Are Standard Lawlike Propositions Metaphysically Necessary? Hildebrand vs. Groarke

Studia Neoaristotelica 11 (2014) / 1 89Articles

Are Standard Lawlike Propositions Metaphysically Necessary?

Hildebrand vs. GroarkeVlastimil Vohánka

1. IntroductionIs it metaphysically necessary that salt dissolves in water with low con-

centration of electrolytes? Or that water is structured as H2O? More gener-ally, are at least some standard natural laws and truths about natural kinds metaphysically necessary?

I will call standard natural laws and standard truths about natural kinds by the umbrella term ‘standard lawlike propositions’. Their modal status is worth inquiring into. For instance, we only know the truth of standard lawlike propositions om observation. So their metaphysical necessity would impose more limits on what God (if any) could do than would appear om our armchairs. These limits on God’s part might be relevant to the problem of evil or the possibility of miracles. Moreover, some philosophers think that science has discovered some standard lawlike propositions to be true not only de facto but with metaphysical necessity. To them, water not only is, but must be, H2O. Are they right? This metaphysical question is at least as interesting as almost any other.

In this study, I juxtapose two ingenious yet mutually isolated authors: Dietrich von Hildebrand (1889–1977), an infl uential German phenomenolo-gist, and Louis Finbarr Groarke (*1953), a renowned British Aristotelian (based in Canada). Groarke deems at least some standard lawlike proposi-tions metaphysically necessary. Hildebrand disagrees. I extract and under-mine the reasons of both authors. At the bottom, Hildebrand claims that no standard lawlike proposition is metaphysically necessary, since none is in principle knowable solely by considering essences. But he gives no good

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Vlastimil VohánkaAre Standard Lawlike Propositions Metaphysically Necessary?

reason for the latter claim or for the implicit claim that all metaphysically necessary propositions are thus knowable. I will argue that at least one of these two claims is quite plausibly false, for the explanation of positive in-stances of at least some standard lawlike propositions by the metaphysical necessity of these propositions is quite plausibly true. On the other hand, Groarke claims at the bottom that some standard lawlike propositions are metaphysically necessary, since their positive instances exempli natural kinds that make all their members necessarily similar in relevant ways. But he does not say what relevant similarity is or how to tell which properties are included in it. I will argue against Groarke’s suggestion that an appeal to relevant similarity is presupposed in all acceptable inductive arguments om samples.

Why do I choose Hildebrand and Groarke? Groarke is a prominent ad-vocate amongst contemporary Aristotelians of the metaphysical necessity of standard lawlike propositions.¹ Hildebrand is a main opponent of this amongst realist phenomenologists. At the same time, realist phenomenolo-gists and contemporary Aristotelians share an interest in essences and es-sentially grounded states of aff airs. Both camps also use coextensive, if not identical, concepts of necessity. Both explain necessities in terms of essences. And both think we know necessities since we know essences. Hence the two camps and their representatives make for good debaters. That’s for the motivation of my paper.

Now some terminology. Hildebrand and Groarke speak of natural laws and of truths about natural kinds but do not say what natural laws and such truths are in general. I shall not try to defi ne them either. I call both types lawlike propositions. These I take to be propositions that are at least universal, true, and supporting counterfactuals. So they truly predicate certain features of all things of the given sort, and entail or make probable counterfactuals

¹ David S. Oderberg is a chief Aristotelian advocate of metaphysical necessity of natural laws. He thinks all genuine laws of natures are laws of natures (essences). But he remains non-committal about the question whether standard examples of natural laws are genuine. See his Real Essentialism (London and New York: Routledge, 2007), 97, 143–151. E. J. Lowe seems to deny metaphysical necessity to all standard lawlike propositions, although he ascribes it to some lawlike propositions bordering on analyticity: e.g., electrons have negative charge. See his Four-Category Ontology (Oxford: Oxford University Press, 2006), 141–173.



to the eff ect that things of that sort would display those features. For in-stance, the law that copper conducts electricity entails or makes probable the counterfactual that if there was a lump of copper in my pocket, there would an electrical conductor in it.

Although the list of standard lawlike truths would diff er om person to person, these natural laws should be counted among the core examples: copper conducts electricity; salt dissolves in water with low concentration of electrolytes; heat expands metals; closed bodies displacing liquid of a greater weight than their own fl oat on it; electricity is directly proportional to charge and inversely proportional to squared distance; gravity is directly proportional to mass and inversely proportional to squared distance. Among standard lawlike propositions are, besides the laws, also some truths about particular natural kinds, even if these truths are not laws in the ordinary scientifi c use of the term. Core examples again: water has the molecular structure H2O; helium is lighter than air; (developed) humans have a heart and a brain; whales and dolphins are mammals; lions are not white; emeralds are green.

I will assume that metaphysical necessity is coextensive with truth in virtue of essences. That is, I will take saying that a proposition p is metaphysi-cally necessary as logically equivalent with saying that p is true in virtue of the essence or essences of something. Examining this assumption is beyond the scope of my paper. The assumption is nevertheless common amongst Aristotelians, including Groarke, and also embraced implicitly by Hildebrand.²

Metaphysically necessary are, e.g., strictly logical propositions (truths in virtue of logical words like ‘any’, ‘some’, ‘and’, ‘not’, etc.), analytic proposi-tions (truths in virtue of logical words and defi nitions of non-logical words), truths of set theory and mathematics, as well as truths of metaphysics (such as that anything that begins to exist has an extrinsic cause). Not all meta-physical necessities are easy to fi nd out. Nor do I wish to imply that all metaphysical necessities are analytic or strictly logical.

Saying of a lawlike proposition that it is metaphysically necessary should be understood in this paper this way: it’s metaphysically necessary that all

² See below the introductory sections to parts 2 and 3 of this paper.



things of the given sort have the features the proposition ascribes to them. E.g., the law that copper conducts electricity is metaphysically necessary if it is metaphysically necessary that all copper conducts electricity.

Finally, I take an essence of a thing to be a feature or determination of what the thing is or would be if it existed (as opposed to what properties it has or would have). This fi ts once again with Hildebrand’s and Groarke’s usage.³ That’s for terminology.

I wil turn fi rst to Hildebrand and his reasons for the conclusion named here as

C⒈ No standard lawlike proposition is strictly necessary.

On Hildebrand’s account of strict necessity, (C1) implies

C⒉ No standard lawlike proposition is metaphysically necessary.

A er Hildebrand, I will turn to Groarke and his reasons for the contradic-tory conclusion

C⒊ Some standard lawlike proposition is metaphysically necessary.

2. HildebrandHildebrand’s own position implies that standard lawlike propositions are

not metaphysically necessary. He does not, however, use the word ‘metaphys-ically necessary.’ Instead, he talks interchangeably about “strict necessity” (or “intrinsic necessity”, “strict and intrinsic necessity”, “stringent necessity”, “absolute necessity”, “absolute and essential necessity”, and sometimes simply about “necessity”). He explains that strict necessity is “rooted in the ideal sphere of essences,”⁴ meaning that strict necessity is rooted in essences re-gardless of whether they are instantiated. I take Hildebrand’s words to imply that strict necessity is coextensive with truth in virtue of essences. Making the assumption that truth in virtue of essences is coextensive with meta-physical necessity, strict necessity is in turn coextensive with metaphysical

³ See Hildebrand, What is Philosophy? (New York: Routledge, 1991), 65–66, 98, 133–134, 114, 119, 217; Louis Groarke, An Aristotelian Account of Induction (Montreal & Kingston, London, Ithaca: McGill-Queen’s University Press, 2009), 74, 215, 404, 425–427.

⁴ Ibid., 65.

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necessity. So on that assumption, Hildebrand’s attack on the strict necessity of standard lawlike propositions is in eff ect an attack on their metaphysical necessity.

Hildebrand even gives three indicia that his concept of strict necessity is identical, not merely coextensive, with that of metaphysical necessity. First, Hildebrand’s examples of strictly necessary propositions and states are examples by which one could introduce metaphysical necessity: being and non-being exclude each other; seven plus fi ve equal twelve; there’s no willing without thinking; colour requires extension; the colour orange lies between the colours red and yellow; anything with a moral value is a person.⁵ Second, Hildebrand contrasts his concept of strict necessity with concepts with which metaphysical necessity has been contrasted: a strictly necessary proposition need not be true in virtue of its logical concepts, nor in virtue of its logical concepts and defi nitions of its non-logical concepts.⁶ Third, as with metaphysical necessity, Hildebrand says that some strictly necessary truths are neither trivial nor easy to fi nd out.⁷ With all the three indications, Hildebrand’s idea of strict necessity seems to be just that of metaphysical necessity.

Hildebrand considers standard laws of nature and lawlike propositions about natural kinds. Here’s how he suggests that the former are never strictly necessary.

[Strictly] necessary states of facts are […] distinguished om the facts treated in physics and chemistry, even though the latter possess a kind of necessity. The fact, “Heat causes a body to expand,” is not a mere-ly individual, concrete fact, but a general one. With respect to its “members,” moreover, it diff ers profoundly om such a fact, as “Caesar crossed the Rubicon.” For there is here a quality of necessity which goes beyond a factual togetherness. The causal link between heating and expansion is not merely a factual bond but it has, moreover, its

⁵ Ibid., 66, 68, 75, 79, 138.⁶ Ibid., 66–67, 77–78, 80, 82–83.⁷ Ibid., 137: “The fact that love is a value response, essentially implying an intentio unionis and

intentio benevolentiae, and the fact that there is a diff erence between the imago Dei and the similitudo Dei are all apriori facts and typical topics of philosophy. They have not, however, the obvious character of ʻTwo plus two equals fourʼ or ̒ Moral values presuppose a person.̓ ” On Hildebrand’s construal, a priori facts are strictly necessary. See part 2.1.


Vlastimil VohánkaAre Standard Lawlike Propositions Metaphysically Necessary?general and necessary foundation in the nature of heat and expansion. Such necessity, however, is manifestly diff erent om that found in such facts such as “Moral values presuppose a person” or “Seven plus fi ve equal twelve.” First of all, its necessity is not absolute, and, second, it is not intelligibly grounded in the essence of the objects in question.

[…] We may, therefore, contrast these essential states of facts to the “laws of nature.”

