Dispositions and Tropes

CHAPTER 10. DISPOSITIONAL TROPE ONTOLOGY 136 no ‘legitimate’ property in which they are discernible the Leibniz principle of the identity of indiscernibles says that there actually is just one thing.

Formalized it runs as follows: ∀x₁∀x₂

∀F F(x₁)⇔F(x₂)

⇒x₁ =x₂ . Can one agree with the conclusion that we actually have just one elec-tron in our system? No, we cannot. We know that we started off with two electrons and we know that the compound system has, for instance, twice the charge of an electron. We cannot be talking about just one electron.

On the other hand it seems to be excluded that we have two electrons as well. So we have reached a certain stalemate. Which alternative we choose we get into trouble.

CHAPTER 10. DISPOSITIONAL TROPE ONTOLOGY 137 substratum theory consists in the fact that once the old nuclear bundles are broken up and rearranged in one new nuclear bundle the question about the identification of the old substances in the new substance disappears.

In a substratum theory, however, this question cannot be suppressed and leads to the described problems with the individuality of identical particles.

If the substratum is to fulfil its role as an individuating basis of an object it would be strange if it could pop in and out of existence as is required for a satisfactory account of ‘identical particles’ as ‘parts’ of many-particle systems.

Let me say the same again with other words. The investigation of quantum physics tells us that quantum objects can quickly win and loose their status of independent concrete particulars, short of being substances.

Let two electrons interact and form one compound 2-electron system and you loose two substances, the electrons, but you win a new substance, namely the electron system. Perform a position measurement on this 2-electron system and, in the case of a detection of an 2-electron, the 2-2-electron system looses its status of a substance while the measured electron becomes a new substance and with it a second electron becomes a substance as well.

Note that it is not legitimate to say or to think that one of the original electrons has been measured and regained its status of a substance.

Now consider the classical substratum theory of substances and the trope bundle theory of substances, i. e. a theory where substances are analysed as bundles of tropes. The question is which ontological conception can explain the quick popping into and out of existence of substances most naturally. I believe that the trope bundle theory of substances rates far better than a substratum theory in this respect. Since substances are construed as bundles it is easily conceivable that these bundles can quickly be rearranged. Bundles are broken up and loose their status of substances.

A different collection of tropes is bundled together and there we have a new substance. From the point of view of trope ontology these restructurings are do not appear mysterious. This is only the case when substances are taken as fundamental entities which cannot be analysed any further.

CHAPTER 10. DISPOSITIONAL TROPE ONTOLOGY 138 Dispositions

Since Carnap’sLogical Construction of the Worldthe definition of disposi-tional predicates has been a point of philosophical debate and the discussion is still going on. The starting point for the debate is the problem whether dispositions can be analysed within the language of extensional logic, first and second order logic. If dispositional predicates like ‘water-soluble’ are defined as material implications of the form “x is water-soluble ≡ if x is put into water, it will dissolve” we get a problem. According to this def-inition all objects have this disposition as long as it is not tested since an implication is true when its antecedens is wrong. Later it turned out that definitions in terms of possible-world semantics a la D. Lewis are very succesful.

Besides non-probabilistic dispositions like ‘water-soluble’ there are prob-abilistic dispositions to get a certain desease with a certain probability when living uder certain conditions. One question about probabilistic dis-positions is whether the probability is due to our ignorance of all details, so that it is inappropriate to assign such a probabilistic disposition as a real property to an object. Opposed to these merely epistemic probabili-ties are objective or real probabiliprobabili-ties which can actually been ascribed as properties of objects.

Quantum physics is a case where we are dealing with objective prop-erties. An ignorance interpretation of quantum probabilities can be ex-cluded.⁴ So-called non-objectification theorems show that the assumption of a merely epistemic understanding of quantum probabilities leads to con-clusions which are in contrast to very well-established experimental results.

When in the following I use ‘prob’ as an abbreviation for ‘probability’ I am refering to these quantum probabilities which I assume to be attributable to single quantum objects. I thus understand quantum probabilities as objective probabilistic dispositions of quantum objects.

4This is only true as long as we stick to the standard formalism of QM. In Bohm’s alternative version of QM the situation is fundamentally different.

CHAPTER 10. DISPOSITIONAL TROPE ONTOLOGY 139