Inheritance

Philosophers often speak somewhat loosely of one thing ‘inheriting’ some feature or features from another. We might say, for example, that the truth of a conjunction is inherited from the truth of its conjuncts, or that wholes inherit features from their parts. Though there has been plenty of research into what is happening in these specific examples, the notion of inheritance itself has received very little attention. We think this is both surprising and problematic. It is surprising because implicit and explicit appeals to inheritance turn out to be remarkably common once you start looking for them. It is problematic because without a good understanding of the nature of these sorts of appeals, large parts of philosophical argumentation cannot be properly evaluated.

Our project investigates these appeals to inheritance, which we call inheritance claims. We argue that when they are to be taken seriously, it is because they are elliptical for a distinctive kind of argument which we call an inheritance argument. When these arguments are successful, we claim that that success must be due in part to the role of an underlying worldly inheritance mechanism. Our project centers around these three notions and proceeds via the investigation of three distinct but overlapping research questions.

RQ1: What are inheritance claims and how do they function?

Inheritance claims are perhaps most common in metaphysics. They include (but are in no way limited to) appeals to: (1) reality inheritance: contemporary metaphysics is awash with claims to the effect that some things exist in virtue of some other (more fundamental) things, and that the former, derivative things ‘inherit’ their reality (and/or existence) from those more fundamental things; (2) feature inheritance: talk of some things inheriting their features from the features of other things (including talk of wholes inheriting their features from the features of their mereological parts; talk of wholes inheriting their features from the features of their non-mereological parts or constituents; and talk of worldly relations (such as grounding) inheriting features from those of explanation); (3) Structure inheritance: realist metaphysicians often think of language as ‘carving nature at the joints’; logical and structural features of our language(s) are ‘inherited’ from the ontological form and structure of reality. Such claims are also found outside of metaphysics. For example, in epistemology; (4) justification inheritance: talk of non-foundational beliefs inheriting their justification from other (foundational) beliefs; (5) truth inheritance: talk of a conclusion inheriting its truth from the truth of the premises that support it.

Inheritance claims are usually made with the aim of doing one or both of the following things:

(a) Stating that because b inherits (some of) its features from a, if Fa then Fb
 (b) Stating that we are justified in believing either something about the nature of b on the basis of what we believe about a (and the relationship between a and b with respect to the relevant sort of inheritance) or that we are justified in believing something about a on the basis of what we believe about b (and the relationship between a and b with respect to the relevant sort of inheritance).

We can therefore distinguish a notion of metaphysical inheritance, which we might think of as ‘inheritance proper’, from epistemic inheritance which is the notion that has to do with what we believe on the basis of an appeal to metaphysical inheritance.

Simple cases of epistemic inheritance run parallel to cases of metaphysical inheritance because we are justified in believing what is established on the basis of sound arguments. However, other cases of epistemic inheritance seemingly run in the opposite direction to that of metaphysical inheritance. For example, it might be that we believe that the world has a certain structure because we believe that our language has a certain structure, and that the structure of our language is inherited from that of the world. Appeals to inheritance often feel somewhat slippery and unclear. We hypothesise that part of the reason for that is a failure properly to distinguish between metaphysical and epistemic appeals to inheritance, especially given that epistemic inheritance claims can run in either direction. Epistemic inheritance is however derivative of metaphysical inheritance, and so metaphysical inheritance is the primary notion.

RQ2: What are inheritance arguments?
RQ3: How are inheritance arguments different from analogy arguments?

Inheritance arguments are rarely made explicit in the literature, but they are in many ways similar to another, better understood, type of argument: the argument from analogy. Arguments from analogy typically move from a claim that a and b resemble one another in some respect(s) to a claim that they resemble one another in a distinct respect. That inheritance arguments are easily confused with such arguments should not be surprising. When regarded simply as forms of reasoning, analogy and inheritance do similar (in fact analogous) work. To see this, note that an inheritance claim – e.g., the claim that grounding inherits its features from explanation – can always be read as a claim about resemblance: because grounding inherits (some of) its features from explanation, grounding resembles explanation. Therefore, if explanation is F, we can expect grounding to be F. However, inheritance claims seem to be stronger than mere claims about resemblance and inheritance arguments stronger than arguments from analogy in the sense that where inheritance entails resemblance, the converse is not true. It could even turn out that successful arguments from analogy presuppose some sort of inheritance mechanism. To see this, note that we can put pressure on the validity of arguments from analogy by noting that most things resemble most other things in at least some respects but that we are not generally on that basis justified in making the relevant kinds of inferences. A stronger or ‘deeper’ metaphysical connection than resemblance is plausibly required to support the conclusions of apparent arguments from analogy. Inheritance and in particular the inheritance mechanisms could then be taken to explain the resemblance between a and b: b resembles a precisely because b inherits some of its features from a. Our next task then is to give some kind of metaphysical account of the inheritance from a to b.

RQ4: What is (are) the mechanism(s) for metaphysical inheritance?
RQ5: What are the conditions under which inheritance arguments are successful?

If epistemic inheritance is derivative of metaphysical inheritance as we have supposed, then key to assessing inheritance claims of all kinds will be an understanding of the mechanism or mechanisms for metaphysical inheritance. When b inherits some feature or features from a, there must be some kind of relation R between a and b such that inheritance can occur.

The possible candidates for R we intend to investigate (while leaving it open that inheritance (and inheritance arguments) might pick out a plurality of different Rs) include:

a. Numerical identity
b. (Partial) qualitative identity
c. Transfer of part
d. Grounding
e. Constitution
f. (Mereological) composition

We aim to spell out the nature of these potential candidates for R, assess how plausible it is that they can play the relevant role in inheritance arguments, and investigate precisely how it is they play that role (if they do). Does R facilitate or enable inheritance? Does R or its instantiation back or ground inheritance? Does inheritance track instantiations of R only in certain circumstances?

How we view the nature of inheritance mechanisms will make a big difference to the strength, plausibility, and validity of inheritance arguments. If, for example, inheritance requires identity or grounding between a and b yet we have good independent reason to suppose that there is no such relation between them, we should consider the relevant inheritance argument invalid, and the corresponding inheritance claims false. There might also be interesting consequences to thinking that some particular inheritance mechanism holds in a particular case. For example, suppose again that the mechanism for inheritance must either be identity or grounding, and consider (4) above. Clearly, not all beliefs are identical to one another, and so we might suppose that the operative mechanism in cases of justification inheritance is grounding. If this is correct, then we might be pushed towards adopting a non-factive account of grounding such that beliefs (rather than merely true propositions) can act as the relata of the grounding relation. How we view the relevant mechanism may also have other sorts of consequences. According to some of those in favor of ‘reality-inheritance’ (such as in (1) for example), if reality is inherited, it must have a ‘source’, i.e., there must be some things whose existence is ‘ungrounded’ or fundamental. If the relevant mechanism is not grounding, it is unclear if this is a consequence we must accept.