This diff erence between the two is rooted in the realities themselves. It exists between the necessity of essence and the necessity of natural laws, which we may term the necessity of nature. The necessity of es-sence is absolute. It has its strict foundation in the essence of the thing as such. On the other hand, the necessity of nature is somehow relative to the contingency of the world. It is not impossible to assume that a body is not expanded even though it has been heated. To assume, however, that an impersonal being such as a stone could be endowed with a moral value, justice or humility, for example, is – though not [explicitly] contradictory – intrinsically impossible.⁸

As we read here, to Hildebrand standard laws of nature are never strictly necessary. In this sense they are, to him, only laws in quotation marks. (Perhaps he even thinks that no laws of nature whatsoever are strictly nec-essary.⁹) Standard laws of nature capture in this view a tight but not strictly necessary connection or unity. He calls this unity “genuine”, “morphic”, “objectively meaningful”, or simply “meaningful”. It contrasts, on the one hand, with strict unity, and on the other with an even looser unity, which, he says, is utterly “chaotic” or at least “accidental”.

On Hildebrand’s opinion, not only standard laws of nature but also standard lawlike propositions about natural kinds – kinds such as water, gold, coal, diamond, dolphin, lion, horse, cat, and species of plants and animals – describe tight yet not strictly necessary connections.¹⁰ Such pro-positions attribute, e.g., certain behaviour or colour, or a certain chemi-cal, physiological or anatomical structure to certain natural kinds. These

⁸ Ibid., 68–69; added italics. In fact, heat does not expand all kinds of bodies. Clay, for in-stance, contracts above a certain threshold, and water expands below another one. But we may view Hildebrand’s example about heat and expansion as implicitly qualifi ed against exceptions.

⁹ Josef Seifert, Hildebrand’s former student, told me in personal communication that Hildebrand nowhere takes a position on this more general point.

¹⁰ Hildebrand, What is Philosophy?, 97–110.



propositions “bear the character of contingencies, of ‘inventions.’ Though certainly beyond the power of man, they are, as it were, inventions of God”, writes Hildebrand.¹¹

All this documents that Hildebrand does deny that standard lawlike propositions, including our core examples, are strictly necessary. But why, exactly?

2.1 The argument from incomparable intelligibilityI read Hildebrand as follows: no standard lawlike propositions are strictly

necessary because none are incomparably intelligible. The latter claim means that none are knowable in principle solely by considering essences. (More on the notion of incomparable intelligibility below.) As he suggests in the last block quote above, standard lawlike propositions are “not intelligibly grounded in the essence of the objects in question”. Here is a further textual evidence for my reading.

The possibility of apriori knowledge depends upon the kind of object known. To gain an absolutely certain and essentially necessary insight, […w]e must have […] a very special kind of such-being and a givenness which is possible only with this type of such-being.¹²

That which irrevocably divides apriori om empirical knowledge is dependent upon the essentially profound diff erence in the objects themselves, the diff erence, namely, between objects which possess an intuitively revealed, intelligibly necessary unity, and others possessing either a contingent but meaningful unity or even a merely accidental such-being unity that is impoverished in meaning.¹³

A priori knowledge is, for Hildebrand, of strictly necessary propositions, om within, and absolutely certain.¹⁴ In other words, S knows that p a priori

¹¹ Ibid., 110.¹² Ibid., 99–100.¹³ Ibid., 128; added italics. Immediately a er this, Hildebrand suggests on the same page that

anything we can know only om without (i.e., a posteriori, om observation) about material (chemical, physiological, anatomical) structures is never strictly necessary: “When […] we deal with unities that can be known only ʻ om without,ʼ by a detour, when we deal with meaning ful but partly hidden and contingent constitutive unities, we can never grasp the grounding of laws of nature in the such-being unity.” (Added emphasis.)

¹⁴ Hildebrand, What is Philosophy?, 63–64.



just when p is strictly necessary, S knows that p om within (i.e., solely om essences), and S is absolutely certain that p. “Such-being” means essence. Hildebrand clearly does not want to say that all objects of a priori knowl-edge are known by intuition, without any argument, for he is happy with deductive a priori knowledge in mathematics. He rather matches “intelligibly necessary” unities against all “other” unities, which he takes to be “contin-gent” (and so either morphic or accidental). Thus he suggests that none but incomparably intelligible unities are strictly necessary. In other words, only unities that are both strictly necessary and incomparably intelligible are strictly necessary. It follows that only unities that are incomparably intel-ligible are strictly necessary. In other words, all strictly necessary unities are incomparably intelligible.

Hildebrand is less clear about his belief that no standard lawlike proposi-tions are incomparably intelligible. But ascribing it to him is reasonable. It explains, in coǌ unction with his claim of incomparable intelligibility of all strict necessities, his claim that no standard lawlike propositions are strictly necessary. The belief that no such truths are incomparably intelligible is then illustrated by the following quote om Hildebrand. He writes in it that incomparable intelligibility absents om propositions that ascribe directly observable features, such as colours, to natural species, such as lions, cats and horses.

The outer, appearance unity of a lion or of a horse […] is […] the result of several observations. […] It has not the intelligibility which would enable us to draw out of it states of facts. Here, too, we can proceed only by observation. [… For instance, i]t may be that in one case a color is typical for a species, for instance lions; and in another case, for instance cats, no specifi c color is typical. Although we fi nd that a certain color is typical for the species lion, it is always possible, in principle, that we discover a lion which is black or white. Only experience, in the sense of observation, can decide whether or not a lion of another color de facto exists. And even if experience should never show us an existing lion which has a white color, we should not be entitled to say that a white lion is strictly impossible. For this type of such-being unity is neither intelligible nor necessary.¹⁵

¹⁵ Ibid., 107–108.



So much for the textual evidence for Hildebrand’s case against the strict necessity of standard lawlike propositions. The case is formulated in the following syllogism.

⒈ Any strictly necessary proposition is incomparably intelligible. Premise⒉ No standard lawlike proposition is incomparably intelligible. PremiseC⒈ No standard lawlike proposition is strictly necessary. From ⑴ and ⑵

This is implicitly a case against the metaphysical necessity of standard law-like propositions, for,

⒊ Any metaphysically necessary proposition is truein virtue of essences.Premise

And as Hildebrand says,

⒋ Any proposition true in virtue of essences is strictly necessary.Premise

So,

⒌ Any metaphysically necessary proposition is strictly necessary. From ⑶ and ⑷

And so,

C⒉ No standard lawlike proposition is metaphysically necessary. From (C1) and ⑸

2.2 Incomparable intelligibilityTo assess the argument om incomparable intelligibility, we need to un-

derstand Hildebrand’s notion of that intelligibility. It is a sort of knowability: a possibility of knowing om within. What is that? Hildebrand explains:

[I]ncomparable intelligibility […] is closely linked with intrinsic neces-sity. When compared to any empirical facts, whether purely individual


Vlastimil VohánkaAre Standard Lawlike Propositions Metaphysically Necessary?or a general “law of nature,” an intrinsically necessary fact is seen to possess an incomparable intelligibility. We “understand” that these necessary facts are such as they are. We grasp not only that something is such, but also why it is. It is only with respect to these facts that we can speak of having an “insight” in the full sense.

Compared to this full intellectual penetration into a necessary state, the grasp of any individual fact, for instance, “Today the sun is shining” or “This table is brown,” is merely a blunt observation.

There is an analogous diff erence between the “insight” into a nec-essary fact and the grasp of a law of nature which is the result of an inductive inference. We can, to be sure, reach the knowledge of the fact that “heat expands bodies,” but a fact of this kind does not possess the luminous intelligibility proper to a truth such as “Moral values presuppose persons” which enables me to “understand” it to accomplish a real intelligere.

This intelligere, this understanding om within, is possible only when the knowledge of an essentially necessary fact is at stake. This “intelligibility,” which allows us to grasp the fact of its inner logos, necessarily presupposes the essential necessity of the fact; it is even deeply rooted in it. This does not imply, however, that every absolutely necessary fact is intelligible for us.

This feature of intelligibility is, of course, related to the question of knowability, and is not purely a characteristic of the state of facts alone, as is the necessity. Nevertheless, as we said above, this intelligibility is deeply rooted in the absolute and essential necessity.¹⁶

This suggests that for Hildebrand a proposition is known to be true om within just when it is known to be true solely om the essences or properties referred to in it. Here, knowledge that p solely om essences should be understood as knowledge that p solely by considering what the things or properties referred to in p are. E.g., although humans can know that triangles have interior angles equal to 180 degrees that way, they cannot know that way that copper conducts electricity. To know the latter, humans need observation of copper pieces as a reason, premise or evidence. To know the former, they may need observation of triangles as an opportunity to

¹⁶ Ibid., 69–70.



realize the fact or to form the concept of a triangle – but they do not need the observation as a reason, premise or evidence.¹⁷

In the preceding block quote, Hildebrand is also saying that a proposition may be incomparably intelligible even if we humans cannot know it om within. Elsewhere he gives the proposition that God exists as an example.¹⁸ So a proposition is incomparably intelligible just when it is possible that some agent knows it om within, regardless of whether the agent is human.

Hildebrand contrasts knowledge om within with knowledge “ om without”. This is knowledge “in a roundabout way, only in detour, only through ‘observations.’”¹⁹ In other words, knowledge om without is “em-pirical, […] rooted in experience as taken to signi blunt observation and induction.”²⁰ So nothing that can be known om within can only be known om observation.

Finally, knowledge om within comes “either by intuition or by de-duction.”²¹ That is, “either through the intuitive givenness of the necessary such-being unity or through a deductive inference om a directly under-stood necessary state of facts.”²² Hildebrand mentions some examples.

Some apriori propositions are seen intuitively as rooted in the essence; for example, the proposition “Being and not-being exclude each other” or “Moral values cannot be embodied by a non-personal being.” Others

¹⁷ In this context, Hildebrand considers the proposition that orange lies between red and yel-low. This is another truth humans can know om within. He adds: “To grasp the truth of the state of facts, the ʻsuch-being,ʼ the essence of the color orange must be given to me. The real, actual existence of the color orange, however, need not be given to me. The fact in question is grounded exclusively in the such-being of red, orange, and yellow. […] Here the perception has only the function of aff ording me the opportunity, by the unfolding of a certain such-being before my spiritual eye, to gain an insight into the truth of the state of facts. But the perception, insofar as it is an observation of an actually existing being, does not act as a proof for the knowledge of the existence of this essential state of facts. In the case of the necessity of natural laws, that is, of the merely though highly probable propositions of chemistry and physics, perception actually does take on this role of proving the truth and reality of states of facts.” Ibid., 75–76.

¹⁸ Ibid., 149.¹⁹ Ibid., 98–99.²⁰ Ibid., 96.²¹ Ibid., 214.²² Ibid., 129.


