.

While logic might allow philosophers to make progress concerning some problems, it uncovers other problems. Famously, e.g., the substitution problems which arise when the verb ‘to be’ is naively regarded as an equation:

Fred is Mike’s brother.
Fred is twenty years old.
Mike's brother is twenty years old.

Fred is smart.
Fred is twenty years old.
Smart is twenty years old.

In addition to the verb ‘to be’ as a copula, a related problem is one of qualities (or ‘properties’) in general. If the proposition that ‘Fred is smart’ is not an equation of the form “a = b”, then what is it? If we answer that it is equivalent to “Fred has smartness,” then we are already deep into the weeds of metaphysical commitment; not that we necessarily wish to avoid such commitment, but we want at least to be aware of such commitments when we make them. We now must explore what ‘smartness’ might be.

We might take ‘smartness’ to be a property. Howard Kahane sets forth some preliminary notions about properties:

There is a long tradition in philosophy which distinguishes properties of objects into two kinds, namely observable, or manifest, properties and dispositional, or power properties.

What we might understand under the heading ‘observable’ would include not only direct sensory perception, but also matters which are indirectly observable (e.g., seeing a photograph of the object instead of seeing the object itself, if the object has the property in question, or seeing evidence about the object, or seeing data recorded about the object, etc.), and matters which are only in principle observable (e.g., we can’t observe whether there is a purple rock on the far side of the planet Pluto, but we can understand what it would mean to make such an observation if it were possible).

Observable properties of objects can be recognized by means of one or more of the five senses, while dispositional properties cannot. Thus, we can observe that something burns, but not that it is flammable (although if it is flammable, and if we ignite it, we can observe that it burns). And we can see that something bends, but not that it is flexible (although if it is flexible, and we apply suitable pressure to it, then we can observe that it bends). Burning and bending are observable properties, while flammability and flexibility are dispositional properties.

The question arises, what, if any, metaphysical commitments we make, if we accept what Kahane calls dispositional properties. Various readings of ‘dispositional properties’ are possible. A more empiricist reading would say that such properties are a linguistic shorthand for expressing the proposition that ‘objects like this have been observed having such a property’ - i.e., to say that ‘paper is flammable’ would be to say that ‘some paper objects have been observed to burn.’

On the other hand, a more metaphysical reading of ‘dispositional properties’ would say that there is a fact about an object which justifies our using the word ‘flammable’ about it. There is something called ‘flammability’ which is a feature of this object. If we say that ‘some liquids are flammable and others are not,’ then we are asserting a difference between the two sets of liquids, a difference which would exist independently of anyone having observed any of them actually burning.

Now, someone might argue that there is no metaphysical commitment in this latter reading of ‘dispositional properties,’ because an explanation could be made using the vocabulary of chemistry, which is an allegedly hard-nosed empirical science. But a closer examination of any such explanation might reveal that the chemist, in explaining 'flammability,' would in fact be invoking further dispositional properties, perhaps by means of making counterfactual statements about how a substance would act under circumstances other than the actual circumstances.

Obviously, the dispositional, nonobservable, property of being flammable is closely connected to the observable property of burning, for to say that something is flammable is to say that it has the power to burn, or the disposition to burn, under certain circumstances. Similarly, the dispositional property of being flexible is closely connected to the observable property of bending, for to say that something is flexible is to say that it has the power to bend, or the disposition to bend, under certain conditions. And so on.

The assertion that 'dispositional properties' are in fact real facts belongs to a view which might roughly be called Aristotelian. The view that such properties are actually a sort of linguistic shorthand for expressing what has been observed and for expressing patterns in what has been observed is a view which might be described as empiricist, as empiricism is exemplified by the likes of David Hume and A.J. Ayer

To argue that an object's burning is caused, at least in part, by its flammability, would seem to some empiricists a double sin: first, to have posited flammability which is not even indirectly observable; second, to have posited a 'cause' for an observed property. Thus Hume's disposition (!) to argue against dispositional properties is an organic outgrowth of his general attack on causation. In An Enquiry Concerning Human Understanding (1748), Hume writes:

Adam, though his rational faculties be supposed, at the very first, entirely perfect, could not have inferred from the fluidity, and transparency of water, that it would suffocate him, or from the light and warmth of fire, that it would consume him. No object ever discovers, by the qualities which appear to the senses, either the causes which produced it, or the effects which will arise from it; nor can our reason, unassisted by experience, ever draw any inference concerning real existence and matter of fact.

Hume, then, would assert that the only statement which can be taken at face value is something like 'I saw the paper burning at time T1 and at place P1' or that 'the paper was observed burning, etc.' or that 'the rock was observed to be purple at time T1, etc.' Any mention of 'flammability' or a 'disposition to burn' would be understood, at best, to be linguistic shorthand, or, at worst, to be a false, or meaningless, or nonsensical, or senseless utterance - to which category of utterance Hume would assign all metaphysical discourse.