A Brief Introduction to Gradualism

by Axel Arturo Barceló Aspeitia

This is the second post I am writing on the many ways philosophers have come up in trying to reconcile opposing views. The first one was on dialetheism – accepting that some features of reality are actually contradictory – and you can read it here. This time I will address gradualism – the claim that some properties come in degrees. Future posts will address both pluralism and relativism.

Gradualism

A first option to reconcile two positions without accepting a contradiction is to postulate a gradation between P and non-P. The key point of these proposals is to argue that the property in question P is not actually a property that an object of the proper kind either has or has not, but rather a gradual property that can only be had to some degree or other. This means that, between things that are P and those that are not-P, there are intermediate cases that are neither P nor not-P. For example, there are those who have argued that the reason why we have conflicting evidence regarding, for example, whether the domestic cat is a natural kind (since it is a biological species of animal) or artificial (since it was artificially created by humans according to their own preferences) is because artificiality is a matter of degree and between the artificial and the non-artificial there are several intermediate cases, including domestic cats, seedless grains, iron, etc. (Dennet 1990, Kroes 2012, Elder 2007, Sperber 2007, Grandy 2007, Asse 2015, p.39). The general strategy is to say that the cases for which we have contradictory evidence are less-P than those in which the overall evidence points towards P, and more-P than those in which our overall evidence points towards not-P. In the aforementioned example, we have completely artificial cases like railroads and paper flowers (for which we have no reason to think they are not artificial) and at the other extreme, we have completely natural objects like the sun or a tree in the middle of the forest (for which we have no reason to think they are artificial); objects in the middle, such as domestic cats, are more artificial than the sun, but not as artificial as railroads.

Consider now the well-known paradox of inevitable wrongdoing, linked to traffic dilemmas in meta-ethics. These are cases where agents face choices where whatever the agent does she will be doing something wrong. We have conflicting evidence regarding the moral assessment of these actions (and omissions): on the one hand, we have good reasons to conceptualise such actions as cases where one “must do wrong in order to do right.” (Thompson 1987) However, people acting in such circumstances “emerge feeling torn, guilty, and tainted and, furthermore, it seems that these are appropriate reactions. We would wonder about the person who could perform a tragic act and come out of it unscathed in these ways.” (Kent 2008, 6) Thus, we have evidence for the person having done right and also for her having done wrong. Gradualism solutions have attempted to solve the paradox by arguing that “wrong” and “right” are too coarse categories to morally assess human action. The very ideas of mitigating and aggravating circumstances in modern law make sense precisely because we understand that some actions are more wrong than others.

In logic, gradualism gave rise to fuzzy logic, i.e., to the development of logical systems explicitly built to better model the logical and semantic behaviour of gradual properties. In these logics, instead of the membership relation of set theory represeneting whether an objects belongs to a predicate’s extension, there is a membership function assigning values within the [0, 1] interval of real numbers to objects and sets representing the preciate’s extension. Thus, we can account for the behaviour of propositions like “John is bald” where John is a borderline case of baldness. Given how widespread vagueness and similar phenomena are, it is not suprirsing that fuzzy logic has found heaps of applications, mostly outside philosophy.

Linguistic Evidence for Gradualism

A good solution to a paradox or conflicting evidence should not only aim at reconciling the conflicting evidence, but also explain why they seemed to be in conflict in the first place. In other words, it is not enough to show that one can incorporate both the evidence for A being P and the evidence for A not being P into a unified account, one should also explain why that evidence seemed irreconciliable in the first place. In this regards, gradualism needs to explain why, if P actually corresponds to a gradual property, we have intuitions that it is something that objects like A simply have or have not. In other words, the main challenge to gradualism is to avoid the  charge of ad-hocery.

One recent, and common way of defending gradualism from this sort of charge has been to appeal to linguistic data. For example, one can point out that, in natural conversational contexts, we usually use intensifier morphemes and adverbs when morally evaluating actions. Thus, we speak of some actions being “very bad” or “worse” than others. Given that the standard semantic account of this constructions presupposes a gradual structure (Kennedy & McNally 2005), this serves as evidence that our everyday moral assessments are gradual. In other words, unless we want to embrace a revisionism regarding moral assessment, we must prefer a theory of morality that respects its gradual nature.

This strategy consists in complementing the metaphysical claim that predicate P corresponds to a gradual property with a couple of semantic claims: first, that the extension of the predicate P (when ocurring without a modifier like “very”, “more”, etc.) is fixed by the set of objects that have the corresponding gradual property at least to a certain degree (Kennedy & McNally 2005). For example, we know that warmth is a gradual property and, therefore, that one location can be warmer than another. However, we still use the adjective “warm” to describe the weather, as if locations were just either warm or not. Our language allows for this dual way of speaking – gradual and non-gradual – thanks to what linguists call a null operator, so that objects or situations count as warm – that is, belogn within the extension of predicate “warm” – only if they are warm to a degree that surprasses some given threshold. This threshold, in turn, can be semantically fixed as part of the lexical meaning of the predicate – in what is commonly called an “invariantist” position – or contextually – in what is known as a “contextualism”. Thus, even though most gradualisms are contextualisms and vice versa, it is important to distinguish between:

1. Gradualism: The metaphysical claim that the property associated to predicate P is gradual

2. Degree semantics: The semantic claim that the extension of predicate P is fixed by a threshold degree of the associated property

3. Contextualism: The claim that the threshold degree that fixes the extension of predicate P is contextually determined

Is dialetheism a kind of gradualism?

At this stage, it is important to take a second to compare the first two positions we have introduced so far. Prima facie, they seem substantially different; however, the similarities run deep actually. As a matter of fact, dialetheism can be easily modelled as a simple sort of gradualism, where true contradictions exist in an intermediate space between full-fledged truth and full-fledged falsity. In order to see this, it is helpful to look a little closer to the usual paraconsistent logics used in dialetheism, these multiple-valued logics effectively make a distinction between two kinds of truths: normal, classical truths for which if something is true, its negation cannot be, and paraconsistent truths for which even if something is true, its negation may also be true as well. However, each sort of truth is not independent of the other, which becomes clearer once we describe the logic in algebraic terms (Dunn 2000) so that there is an ordering relation between them. In this representation, paraconsistent truth is literally an intermediate truth value between classical truth and classical falsity. This is starting to look a lot like a truth gradualism. It seems like dialetheism takes “true” to be a predicate associated to a gradual property – truth – that can be had completely (in the case of classically true propositions), to no degree (in the case of false propositions) and to some degree, but not completely (in the case of paraconsistently true propositions). Now, the extension of the “true” predicated is fixed on this graduation by all the propositions that have true to at least some degree (in other words, it is an existential predicate, in linguistic’s terminology), and not contextually.

[in the case of analetheism, all that changes is that the condition is that a proposition needs to be true to the highest degree in order to belong in the extension of the “true” predicate].