Vlastimil VohánkaAre Standard Lawlike Propositions Metaphysically Necessary?are deductive conclusions, like most of the geometric and arithmetical propositions.²³

To wrap up Hildebrand’s idea of an incomparably intelligible proposi-tion, a proposition p is incomparably intelligible if and only if it is (strictly) possible that some agent (human or not) knows that p solely om essences (intuitively or deductively).

2.3 Undermining the premisesWith the notion of incomparable intelligibility explicated, what of the

above premises ⑴ and ⑵ ? Well, they both may be true. But are they re-ally? Hildebrand fails to show they are. To undermine their coǌ unction, I propose an argument against it. Before doing so, I also ask a few questions about each. Although I do not show the premises to be false, I hope to spark a reasonable doubt about them.

Premise ⑴ amounts to this: for any strictly necessary proposition p, it is possible that some agent (human or not) knows that p solely om essences. However, Hildebrand nowhere argues for ⑴ . Why no defence? Presumably because he sees no need of it. But to many ⑴ is not obvious at all. Strict necessity does not imply incomparable intelligibility by defi nition. For what if all agents are with strict or metaphysical necessity deprived of knowing om within certain most advanced truths of, say, transfi nite arithmetic? How are we to tell whether the essences of all strictly or metaphysically possible agents allow at least some of them to know om within all truths of transfi nite arithmetic?

Somebody might reply there is a God knowing all transfi nite truths om within. Or that all transfi nite truths describe possible aspects of being, all knowable in principle due to a convertibility of being and truth, and all knowable om within if knowable at all. Yet Hildebrand provides no such reason for ⑴ .

But suppose ⑴ to be true. What then of premise ⑵ ? It amounts to this: for any standard lawlike proposition p, it is not possible that some agent (human or not) knows that p solely om essences. Again, Hildebrand does not show that ⑵ holds true. Yet ⑵ , too, is in need of an argument. Why

²³ Ibid., 74.



should there be no standard lawlike propositions knowable in principle solely om essences (i.e., by considering only what certain things or properties are) but for humans only om observation?

Hildebrand might reply this option is out of the question, because any-thing knowable in principle solely om essences is strictly necessary. But that reply would be circular, since assuming conclusion (C1). In other words, that reply would be unsatisfactory so long as (C1) is not regarded as true in the fi rst place.

Hildebrand might also reply that ⑵ holds since all incomparably intel-ligible propositions can be known by a human or other agent apart om observation, and no standard lawlike proposition can be thus known by any agent. But this would beg another question. If an agent can know something solely om essences (i.e., om within), he can know it apart om observa-tion (i.e., not om without). So why should it be impossible that some agent, human or not, knows a standard lawlike proposition solely om essences and hence apart om observation? Hildebrand does not say. In short, nothing in Hildebrand shows ⑴ to be true. And even supposing ⑴ , he does not help us to see that ⑵ is the case.

Worse, arguments against the coǌ unction of ⑴ and ⑵ are available. If (C2) – i.e., the claim that no standard lawlike proposition is metaphysically necessary – is quite plausibly false, then also ⑴ or ⑵ are quite plausibly false. For they jointly entail (C2) via (C1) – i.e., the claim that no stand-ard lawlike proposition is strictly necessary. There is in fact a tradition of arguments against (C2). In part 3 below, I mention those by Brian Ellis, Hillary Putnam, Saul Kripke and Louis Groarke. Although I say there why I fi nd these arguments unpersuasive, I still deem the denial of (C2) somewhat plausible. Why? Because the metaphysical necessity of standard lawlike propositions is, intuitively, quite a plausible explanation of their positive instances. This point was put well recently by Stanislav Sousedík, the founder of this journal.

[Suppose that] a number of empirical individuals a1, a2, a3, … an of natural kind F have in conditions p1, p2, p3, … pn descriptive property G. When this assumption is satisfi ed, and the number n is suffi cient, it can be inferred that each individual of kind F has in conditions p1, p2, p3, … pn property G, and the accident g denoted by it, necessarily.



This conclusion does not follow in formal logic, and a question arises what entitles us to make the inference. The entitlement is given to us by the fact that when a suffi cient number of individuals of a certain kind have under the same conditions property G, then it must have some reason. A suffi cient reason appears to be only natural kind or essence F of the surveyed individuals: the essence is such that under certain circumstances it is necessarily accompanied in the individual by property G. So when an individual has essence F, it necessarily has also property G and, in consequence, also the accident g denoted by it.

What number of individuals a1, a2, a3, … an is suffi cient for such an argument to be valid? In general, it must be a number adequate for making it possible to grasp that property G does not belong to the given individual contingently but that it is linked to kind or es-sence F necessarily. For that just one individual is enough in some cases (like when we learn om just one specimen of a certain mineral what crystalline structure all other specimens of the same kind necessarily have), but most times – if we are to rule out that property G belongs to individuals of the considered kind accidentally – observation of more or less large number of specimens is required.²⁴

This thought inspires arguments for the metaphysical necessity of at least some standard lawlike propositions. As an example, take the law that salt dissolves in water with low concentration of electrolytes.

²⁴ Stanislav Sousedík, Identitní teorie predikace [Identity Theory of Predication] (Prague: Oikoymenh, 2006), 62. “[Dejme tomu, že] nějaký počet empirických individuí a1, a2, a3, … an

přirozeného druhu F má za podmínek p1, p2, p3, … pn charakterizační vlastnost G. Je-li splněn tento předpoklad, lze – je-li počet n dostatečný – učinit závěr, že každé individuum přirozeného druhu F má za podmínek p1, p2, p3, … pn vlastnost G a jí označovaný akcident g nutně. Závěr z předpokladu neplyne formálně logicky, a vzniká otázka, co nás opravňuje jej vyvodit. Oprávnění nám k tomu dává skutečnost, že má-li dostatečný počet individuí určitého druhu za týchž podmínek vlastnost G, musí to mít určitý důvod. Dostatečným důvodem se však jeví pouze přirozený druh čili esence F zkoumaných individuí: to, že je tato esence taková, že ji za určitých podmínek v individuu nutně provází vlastnost G. Má-li tedy individuum esenci F, má nutně také vlastnost G, a v důsledku toho i jí označený akcident g. Jaký počet individuí a1, a2, a3, … an je dostatečný k tomu, aby argument platil? Všeobecně lze říci, že se musí jednat o počet přiměřený tomu, aby umožnil nahlédnout, že vlastnost G nenáleží individuu nahodile, nýbrž je spojena s druhem čili esencí F nutně. K tomu postačí v některých případech jediné individuum (jako když z jediného exempláře určitého nerostu poznáme, jakou mají všechny ostatní exempláře téhož druhu nutně krystalickou strukturu), většinou však, máme-li vyloučit, že vlastnost G náleží individuím uvažovaného druhu náhodně, je třeba pozorovat více méně velký počet exemplářů.”


Vlastimil VohánkaAre Standard Lawlike Propositions Metaphysically Necessary?⒍ In a large number of cases, salt dissolves in water

with low concentration of electrolytes.Premise

⒎ All true propositions have a true explanation.Premise

⒏ ⑹ has a true explanation.From ⑹ and ⑺

⒐ A true explanation of ⑹ is that in virtue of the essence of salt, salt dissolves in water with low concentrations of electrolytes.Abductively from ⑻

⒑ Any proposition true in virtue of essencesis metaphysically necessary.Premise

⒒ It is metaphysically necessary that salt dissolves in waterwith low concentrations of electrolytes.From ⑼ and ⑽

In what sense is step ⑼ abductive? In this: that salt dissolves in wa-ter with low concentrations of electrolytes in virtue of the essence of salt is a reasonable explanatory hypothesis for the fact that water does so in a large number of cases. Admittedly, the hypothesis mentioned in ⑼ is not a very informative, scientifi c statement. But it is sensible and compat-ible with the scientifi c explanations in chemistry and physics. It is also far om tautological. Otherwise philosophers who dislike appeals to essences would not dispute it.²⁵ As Sousedík wrote in correspondence, the hypothesis of ⑼ does not follow deductively. To him the hypothesis is a “theoretical suggestion, like when a wet spot appears on your ceiling, and the explana-tion occurs to you that the roof leaks.”²⁶ Sousedík also mentioned why the hypothesis is plausible: it has not been falsifi ed; the phenomena described

²⁵ Similarly Christopher F. J. Martin, Thomas Aquinas (Edinburgh: Edinburgh University Press, 1997), 189–190.

²⁶ Correspondence, October 29, 2008.



in ⑹ are probable on it; and there is no plausible rival hypothesis which would explain them.²⁷

In all fairness, I should doubt the last point of Sousedík. One rival hypothesis would be that salt dissolves with strong but not metaphysically necessitating propensity. Such propensity resembles what Hildebrand calls morphic unity.²⁸ Another rival option would be that salt dissolves by God’s design, not with metaphysical necessity.²⁹ Now some philosophers of science have argued that unlimited physical quantities are simpler and so, other things being equal, more probable than limited quantities. That is why the speed of light had o en been regarded as infi nite, until its high but fi nite magnitude was fi gured out. So perhaps also metaphysically necessitating propensities are somewhat simpler and more probable than merely strong propensities. Similarly also the appeal to the designer is perhaps less simpler, in terms of the number of postulated entities, than the appeal to essences. But these are highly contentious proposals. It is unclear that simplicity always increases probability. Typically, advocates of the sweeping claim that it always does only throw in a few examples om the history of science, like the one about the speed of light. It is also unclear how strongly simplicity contributes to probability.³⁰ Therefore I think the suggested rival options are not ruled out easily.

But even so, step ⑼ retains signifi cant plausibility. I do not claim it is more probable than not, as Sousedík does. Yet ⑼ still is one of several live, rival candidates for a true explanation of ⑹ . Given the pros and cons, agnosticism about ⑼ seems reasonable: the chances of ⑼ being true are about as high as the chances of it being false. Moreover, the premises of

²⁷ Correspondence, October 30, 2008.²⁸ Similarly Michael Tooley, “The Nature of Laws”, Canadian Journal of Philosophy 7 (1977):

667–698; Fred Dretske, “Laws of Nature”, Philosophy of Science 44 (1977): 248–268; and D. M. Armstrong, What is a Law of Nature? (Cambridge: Cambridge University Press, 1983).

²⁹ See Richard Swinburne, “Relations Between Universals, or Divine Laws?”, Australasian Journal of Philosophy 84 (2006): 179–189; Robin Collins, “God and the Laws of Nature”, Philo 12 (2009): 142–171.

