Calculus and counterpossibles in science

McLoone, Brian

doi:10.1007/s11229-020-02855-1

Cited by 10 publications

(10 citation statements)

References 25 publications

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“…But this doesn't seem only nomologically impossible; this seems "flat-out" impossible. The sorts of things that organisms are could not be the sorts of things that there could possibly be infinitesimal fractions of, following McLoone (2020). And as I have argued in previous work (Tan, 2019), whether one considers these kinds of possibility-claims de re or de dicto, they still look to be flat-out impossible, i.e., metaphysically impossible.…”

Section: The Baseline Problem: the Fallibility Of Hypothetical Modelingmentioning

confidence: 93%

Two epistemological challenges regarding hypothetical modeling

Tan

2022

Synthese

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Sometimes, scientific models are either intended to or plausibly interpreted as representing nonactual but possible targets. Call this "hypothetical modeling". This paper raises two epistemological challenges concerning hypothetical modeling. To begin with, I observe that given common philosophical assumptions about the scope of objective possibility, hypothetical models are fallible with respect to what is objectively possible. There is thus a need to distinguish between accurate and inaccurate hypothetical modeling. The first epistemological challenge is that no account for the epistemology of hypothetical models seems to cohere with the most characteristic function of scientific modeling in general, i.e., surrogative representation. The second epistemological challenge is a version of "reliability challenges" familiar from other areas. There is a challenge to explain how hypothetical models could be a reliable guide to what is possible, given that they are not and cannot be compared against their nonactual targets and updated accordingly. I close with some brief remarks on possible solutions to these challenges.

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Section: The Baseline Problem: the Fallibility Of Hypothetical Modelingmentioning

confidence: 93%

Two epistemological challenges regarding hypothetical modeling

Tan

2022

Synthese

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“…For example, the Lotke-Volterra equations in population ecology tells us how predators and prey would interact given certain assumptions -like that populations are continuous -but it's metaphysically impossible that a population of rabbits, say, is continuous. You can't, in the relevant sense, have a population made up of 482.843 rabbits (Jenkins and Nolan, 2012;McLoone, 2021).…”

Section: Triviality Of Counterpossiblesmentioning

confidence: 99%

Moral principle explanations of supervenience

Bhogal

2022

Philos Stud

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Here's a very common challenge for defenders of non-naturalism about morality. The moral facts supervene upon the natural facts -there cannot be a change moral facts without a change in the natural facts. More specifically, a certain action with certain moral properties couldn't have had some other moral properties without having different natural properties (including, perhaps extrinsic or relational natural properties). And similarly for other bearers of moral properties, not just actions.Here's a common formalization of this idea:where M is the set of moral properties and N is the set of natural properties. This principle says that: For every moral property F, if something has F then it has a natural property G such that it's metaphysically necessary that anything that is G is F.Perhaps some nuances need to be added to this formulation (see, for example, Atiq (2020)), but those don't matter for our purposes.Explaining supervenience is a central challenge for the non-naturalist. The supervenience principle we just wrote down describes a very specific type of moral choreography -the moral and the natural properties dance together in a highly regimented way. But, the non-naturalist says, moral properties are sui generis. They are completely distinct from the natural properties. So, on the face of it, it's not easy to see what explains this choreography. 1 But there is a non-naturalist strategy which purports to explain supervenience rather simply. So simply, in fact, that Fogal and Risberg (2020, p. 177) say that, in light of it 'the attention garnered by Strong Supervenience (and its ilk) in recent decades looks rather misplaced'. They call it the Divide and Conquer strategy, and I will follow them in that terminology.* Thanks to Daniel Fogal, Olle Risberg and two anonymous reviewers.1 Perhaps explaining supervenience is also a challenge for other views of the metaphysics of morality, but I'll focus on non-naturalism.The divide and conquer strategy was most influentially defended by Scanlon (2014). 2 The strategy starts with claiming that particular moral facts are explained by general moral principles, along with matters of natural fact. The way that Fogal and Risberg (p. 175) put it is that moral explanations have this structure:Explanans: particular natural fact(s) (e.g. a is a lie).Principle: general explanatory moral principle (e.g. lying is wrong).Explanandum: particular moral fact (e.g. a is wrong).Given that all particular moral facts are explained in this way there is a quick argument to supervenience. Moral facts are either general explanatory moral principles or particular moral facts. If we assume, as seems reasonable to most, that the general moral principles are necessary, then, trivially, they can't change without the natural facts changing, because they can't change at all. 3 Particular moral facts, on the other hand, are determined by the moral principles and the natural facts, as per the structure of moral explanations just described. And since the moral principles can't change, this implie...

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Section: Introductionmentioning

confidence: 99%

“…Recently, some have argued that there are non-vacuous counterpossibles in science (Jenkins & Nolan, 2012 ; Jenny, 2018 ; McLoone, 2021 ; Tan, 2019 ). One example comes from the use of differential equations to model the dynamics of a population of objects that are discrete as a matter of metaphysical necessity (McLoone, 2021 ; Tan, 2019 ). 1 For instance, the logistic equation is a differential equation from ecology that models the dynamics of population size ( N ) when a habitat has a “carrying capacity” ( K ), that is, a limit on how many individuals it can support.…”

Section: Introductionmentioning

confidence: 99%

“…That means one of the assumptions of the model is impossible. But take the following two counterpossibles, from McLoone ( 2021 , p. 12161): If some population of rabbits satisfied the assumptions of the logistic equation, then the size of the population ( N ) would eventually be equal to the carrying capacity ( K ). If some population of rabbits satisfied the assumptions of the logistic equation, then the population would eventually go extinct.…”

Section: Introductionmentioning

confidence: 99%

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Counterpossibles in science: an experimental study

2023

Self Cite

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A counterpossible is a counterfactual whose antecedent is impossible. The vacuity thesis says all counterpossibles are true solely because their antecedents are impossible. Recently, some have rejected the vacuity thesis by citing purported non-vacuous counterpossibles in science. One limitation of this work, however, is that it is not grounded in experimental data. Do scientists actually reason non-vacuously about counterpossibles? If so, what is their basis for doing so? We presented biologists ( N = 86) with two counterfactual formulations of a well-known model in biology, the antecedents of which contain what many philosophers would characterize as a metaphysical impossibility. Participants consistently judged one counterfactual to be true, the other to be false, and they explained that they formed these judgments based on what they perceived to be the mathematical relationship between the antecedent and consequent. Moreover, we found no relationship between participants’ judgments about the (im)possibility of the antecedent and whether they judged a counterfactual to be true or false. These are the first experimental results on counterpossibles in science with which we are familiar. We present a modal semantics that can capture these judgments, and we deal with a host of potential objections that a defender of the vacuity thesis might make.

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Calculus and counterpossibles in science

Cited by 10 publications

References 25 publications

Two epistemological challenges regarding hypothetical modeling

Two epistemological challenges regarding hypothetical modeling

Moral principle explanations of supervenience

Counterpossibles in science: an experimental study

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