³⁰ For a survey of discussions about simplicity as evidence for truth, see Alan Baker, “Simplicity”, in The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), ed. E. N. Zalta, url = ⟨http://plato.stanford.edu/archives/fall2013/entries/simplicity/⟩.



argument ⑹ –⑾ seem right.³¹ (Hildebrand, anyway, would embrace them all.) But then ⑼ in coǌ unction with them constitutes quite a plausible case for ⑾ . That is, ⑼ in coǌ unction with the premises makes conclu-sion ⑾ about as probable as its negation. And as I said, ⑾ contradicts the coǌ unction of Hildebrand’s premises ⑴ and ⑵ by contradicting (C2). Hence the coǌ unction of ⑴ and ⑵ is not more probable than its negation. In a word, it is not probable. This way the argument ⑹ –⑾ is a serious reason to doubt that both ⑴ and ⑵ are true. So long as the argument remains quite plausible, the coǌ unction remains quite plausibly false. Or put yet otherwise, the argument ⑹ –⑾ is an undermining defeater for the coǌ unction of ⑴ and ⑵ .

2.4 Modifying the argumentSuppose your confi dence about the coǌ unction of Hildebrand’s premises

⑴ and 2) is shaken. You still might try to modi them into something else. If incomparable intelligibility was knowability for humans, not know-ability in principle, then instead of premise ⑵ we would have something more acceptable:

2′. No standard lawlike proposition is incomparably intelligible for humans.

That would mean the following: for any standard lawlike proposition p, no human can know that p solely om essences. This premise seems right, assuming humans can know such propositions only om observation (i.e., only om without), and assuming that what somebody can know only om observation he cannot know solely om essences (i.e., om within). But this move redefi nes incomparable intelligibility. Remember that its original notion was one of an in principle knowability. To preserve validity, we must also barter ⑴ for something less acceptable:

1′. Any strictly necessary proposition is incomparablyintelligible for humans.

³¹ For a defence of (7), see Alexander R. Pruss, The Principle of Suffi cient Reason (New York: Cambridge University Press, 2006).



That would mean: for any strictly necessary proposition p, some hu-man can know that p solely om essences. But this is stronger and even less obvious than ⑴ . Even if all strict necessities are in principle knowable om within, why all should be knowable om within for humans? Authors who accept ⑴ for some theistic or metaphysical reason would equently reject (1′). They would think that there are some metaphysically necessary standard lawlike truths that humans can know only om observation and never solely om essences. And this for reasons mentioned in the preceding section. Just recall the law about salt and water. So redefi ning incomparable intelligibility does not help us to get closer to (C1). Moreover, Hildebrand himself doubts (1′). As said, he concedes that God’s existence may be in-comparably intelligible, even if not for us humans.

2.5 Whence the slipWhy does Hildebrand hold to (C1) despite the said problems? And why

has he sounded convincing to other realist phenomenologists?³² I can only guess. One option would be occasional confusion of ⑴ with (1′), and of ⑵ with (2′). That would not mean that Hildebrand in fact never held to ⑴ and ⑵ , nor that he always held to (1′) and (2′) instead. He gives clear signs of accepting ⑴ and ⑵ . But when assuring oneself about his premises, one may be tempted to mistake them for a moment with something else but more easily known to be true. Perhaps Hildebrand succumbed to this temptation.

³² Balduin Schwarz, “Dietrich von Hildebrands Lehre von der ‚Soseinfahrung‘ in ihren philosophiegeschichtlichen Zusammenhängen”, in Wahrheit, Wert und Sein, ed. B. Schwarz and D. von Hildebrand (Regensburg: Habbel, 1970), 46–48; Josef Seifert, Leib und Seele (Salzburg and Munich: Pustet, 1973), XXX and 264; William A. Marra, “A Minimum Epistemology”, Rehabilitierung der Philosophie, ed. B. Schwarz and D. von Hildebrand (Regensburg: Habbel, 1974), 95–96; Fritz Wenisch, Die Philosophie und ihre Methode (Salzburg: Pustet, 1976), 57–59; Josef Seifert, Back to ‘Things in Themselvesʼ (New York and London: Routledge & Kegan Paul, 1987), 31, 200–208; John R. White, “Kant and von Hildebrand on the Synthetic A Priori: A Contrast”, Aletheia V (1992): 313–315; James M. DuBois, “An Introduction to Adolf Reinach’s ‘The Supreme Rules of Inference According to Kant’”, Aletheia VI (1993/1994): 74–75; Josef Seifert, “Die Realistische Phänomenologie als Rückgang auf Platon und als kritische Reform des Platonismus”, Aletheia VI (1993/1994): 152–153; James M. DuBois, Judgement and Sachverhalt (Dordrecht: Kluwer, 1995), 101–105, 113; Josef Seifert, Discours des Méthodes (Frankfurt a. M.: Ontos Verlag, 2009), 24–26.



Moreover, perhaps the temptation was nourished by the terminology of his teacher Adolf Reinach (1883–1917).³³ Reinach calls “a priori” both ⒤ states of facts known or knowable for us not om observation³⁴ and (ii) states of facts grounded in essence of the subject matter.³⁵ He does so without any worry whether the two notions amount to the same or are coextensive. Reinach might thus have sown in his student Hildebrand a sympathy for the claim that all strictly necessary propositions can be known by us apart om observation. Hildebrand may be denying this when he says that God’s existence is strictly necessary yet unknowable for us a priori. But he may not be realizing the tension. The said claim, that all strictly necessary proposi-tions can be known by us apart om observation, implies in turn (C1). It implies it at least on the assumption that standard lawlike propositions are not knowable for us apart om observation. In this way Hildebrand, and via him other realist phenomenologists, might be inclined by Reinach to (C1) and to lapses favourable to it.

Whatever the cause of the opposite appearance, Hildebrand fails to show that all standard lawlike propositions lack strict necessity. So he does not help to a convincing case om (C1) to (C2). For all he says, some standard lawlike propositions may be metaphysically necessary. Let’s turn to Groarke, who contends this is really the case.

3. GroarkeLike Hildebrand does with strict necessity, Groarke distinguishes meta-

physical necessity om analyticity and strictly logical necessity and deems

³³ Thanks for reminding me of this possibility go to Daniel von Wachter.³⁴ Adolf Reinach, “Concerning Phenomenology”, trans. Dallas Willard, url = ⟨http://www

.dwillard.org/articles/artview.asp?artID=21⟩; Reinach, “Über Phänomenologie”, in Anthologie der Realistischen Phänomenologie, ed. J. Seifert and C. M. Gueye (Frankfurt a. M.: Ontos Verlag, 2009), 438–439.

³⁵ Reinach, “Concerning Phenomenology”; Reinach, “Über Phänomenologie”, 440. Elsewhere, Reinach says that a priori are general and necessary states of facts. See Adolf Reinach, “The Apriori Foundations of the Civil Law”, trans. John F. Crosby, Aletheia III (1983): 5; DuBois, Judgement and Sachverhalt, 79–81.



it coextensive with truth in virtue of essences.³⁶ Let’s document his belief in the metaphysical necessity of at least some standard natural laws and at least some standard truths about natural kinds.

The universal law of gravitation is not like the social custom of holding your fork in the right or le hand. You can do either. Gravitation is, in contrast, something logically or at least metaphysically necessary. (At least, this is what most scientists claim.)³⁷

As new essentialists [led by Brian Ellis] indicate, modern science has discovered “necessary facts” about the physical world. For example, the claim that “Water is H2O” is a necessary fact. Scientists came to know water is H2O, through experiments and observations, but […] they also claim that water is necessarily H2O. The nature of water follows necessarily om its molecular structure.³⁸

Groarke also thinks it metaphysically necessary that copper wires con-duct electricity; that closed bodies displacing water of a greater weight than their own fl oat on it; that energy is conserved in closed systems; that helium is lighter than air; that emeralds are green and lapis lazuli blue; and that humans have a brain.³⁹

What are Groarke’s reasons? As with Hildebrand, the answer must be gathered up om various places. But before that I want to mention other authors who argue diff erently for the metaphysical necessity of at least some standard lawlike propositions.

Brian Ellis contends that some standard lawlike proposition are meta-physically necessary since they concern natural kinds (e.g., water) or uni-versal properties (e.g., gravity, mass, distance) we can only identi and distinguish by means of the lawlike propositions themselves. Thus the very essence of the natural kinds and of the universal properties encompasses standard lawlike propositions. These are then true in virtue of essences, and

³⁶ Groarke, Aristotelian Account of Induction, 215, 404; Louis Groarke, “Aristotle: Logic”, Internet Encyclopedia of Philosophy, ed. J. Fieser and B. Dowden, url = ⟨http://www.iep.utm.edu/aris-log/⟩, § 4.

³⁷ Groarke, Aristotelian Account of Induction, 54.³⁸ Ibid., 401.³⁹ Ibid., 67, 114, 145–146, 178, 197, 214–215, 224–225, 365, 367.



so metaphysically necessary. ⁴⁰ This argument has been criticized. It stumbles over the distinction between essence on the one hand and indispensable criterion on the other. The fact that we can distinguish x om other things by means of y does not imply in general that the essence of x requires y.⁴¹ Similarly, even when we can only tell a particular man om other men by his scar, this does not mean he has it in virtue of his essence.

Hillary Putnam and Saul Kripke claim that water is necessarily H2O since chemical substances have their molecular structure in virtue of their essences.⁴² This has been criticized, too, this time by the distinction between de dicto and de re reference. Even if any chemical substance must have some unique molecular structure (de dicto reference), this does not mean that a given chemical substance (say, water) must have the particular molecular structure it has (H2O, de re reference). Similarly, even if any man must have a unique father, this does not mean that a given man (say, John) must have the particular father he has (say, Peter).⁴³ Finally, as said above, Stanislav Sousedík argues non-deductively that the metaphysical necessity of standard lawlike propositions is a true explanation of their positive instances.

Groarke’s position is this. We can know about some standard lawlike propositions intuitively – not by argument – that they are metaphysically necessary. Such intuitive knowledge is somehow triggered in us by observa-tion of their positive instances. This resembles Sousedík’s sudden idea that the metaphysical necessity of a standard lawlike proposition is a true expla-nation of its positive instances. But Sousedík would defend this brainwave by a non-deductive argument. Groarke, on the other hand, gives a deductive argument. Some standard lawlike propositions are in his view metaphysically necessary since their positive instances exempli natural kinds that make all their members necessarily similar in relevant ways.

⁴⁰ See Brian Ellis, “Causal Powers and Laws of Nature”, in Causation and Laws of Nature, ed. H. Sankey (Dordrecht: Kluwer, 1999), 19–34.

⁴¹ See Lowe, Four Category Ontology, 149–152.⁴² Hilary Putnam, “The Meaning of ‘Meaning’”, in Mind, Language and Reality (Cambridge:

Cambridge University Press, 1975), 215–271; Saul A. Kripke, Naming and Necessity (Oxford: Clarendon Press, 1980), 106–134, 164.

⁴³ See E. J. Lowe, “A Problem for A Posteriori Essentialism Concerning Natural Kinds”, Analysis 67 (2007): 286–292; E. J. Lowe, “Reply to Bird on A Posteriori Essentialism”, Analysis 68 (2008): 345–347.



I turn fi rst to Groarke’s proposal of the intuitive knowledge.

3.1 Intuition upon observationGroarke talks of a special sort of intuitive – i.e., non-argumentative –

knowledge triggered by observation. He calls the intuition true induction, strict induction, induction proper, or epagoge proper. (Labelling an intuition as ‘induction’ sounds idiosyncratic to most post-Humean ears but familiar within pre-Humean Aristotelian philosophy.⁴⁴) According to Groarke, we cognize various realities by true induction: We apprehend universals and universal (specifi c or generic) essences. We grasp real defi nitions. We intuit the truth of universal propositions that hold with metaphysical necessity – not only necessary principles of logic, mathematics, metaphysics, and ethics, but even of natural science. And we intuit not only their truth but also their metaphysical necessity.⁴⁵

These are Groarke’s examples of universal propositions which are meta-physically necessary and the truth of which is known intuitively, by true induction: the same proposition cannot be true and false; if a = b and b = c, then a = c; if a > b and b > c, then a > c; 2 + 2 = 4; for each natural number there exists only one successor number; the shortest distance between two points is a straight line; circle has a radius through 360 degrees; circle is a closed fi gure with every point equidistant om a centre; triangle has inte-rior angles equal to 180 degrees; the colour red is not the colour green; every eff ect has a cause; the past does not change; dishonesty is a vice; murder is wrong; promise-keeping is a duty; energy is conserved; gravity is directly proportional to mass and inversely proportional to squared distance; helium is lighter than air; s-electrons in helium have no empty orbitals; human beings need oxygen.⁴⁶ As we see, Groarke thinks that intuition in the form of true induction can fi nd out truths of diverse sorts.

How do we, in Groarke’s view, come to true induction of a universal proposition that is metaphysically necessary? We observe one, several, or

⁴⁴ See Groarke, Aristotelian Account of Induction, 9, 26–31, 121–123; Groarke, “Aristotle: Logic”, § 13; W. D. Ross (ed.), Aristotle’s Prior and Posterior Analytics (Oxford: Clarendon Press, 1965), 47–50.

⁴⁵ Groarke, Aristotelian Account of Induction, 19, 27, 157–206.⁴⁶ Ibid., 26, 178, 199–200, 365, 393.



many positive instances of the proposition. Sometimes this triggers in us intuitive knowledge that the proposition is true. The observation may even trigger intuitive knowledge that the proposition is true with metaphysical necessity. And the proposition may even be a standard lawlike one. E.g., following observation of several positive instances, we can know intuitively – “in a sort of mental illumination” and “without argument” – that all humans need oxygen, that helium is always lighter than air, and that all s-electrons have empty orbitals, and also that all “this must be the case”.⁴⁷

This is the end of Groarke’s intuitive story. He knows the story is quite short. He writes: “For whatever reason (or for no reason at all), we possess an active sense of discernment to enable us to pull more out of the less” – i.e., the universal om the particular, and the necessary om the universal.⁴⁸ “How do we manage this? All this happens through a kind of inspiration. How do we explain it? Explaining this inspiration is impossible.”⁴⁹ “We can do […] these things because we have intelligence. That is the end of the line. We have nothing more to say […]”⁵⁰

So in the upshot Groarke simply contends that some standard lawlike propositions are upon observation of their positive instances intuitively known to be metaphysically necessary. But he refuses to give any further directions how to gain this knowledge. Rather, he compares acquisition of such intuitive knowledge to production of great art. He says that in both cases there is “no recipe, no algorithm, no surefi re method.”⁵¹

Interestingly, some phenomenologists in the Hildebrand tradition also claim that positive instances of a universal proposition can spark intui-tive knowledge of its necessity. According to Hildebrand himself, positive instances of strictly necessary universal propositions form starting points for (intuitive) insights into both their truth and strict necessity. Amongst such propositions there are those such as that being and non-being always exclude each other, there’s no willing without thinking, any colour requires extension, any value requires an adequate response, or moral value can never

⁴⁷ Ibid., 178.⁴⁸ Ibid., 348.⁴⁹ Ibid., 326.⁵⁰ Ibid., 348.⁵¹ Ibid., 326; see also 332.



be attributed to an impersonal being.⁵² Josef Seifert (*1945), a German realist phenomenologist and Hildebrand’s former student, asks: how are the claims of strict necessity to be verifi ed? He answers in the same vein as Hildebrand: “Ultimately through an immediate cognition of the sort which Aristotle has declared to be the foundation for all arguments.” The necessities “are given in superior form of cognition than argument: by insight”. At the same time, “carefully studied examples of such essential necessities […] can serve as methods […] for gaining such insights.”⁵³

But phenomenologists in the Hildebrand tradition balk incredulously at Groarke’s suggestion that positive instances of a standard lawlike proposition can trigger intuitive knowledge of its metaphysical necessity. Hildebrand’s teacher Edmund Husserl (1859–1938) asks rhetorically: how should one have insight – i.e., intuitive knowledge – of such propositions?⁵⁴ The suggestion made is that of course one can’t. Seifert even announces a contrary insight – i.e., intuitive knowledge that no standard lawlike proposition is strictly nec-essary. He says: “We can gain a philosophical insight into the datum of the contingency of essence, into the non-absoluteness of the necessity of these facts. There is nothing intrinsic to these facts which would, absolutely speaking, forbid their being otherwise.”⁵⁵

On the other hand, it is hard to fi nd in Husserl a persuasive reason for his position. And as for Seifert, he does not tell us how to have the contrary intuition of the contingency of standard lawlike propositions. Of course, if we happen to eǌ oy either Groarke’s intuitive knowledge of the metaphysical necessity of some standard lawlike proposition, or Seifert’s intuitive knowl-edge of metaphysical or strict contingency of all such propositions, then the issue is solved for us. But it is not solved if we have none of these intuitions. Scolding us for not getting intuitively what some others allegedly are getting intuitively is unhelpful.⁵⁶ So let us explore further.

⁵² Hildebrand, What is Philosophy?, 134–139, 220–221.⁵³ Josef Seifert, “Editor’s Introductory Essay”, in Hildebrand, What is Philosophy?, xlviii.⁵⁴ Edmund Husserl, “Prolegomena to Pure Logic”, § 22, in Logical Investigations, Vol. 1, trans.

J. N. Findlay (London and New York: Routledge, 2001), 49.⁵⁵ Seifert, Back to ‘Things in Themselves’, 201.⁵⁶ A similar point is made by John P. McCaskey, “Review of Louis Groarke, An Aristotelian

Account of Induction”, Notre Dame Philosophical Reviews (April 2010), url = ⟨http://ndpr.nd.edu/news/24325-an-aristotelian-account-of-induction-creating-something- om-nothing/⟩.



3.2 Arguments from relevant similarityGroarke suggests how the intuitive knowledge of metaphysical necessity,

once gained, can be chopped, by a conceptually sophisticated agent, into an argument. “We can”, he says, “turn an inductive insight into an argument.”⁵⁷ Such an argument is “an expression of a deeper, more comprehensive mental process”, “a logical analogue to the illuminative or inspirational process of true induction”.⁵⁸

Such an argument for the metaphysical necessity of a given universal prop-osition starts with its positive instances. Then it notes that they exempli a natural kind all members of which are necessarily similar in relevant ways. It concludes that the universal proposition is metaphysically necessary. The main weak point is the diffi culty of telling what counts as relevantly similar.

To lay out the whole pattern of this argument and its so spots more clearly, I will fi rst put together Groarke’s overall idea. Groarke explains it most fully on the example of Aristotle’s claim that bileless animal are long lived. Then I will note the same pattern applied on behalf of the necessity of a standard natural law endorsed by Groarke: closed bodies displacing water of a greater weight than their own fl oat on it.

3.2.1 Bileless animalsGroarke makes a detailed proposal how to understand Aristotle’s way to

the claim that all animals with no or almost no bile have a potential to live long. Put shortly this claim reads, bileless animals are long lived. Aristotle motivates it by observation of its positive instances: several men, horses, and mules.⁵⁹ Here is Groarke’s view how.

First the ancient biologist observes several dissected men, horses, and mules. He notes that all of them are both bileless and long lived. This “can spur” in the biologist “the leap to the understanding” that all bileless ani-mals are long lived. “This is the process of [intuitive, non-argumentative] discovery that the bileless syllogism parallels.”⁶⁰

⁵⁷ Groarke, Aristotelian Account of Induction, 27.⁵⁸ Ibid., 9, 302.⁵⁹ Aristotle, Prior Analytics, bk. 2, ch. 23, 68b8–36.⁶⁰ Groarke, Aristotelian Account of Induction, 130.



Although the syllogism, which is laid out below, “depends on an out-dated model of biology”, Groarke thinks “we can make a logical sense of it.”⁶¹ More importantly for us, he also suggests in passing that we can even make a logical sense of the reasoning for the metaphysical necessity of its conclusion.

So suppose we observe several men, horses, and mules to be both long lived and bileless. Groarke implores us not to require a great sample. Even a small sample of men, horses, and mules might justly lead to the conclusion that all specimens of these species are long lived and bileless, for animals like that “possess the same internal constitution.”⁶²

Here we should wonder about two things. First, what animal species are supposed to be “like” men, horses, and mules? Groarke provides no complete list or a general defi nition of those species. Nor does Aristotle. They only adduce several additional kinds: roe deer, fallow deer, seal, dolphin, ass, some kinds of pigs, camel, and also the genus of (viviparous) quadrupeds.⁶³ But Groarke simply uses the umbrella term “men, horses, mules, etc.” He thinks it unimportant what exactly hides under ‘etc.’ so long as the group of all men, horses, mules, etc. is necessarily convertible with the group of all bileless animals. This means: so long as the two groups necessarily have the same extensions.

Second, what does it mean, for Groarke, to possess the same internal constitution? To possess the same universal (specifi c or generic) essence. This in turn amounts to being of the same natural kind.⁶⁴ So Groarke’s claim is that all animals like men, horses, mules, etc. are of the same natural kind.

Groarke does not say what a natural kind is. He only gives some exam-ples, with a note that natural kinds are not “counterfeit”.⁶⁵ In contrast to counterfeit kinds, natural kinds are in Groarke’s view “objective, ‘out there’

⁶¹ Ibid., 124.⁶² Ibid., 130–131.⁶³ See ibid., 116–117, 131.⁶⁴ Ibid., 144.⁶⁵ Ibid., 428: “The term ‘natural kind’ is usefully ambiguous. We might claim that an elephant

is a natural kind, so too an electron, and a volcano – that even an angel is a natural kind. We can extend the term to non-substances, to activities, properties, and dispositions. An irrational number is, in this secondary sense, a natural kind, also sexual reproduction, gender, courage, and so on. I will not attempt at any taxonomy here; nor shall I try to distinguish, in any comprehensive way, genuine from



in the world”.⁶⁶ So he seems to concur with this account of natural kinds, penned by Alexander Bird and Emma Tobin: “To say that a kind is natural is to say that it corresponds to a grouping or ordering that does not depend on humans.”⁶⁷

But there is more than one natural kind exemplifi ed by all animals like men, horses, and mules. Say, the natural kinds body and animal – and per-haps even some others. Then Groarke’s claim is, presumably, that all animals like men, horses, and mules share in some relatively specifi c natural kind. Otherwise the kind covers too mixed a bag of marbles to warrant sharing in the investigated features (longlivedness and bilelessness).

Next, Groarke regards as necessary and self-evident a principle due to which “our knowledge of the properties of [even] one instance of a natural kind can be transferred to all other such instances.”⁶⁸ Elsewhere he contrasts the principle with the well-known law of indiscernibility of absolutely iden-tical things. He calls the principle “the little law of identity or the law of resemblance.”

This law might be formulated in various ways: things which are identi-cal in some specifi c way are identical in that specifi c way; things which resemble one another must, in the relevant sense, possess identical attributes; things which possess identical attributes must possess the same attributes, and so on. This little law of identity does not have to be proved. It is a self-evident principle of reason. [… In other words,] x is like y in some relevant sense, so x must, in that specifi ed sense, possess the same attributes as y. [… In yet other words, if things] resemble one another they […] have to be alike in the relevant sense. [… Or, a]nything that is the same thing x […] must have the same characteristics. [… This] is a basic law of thought; it is necessarily, self-evidently true; it is true in all possible worlds; it is a prior condition for logical discourse, [… a] self-evident rule of logic […] To claim that

counterfeit natural kinds.” Groarke’s examples of counterfeit kinds are the all-terrain vehicle and the baseball strike (ibid., 181, 209).

⁶⁶ Ibid., 129, 396, 415.⁶⁷ Alexander Bird and Emma Tobin, “Natural Kinds”, in The Stanford Encyclopedia of

Philosophy (Winter 2012 Edition), ed. E. N. Zalta, url = ⟨http://plato.stanford.edu/archives/win2012/entries/natural-kinds/⟩.

⁶⁸ Groarke, Aristotelian Account of Induction, 428.


Vlastimil VohánkaAre Standard Lawlike Propositions Metaphysically Necessary?things which resemble one another do not possess the same attributes would be logically unintelligible.⁶⁹

Now whatever Groarke thinks, not all these formulations of the law of resemblance do warrant that all things of the same natural kind share the investigated features. Some of the formulations do not warrant, e.g., that all animals like men, horses, and mules are long lived and bileless. Take the formulation: all things identical in some specifi c way are identical in that way. This is a self-evident truism. But what we need is rather that all things identical in some specifi c way are identical also in a certain other way. Else we only get that all animals like men, horses, and mules are identical in being animals; not that they all are identical also in being long lived and bileless.

Assuming that shared identity amounts to sharing in a relatively specifi c natural kind (whatever that means), and that shared identity implies relevant similarity (whatever that means), I suggest this formulation of the law of resemblance: all things sharing in a relatively specifi c natural kind are rel-evantly similar. This is the best I can make of the law that Groarke purports to convey. With the law thus formulated, we get closer to the desired claim that all animals like men, horses, and mules are long lived and bileless.

Now join the law of resemblance to these two inputs om above: several men, horses, and mules are both long lived and bileless; and all animals like men, horses, and mules share in some relatively specifi c natural kind. Groarke thinks it follows that it is metaphysically necessary that all animals like men, horses, and mules are both bileless and long lived. This because being bileless and long lived falls under the relevant similarity of all such animals.⁷⁰

Now take that result: all animals like men, horses, and mules are long lived and bileless. (Indeed, necessarily so.) Join it to the convertibility: all animals like men, horses, and mules are bileless, and all bileless animals are those like men, horses, and mules. (Again, necessarily so.) It follows that all bileless animals are long lived. To abbreviate: All S is P and M; so all S is P. Moreover, all S is M and all M is S; so all M is S. Hence, all M is P.⁷¹

⁶⁹ Louis Groarke, “A Deductive Account of Induction”, Science et Esprit 52 (2000): 360–361, 363–365. Similarly Groarke, Aristotelian Account of Induction, 144.

⁷⁰ See Groarke, Aristotelian Account of Induction, 145, 148.⁷¹ Ibid., 125 and 133.



We obtain similarly the metaphysical necessity of longevity of bileless ani-mals, although Groarke does not bother to state the argument explicitly. The necessity follows when the modal terms are explicit: Nec(All S is P and M); so Nec(All S is P). Moreover, Nec(All S is M and all M is S); so Nec(All M is S). Hence, Nec(All M is P).

This, all in all, is how Groarke makes a logical sense of the reasoning that leads to metaphysically necessary longevity of bileless animals.

3.2.2 Floating bodiesHow is the reasoning about bileless animals relevant for the metaphysical

necessity of standard lawlike propositions? Groarke does not say that the conclusion of the reasoning or all its premises are true. As said, he writes the reasoning depends on “outdated biology”. Perhaps he deems outdated the premise of convertibility. But the reasoning strikes him as logically correct. He also embraces the law that closed bodies displacing water of a greater weight than their own fl oat on it.

As [Robert] Schmidt points out, we cannot grasp the physical principle that explains why boats fl oat on water om mere enumeration. It does not follow that because this and that and that boat fl ows on water, all boats fl oat on water. We need to be able to somehow set through indi-vidual instances of fl oating boats to the underlying physical principle that the phenomenon “fl oating” results whenever an object displaces an amount of water that is heavier than their own weight. As Schmidt explains, “From the fact that some vessels fl oat on water we cannot judge that all vessels fl oat on water; but if those which fl oat on water are seen to agree in the property of displacing water of a greater weight then their own, then we can judge that every watertight vessel that displaces more water than would equal itself in weight fl oats on water.” But grasping this principle is a heady feat. […] We must be able (like Archimedes) to penetrate, by some creative stroke of genius, the surface appearances and discern the underlying cause of fl oating.⁷²

Now Groarke should be willing to transform such intuition into the fol-lowing argument.

⁷² Ibid., 114; see also 142, 144, 148; Groarke, “A Deductive Account of Induction”, 361–363. Robert Schmidt, The Domain of Logic According to Saint Thomas Aquinas (The Hague: Martinus Nĳ hoff 1966), 279.



Let us abbreviate: S = boat, or vessel, etc.; where ‘etc.’ covers all the remaining sorts of closed bodies displacing water of a greater weight than their own. P = body fl oating on water. M = closed body displacing water of a greater weight than its own. N = sharing in a relatively specifi c natural kind. R = relevantly similar.

⒓ Several boats and vessels fl oat on water and are closed bodies displacing water of a greater weight than their own.Premise

Several S are P and M.

⒔ It is metaphysically necessary that all bodies like boats and vessels share in a relatively specifi c natural kind.Premise

Nec(All S is N).

⒕ It is metaphysically necessary that all things sharing in a relatively specifi c natural kind are relevantly similar.Premise; the law of resemblance

Nec(All N is R).

⒖ It is metaphysically necessary that all bodies like boats and vessels are relevantly similar.From ⒀ and ⒁

Nec(All S is R).

⒗ If several boats and vessels fl oat on water and are closed bodies displacing water of a greater weight than their own; and if it is metaphysically necessary that all bodies like boats and vessels are relevantly similar; then it is metaphysically necessary that all bodies like boats and vessels fl oat on water and are closed bodies displacing water of a greater weight than their own.Premise

If several S are P and M, and Nec(All S is R), then Nec(All S is P and M).


Vlastimil VohánkaAre Standard Lawlike Propositions Metaphysically Necessary?⒘ It is metaphysically necessary that all bodies like boats and

vessels fl oat on water and are closed bodies displacing water of a greater weight than their own.From ⑿ , ⒂ , and ⒃

Nec(All S is P and M).

⒙ It’s metaphysically necessary that all bodies like boats and ves sels are closed bodies displacing water of a greater weight than their own; and that all closed bodies displacing water of a greater weight than their own are bodies like boats and vessels.Premise

Nec(All S is M and all M is S).

⒚ It is metaphysically necessary that all closed bodies displac-ing water of a greater weight than their own fl oat on it.From ⒄ and ⒅

Nec(All M is P).Hence,

C⒊ Some standard lawlike propositionis metaphysically necessary.

The argument om ⑿ to (C3) is valid. Suppose somebody would construe its parallel for a false conclusion. Say, for the conclusion that all swans are pure white, even necessarily. For yes, some swan species are pure white: e.g., the mute swan, the trumpeter swan, and the whooper swan. But some are white and black, and some are almost entirely black. So suppose you observe several members of the three swan species to be pure white. Let S = mute swan, or trumpeter swan, or whooper swan, etc.; where ‘etc.’ covers all the remaining swan species. Also, let P = white, and M = swan. Why the parallel does not hold? Perhaps because the premise parallel to ⒃ would be false. Although all swans are relevantly similar, perhaps being white is no facet of this similarity amongst all swans. On the other hand, Groarke adds, there is a sound parallel argument for a restricted conclusion: that all swans of the Northern Hemisphere are pure white, even necessarily. Let S = mute swan, or trumpeter swan, or whooper swan, etc.; where ‘etc.’



covers all the remaining species of swans of the Northern Hemisphere, but not species om elsewhere. Let M = Northern Hemisphere swan. Now the premise parallel to ⒃ might be true.⁷³ As we see, Groarke proposes a way of discriminating between correct and incorrect uses of the argumentative pattern. So what is the problem?

3.3 Undermining the argumentThe weak points of the above argument om ⑿ to (C3) are premises

⒀ , ⒁ , and ⒃ .First, premise ⑿ is shaky since the involved concept of a relatively

specifi c natural kind is obscure. Groarke contends we can identi natural kinds of various things intuitively, without argument: “we can intuit natural kinds.”⁷⁴ Even small children and mentally handicapped people can.⁷⁵ And in his opinion, conceptually sophisticated people can even form and apply in-tuitively not only concepts for specifi c natural kinds (e.g., apple, horse, cow), but also the meta-concept of a natural kind. They “can see, for example, that this apple is fundamentally like other apples”; and on the other hand, that the horse and the cow are “clearly diff erent kinds of things”.⁷⁶ Similarly for the meta-concept of a relatively specifi c natural kind. So Groarke would take this claim as obvious:

⒔ ⒈ All bodies like boats and vessels sharein a relatively specifi c natural kind.

And he would probably add that all such claims are metaphysically neces-sary, which would yield ⒀ . But the problem is that the concept of a rela-tively specifi c natural kind is too vague and rough for (⒔ 1) to be obvious. It is hard to tell what falls under such a concept. It is hard to tell where to draw the line. For what qualifi es as specifi c enough? Groarke does not say. He writes his goal “is not to stipulate precise conditions which would be neces-sary, in any particular case, for a relation of [shared] identity [i.e., sharing in

⁷³ Cf. Groarke, Aristotelian Account of Induction, 134–135, 151–152.⁷⁴ Ibid., 148; see also 170, 197, 225, 415.⁷⁵ Ibid., 211–212, 234.⁷⁶ Ibid., 80, 418.



a relatively specifi c natural kind].”⁷⁷ Then, however, he leaves his audience wondering what to make of claims such as ⒀ and (⒔ 1).

Second, premise ⒁ is shaky since also the involved concept of relevant similarity is obscure. Groarke does not explicate what relevant similarity is in general. Hence the meaning of ⒁ remains unclear. Repeated proclaiming it self-evident does not help to clari it. As with ⒀ , it is even hard to argue about ⒁ as it is not even clear what that claim means.

Third, suppose you know what relevant similarity is in general. Still, premise ⒃ is shaky since it is unclear how to tell that certain features fall under relevant similarity. Even if, e.g., all swans are with metaphysical necessity relevantly similar, pure white is in Groarke’s view no aspect of the relevant similarity amongst all swans. He thinks you would be wrong in thinking that it is, even if you observed many pure white swans and no other. On the other hand, in ⒃ he presupposes that since all bodies like boats and vessels are relevantly similar, they are such in respect of displac-ing water of a greater weight than their own. But how are we to tell the diff erence? How are we to know that a certain feature is, or even must be, an aspect of relevant similarity amongst all things of the given sort? More specifi cally, how are we to know that the water displacement is a respect in which all bodies like boats and vessels are (must be) relevantly similar? Again, Groarke does not say. He does not provide any reason or guidelines. (Perhaps for the reason that – as he believes – inductive knowledge cannot be wholly turned into mechanical rules or an algorithm.⁷⁸) But some reason or guideline is needed.

For at least one of the three stated reasons, arguments om relevant similarity, like the one about fl oating bodies, fail to show that (C3) is true. Although they are valid, their premises lack in credence because they are obscure (like 13 and 14) or unprincipled (like 16).

3.4 Sampling argumentsI want to anticipate and address a reply. Groarke would say the worry

about premises ⒀ , ⒁ , and ⒃ is insincere if sampling arguments are

⁷⁷ Groarke, “A Deductive Account of Induction”, 360.⁷⁸ See Groarke, Aristotelian Account of Induction, 143, 148–149, 223, 262–263, 326, 327–332, 375.



acceptable. Such arguments move inductively om a property’s percentage or percentage interval in one or more samples to its percentage or percent-age interval in the target population. E.g., because in several large samples of smokers more than 15 per cent die before the age of fi , one concludes that more than 15 per cent of all smokers die before that age. Groarke views sampling arguments as explicitly or implicitly including claims like premises ⒀ , ⒁ , and ⒃ . So he would say, if sampling arguments are acceptable, so are also those premises.

Groarke is most clear about the alleged indispensability of premise ⒁ . He writes: “every induction relies on an appeal to the law of resemblance”;⁷⁹ “the principle of shared identity is […] the logical step on which any induc-tion depends.”⁸⁰ He also depicts sampling arguments as parallel to those about bileless animals and fl oating bodies:

Suppose we set out to study premature morbidity among smokers. We study three sample populations, A, B, and C, and discover that more than 15 per cent of smokers in each sample die before they reach the age of fi . We conclude that more than 15 per cent of smokers die before they reach the age of fi . We can easily express this line of reasoning as an inductive syllogism. Defi ne our terms: S, individual sample populations such as A, B, C (etc.); P, having a morbidity rate of more than 15 per cent for individuals less than fi years old; and M, populations of smokers. The inductive syllogism will take the form, “All sample populations A, B, C, etc., have a 15-per-cent mortality rate for individuals less than fi years old. All sample populations A, B, C, etc., are populations of smokers. Therefore, all populations of smok-ers have a 15-per-cent mortality rate for individuals under fi years old.” Symbolically, “All S is P. (All S is M, convertible to) All M is S. Therefore, all M is P.”

This argument hinges […] on the claim that […] the term “individual sample populations such as A, B, C, etc.,” is interchangeable with the term “populations of smokers.” But this reduces to the equivalent claim made by modern logicians that in sound induction, sample populations must be representative of the target. To say that “individual sample populations such as A, B, C, etc.,” are representative of “populations of

⁷⁹ Groarke, “A Deductive Account of Induction”, 366; see also 363–364, 368.⁸⁰ Groarke, Aristotelian Account of Induction, 146–147; see also 222–223.


Vlastimil VohánkaAre Standard Lawlike Propositions Metaphysically Necessary?smokers” is to say that these various groups possess the same nature; they must be, in the relevant sense, interchangeable with one another.⁸¹

Let us make the parallel with the argument about fl oating bodies more perspicuous.

Abbreviate as follows: S = population A, B, or C, etc.; where ‘etc.’ covers all the remaining (sample and target) populations of smokers. P = having a morbidity rate of more than 15 per cent for individuals less than fi years old. M = population (sample or target) of smokers. N = sharing in a relatively specifi c natural kind. R = relevantly similar.

12′. A, B, and C are several populations of smokers and have a morbidity rate of more than 15 per cent for individuals less than fi years old.Premise

Several S are P and M.

13′. It is metaphysically necessary that all populations like A, B, and C share in a relatively specifi c natural kind.Premise

Nec(All S is N).

⒕ It is metaphysically necessary that all things sharing in a relatively specifi c natural kind are relevantly similar.Premise; the law of resemblance

Nec(All N is R).

15′. It is metaphysically necessary that all populations like A, B, and C are relevantly similar.From (13′) and ⒁

Nec(All S is R).

16′. If A, B, and C have a morbidity rate of more than 15 per cent for individuals less than fi years old and are populations of smokers; and if it is metaphysically necessary that all populations like A, B, and C are relevantly similar; then it is metaphysically necessary that all populations like A, B, and

⁸¹ Ibid., 133; added italics. See also 146–147.



C have a morbidity rate of more than 15 per cent for individ-uals less than fi years old and are populations of smokers.Premise

If several S are P and M, and Nec(All S is R), then Nec(All S is P and M).

17′. It is metaphysically necessary that all populations like A, B, and C have a morbidity rate of more than 15 per cent for individuals less than fi years old and are populations of smokers.’From (12′), (15′), and (16′)

Nec(All S is P and M).

18′. It is metaphysically necessary that all populations like A, B, and C are populations of smokers; and that all populations of smokers are populations like A, B, and C.Premise

Nec(All S is M and all M is S).

19′. It is metaphysically necessary that all populations of smokers have a morbidity rate of more than 15 per cent for individu-als less than fi years old.From (18′) and (18′)

Nec(All M is P).

⒛ The population of all smokers has a morbidity rate of more than 15 per cent for individuals less than fi years old. From (19′)

So Groarke’s defence of premises ⒀ , ⒁ , and ⒃ might be stated this way: Any acceptable sampling argument for conclusion ⒇ is like the one above. But then also claims ⒀ , ⒁ , and ⒃ are acceptable, for these are parallel.

One obstacle to this reasoning is the implausibility of premise (13′). It implies that all groups of smokers share in a natural kind. But that is false. At least some groups of smokers do not form natural kinds, at least because some correspond to a grouping or ordering dependent on humans. Think



of smokers in red shirts. Step (19′) is also false. It implies that all groups of smokers are necessarily in more than 15 per cent composed of those who die before the age of fi . However, it is possible to gather a group of smokers older than fi years yet alive. And this even if it is in fact true that more than 15 per cent of all smokers die before that age.

Another weak point is this false dilemma: either swallow ⒀ , ⒁ , and ⒃ , or end up without acceptable sampling arguments. The dilemma is forced by the false assumption that all acceptable sampling arguments are arguments om relevant similarity. Some acceptable sampling arguments that do not seem to presuppose anything like the law of resemblance. Nor do they seem to include claims about metaphysical necessity, about sharing in a natural kind or about relevant similarities. To think otherwise is to ignore alternative approaches to sampling arguments.⁸²

3.4.1 Bernoullian sampling argumentsLet me pinpoint the Bernoullian approach. It is an alternative to Groarke’s

sampling argument om relevant similarity. It is also less known yet more convincing than other philosophical approaches to sampling.⁸³ It employs Bernoulli’s theorem and the rule of proportional syllogism.

The scheme is this. Firstly, if at least n per cent of S is P; a is S; and there is no evidence that a is not P; then the probability that a is P is at least n per cent. This seems intuitively correct and is known in the literature as the rule of proportional (or, statistical) syllogism.

Secondly, according to a theorem proved by the Swiss mathematician Jacob Bernoulli (1655–1705), the overwhelming majority of possible, distinct and suffi ciently large samples has approximately the same percentage for any

⁸² See John Vickers, “The Problem of Induction”, in The Stanford Encyclopedia of Philo-sophy (Spring 2013 Edition), ed. E. N. Zalta, url = ⟨http://plato.stanford.edu/archives/spr2013/entries/induction-problem/⟩.

⁸³ For its advocates, see Donald C. Williams, The Ground of Induction (Harvard: Harvard University Press, 1947); David C. Stove, The Rationality of Induction (New York: Oxford University Press, 1986); Scott Campbell, “Fixing a Hole in the Ground of Induction”, Australasian Journal of Philosophy 79 (2001): 553–563; Timothy J. McGrew, “Direct Inference and the Problem of Induction”, in Probability Is the Very Guide of Life, ed. H. E. Kyburg Jr. and M. Thalos (Chicago and La Salle: Open Court Publishing, 2003), 33–60; Scott Campbell and James Franklin, “Randomness and the Justifi cation of Induction”, Synthese 138 (2004): 79–99.



single feature as the target population. This is a piece of non-trivial math-ematics.⁸⁴ Its consequences are noteworthy. E.g., at least 95 per cent of pos-sible distinct samples of size 2,000 drawn om an urn of balls matches the percentage of red balls in the urn itself, ± 5 per cent. And at least 75 per cent of possible distinct samples of size 100 drawn om an urn of balls matches the percentage of red balls in the urn itself, ± 10 per cent. Similarly for the percentage of cold, jelly, or agrant balls in the urn. Also, absolute size of the sample is relevant here, not its ratio to the size of the target population.⁸⁵ But knowing the ratio helps further in raising the lower bound of probability and in narrowing the margin of error.

Now suppose you have a suffi ciently large sample a* of S but no evidence that its percentage for the given feature P does not match the percentage in the population of all S. You infer by proportional syllogism that the sample a* very probably does match. Thus with the 2,000-fold sample of balls, you infer at least 95-per-cent probability that its percentage of red balls matches the percentage of red balls in the urn, ± 5 per cent. And with the 100-fold sample of balls, you infer at least 75-per-cent probability that its percentage of red balls matches the percentage of red balls in the urn, ± 10 per cent. If 58 per cent of S in your sample a* display P, then P very probably has the rate of about 58 per cent in the population of all S. Thus, if 58 per cent of balls in the 2,000-fold sample are red, there is at least 95-per-cent probability that the percentage of red balls in the urn is 58, ± 5 per cent. And if 58 per cent of balls in the 100-fold sample are red, there is at least 75-per-cent probability that the percentage of red balls in the urn is 58, ± 10 per cent.

This Bernoullian pattern is perspicuous. And what is important, you can apply it not only to urns but also to other target populations, including those of smokers. When doing so, you need not appeal to metaphysical necessities, natural kinds, or relevant similarities. So at least some acceptable sampling arguments are ee om claims like (13′), ⒁ , and (16′).

Groarke disagrees, for three reasons, but unconvincingly in my opinion. First, he thinks that even if some Bernoullian sampling arguments are ac-ceptable, appeals to relevant similarity – like (13′) and ⒁ – are somehow

⁸⁴ See William Kneale, Probability and Induction (Oxford: Clarendon Press, 1952), 136–142.⁸⁵ See McGrew, “Direct Inference and the Problem of Induction”, 41.



implicit in all of them. As we saw in part 3.4, to say of a sample that it matches or is representative of its target population means to Groarke that the sample is relevantly similar to the target population. This, however, is a biased reading of statistical terminology. Whatever relevant similarity is, it does not appear in statistical defi nitions of a matching or representative sample. A sample matches its target population ideally when it has the same percentage for any single feature within the population. It matches with a certain margin or error when its percentage for any single feature (or at least for any single explored feature) is within the margin around the percentage in the population.⁸⁶ No need to draw the concept of relevant similarity into the concept of a representative sample.

Second, Groarke thinks that Bernoullian sampling arguments somehow beg the question. They depend, in his view, on the probability calculus. And the calculus, in turn, assumes that the course of nature is uniform.⁸⁷ Elsewhere he says the calculus assumes that the more examples of a certain sort are observed to have a certain property, the more probably something of that sort has that property. ⁸⁸ But Groarke is here wrong. Bernoulli’s theorem is proved in combinatorics, independently of the probability calculus. The probability calculus itself may be defended regardless of the two assump-tions stated by Groarke. E.g., some argued for the calculus by means of Boolean algebra, functional equations, and these two intuitive axioms: the probability of any proposition determines the probability of its negation; and the probability of any coǌ unction of two propositions is determined by the probability of one of these propositions and the probability of the same proposition on the other proposition.⁸⁹ Also, to view Bernoullian sampling arguments as dependent on any of the assumptions stated by Groarke is to miss the point. These arguments end, rather than start, with uniformity in nature.

⁸⁶ See David J. Hand, Statistics (New York: Oxford University Press, 2008), 51–53.⁸⁷ In other words of Groarke, the calculus assumes that, similar causes have similar eff ects.

See his Aristotelian Account of Induction, 39, 152–153.⁸⁸ Louis Groarke, “Jumping the Gaps: Induction as First Exercise of Intelligence”, in Shifting

the Paradigm, ed. P. C. Biondi and L. Groarke (Berlin and Boston: Walter de Gruyter, 2014), 455.⁸⁹ See Richard T. Cox, The Algebra of Probable Inference (Baltimore: The Johns Hopkins

University Press, 1961), ch. I.

Vohanka Vlastimil

Vkládaný text

ff



And third, Groarke thinks Bernoullian sampling arguments are unsat-isfactory since they omit to consider the prior probability of the percentage interval in the target population.⁹⁰ This is the interval’s probability prior to observation of the percentage in the sample. The probability of the interval prior to the observation may be too low for its probability to be high a er it. Bernoullian sampling arguments do not tell a word about prior probability, so they cannot assess the posterior probability either.⁹¹ But the Bernoullian may simply reply that posterior probabilities need not be assessed via prior probabilities. Sampling arguments rather show that we can assess posteriors without assessing the priors. Once we arrive at a high posterior probability in that way, we can say that whatever the prior probability, it is suffi cient for the posterior probability to be high.⁹²

In brief, there are acceptable sampling arguments which do not presup-pose claims like (13′), ⒁ , and (16′). So it is unclear why acceptable sampling arguments should commit us to premises ⒀ and ⒃ .

4. ConclusionHildebrand and Groarke agree that necessities hold in virtue of essences

and can be known intuitively om examples. They disagree about whether at least some standard lawlike propositions are metaphysically necessary. Groarke says that they are, Hildebrand that they are not. Although both suggest logically valid arguments, both fail to establish their premises.

Hildebrand fails to defend that all strictly (or metaphysically) neces-sary propositions are in principle knowable solely by considering essences; and that no standard lawlike proposition is thus knowable. None of these two premises is obvious. In fact, at least one is quite plausibly false, for the explanation of positive instances of at least some standard lawlike proposi-tions by the metaphysical necessity of these propositions is quite plausibly (though not probably) true.

⁹⁰ Groarke, “Jumping the Gaps”.⁹¹ Patrick Maher has raised this worry in “The Hole in the Ground of Induction”, Australasian

Journal of Philosophy 74 (1996): 423–432.⁹² More in Campbell, “Fixing a Hole in the Ground of Induction”.



Groarke contends that we know intuitively at least some standard lawlike propositions to be metaphysically necessary. But he gives no rules for acquir-ing this intuition. He is also opposed by authors like Hildebrand. These are happy to proclaim intuitive knowledge of the necessity of some logical, metaphysical, and ethical truths, but never of standard lawlike truths. When Groarke resorts to arguing, these claims are among his premises: all things sharing in a relatively specifi c natural kind are relevantly similar; certain things (e.g., closed bodies) share in a relatively specifi c natural kind; these things therefore share certain non-trivial features (e.g., displacing water of a greater weight than their own). But the fi rst two claims lack in clear mean-ing and the third in justifi cation. Groarke is also wrong to say that similar premises are presupposed in all acceptable sampling arguments.

For all Hildebrand and Groarke say, it may be that some standard law-like propositions are metaphysically necessary, and it may be that none are. I hope this paper facilitates the debate.⁹³

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Mgr. Vlastimil Vohánka, Ph.D., is a post-doctoral fellow at the Depart-ment of Philosophy and Patrology, Sts Cyril and Methodius Faculty of Theology, Palacký University Olomouc.Address: Univerzita Palackého, Cyrilometodějská teologická fakulta, Katedra fi losofi e a patrologie, Univerzitní 22, 771 11 Olomouc.E-mail: [email protected]: https://sites.google.com/site/vvohanka/

Keywords: metaphysical necessity; laws of nature; intuition; induction; Dietrich von Hildebrand; Louis Groarke



SUMMARIUMHabentne typicae propositiones nomologicae

necessitatem metaphysicam?In tractatu proposito auctor doctrinas Theoderici von Hildebrand, phaenomenologi rea-listae, et Ludovici Groarkii Aristotelici examinat. Qui viri docti licet in epistemologia modalique metaphysica multum inter se consonent, diversas tamen de necessitate meta-physica solitarum propositionum nomologicarum (quae scil. sunt leges naturae ac veritates de generibus naturalibus) sententias profi tentur. Auctor huius tractatus rationes utriusque auctoris extrahit et impugnat. Hildebrandus sentit nullam solitam nomologicam proposi-tionem necessitate metaphysica gaudere, quia nulla, ex mera essentiarum consideratione cognosci potest, secundum ipsum. Quod quidem auctor impugnat arguens, explicationem saltem aliquarum huiusmodi propositionum sustentabiliter (etsi non probabiliter) veram esse. Groarke e contra aliquas dictas propositiones metaphysice necessarias esse contendit, nam secundum ipsum subiecta singularia, de quibus verifi centur, in generibus naturalibus collocantur, quae necessario omnia sua membra signanter consimilia faciunt. Hoc quoque ab auctore impugnatur, quia consimilitudo illa, de qua loquitur, nimis obscura est. In fi ne auctor sententiam Groarkii refutare conatur dicentem consimilitudinem illam praesumi

in omni ratione inductiva ex singulis exemplis hausta.

ABSTRACTAre standard Lawlike Propositions Metaphysically Necessary?

I discuss Dietrich von Hildebrand, a realist phenomenologist, and Louis Groarke, an Aristotelian. They are close in epistemology and modal metaphysics, but divided about the metaphysical necessity of standard lawlike propositions – i.e., standard natural laws and standard truths about natural kinds. I extract and undermine the reasons of both authors. Hildebrand claims that no standard lawlike proposition is metaphysically necessary, since none is in principle knowable solely by considering essences. I undermine this when I argue that the explanation of positive instances of at least some standard lawlike propositions by the metaphysical necessity of these propositions is quite plausibly (though not probably) true. Groarke claims that some standard lawlike propositions are metaphysically neces-sary, since their positive instances exemplify natural kinds that make all their members necessarily similar in relevant ways. I undermine this, too, as I point out the obscurity of relevant similarity. Finally I argue against Groarke’s suggestion that an appeal to relevant

similarity is presupposed in all acceptable inductive arguments from samples.

Are Standard Lawlike Propositions Metaphysically Necessary? Hildebrand vs. Groarke

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