Julien Tricard

Que sont les « lois de la nature » que les sciences empiriques, et en premier lieu la physique, tentent de saisir? Et si les scientifiques ne peuvent les découvrir, ou du moins les confirmer, que sur la base de l’expérience, quels sont la nature et le fondement de leurs opérations inductives? Comment garantir la possibilité d’une authentique connaissance de ces lois qui structurent la réalité? Ce livre propose une enquête épistémologique et métaphysique au cours de laquelle deux fils directeurs s’entremêlent. Il s’agit d’une part de s’interroger sur la nature ontologique des lois, à partir des débats contemporains en philosophie analytique des sciences. Les lois de la nature sont-elles, comme le pensent les empiristes humiens, de simples régularités factuelles universelles? Ou bien devraient-elles être conçues comme des faits nomiques d’un autre ordre, capables de rendre nécessaires les régularités que nous observons? Il s’agit d’autre part de remettre sur le métier le problème classique de l’induction que nous héritons de Hume. L’induction n’est-elle que l’opération de généralisation qualitative à partir de l’expérience? Exige-t-elle, comme on le suppose souvent, de montrer que la nature est uniforme et que les lois sont stables dans le temps? Pour résoudre ces problèmes, nous développons une théorie inédite des lois, centrée sur l’analyse de leur nature quantitative, et proposons un fondement nouveau à l’induction scientifique, qui repose sur l’existence, dans la réalité physique, de structures quantitatives. Nous montrons ainsi que c’est la possibilité d’appliquer les mathématiques, dans la formulation des lois physiques, qui garantit la connaissance inductive.

Within the metaphysics of quantity, the debate rages between Absolutism and Comparativism. In retrospect, Armstrong appears to be an absolutist, for he claims that magnitudes like being 1 kg in mass are intrinsic properties of particulars, in virtue of which relations like being twice as massive as hold. More importantly, his theory is an instance of what I call ‘Radical Absolutism’, for he does not merely argue that relations are grounded in magnitudes, but also tries to explain how they “flow from” the intrinsic features of magnitudes. The goal of the paper is not to support his theory, but to better understand why it fails, and why this must be of concern to contemporary absolutists.

Among those who posit properties, liberals (mostly nominalists) admit abundant, ontologically free properties, which particulars possess whenever they satisfy the same predicate and belong to the same class, however artificial. I call them “L-properties” (for “Liberal”). Some liberals also admit that some few L-properties are natural, while most of them are artificial (the same applies to the corresponding classes). Others (mostly but not only realists) commit to a more discriminating use of the category: properties are sparse, they make for the objective similarities among particulars, and more importantly, they allow to analyze “objective similarity” and “class naturalness” in terms of property-possessing and sharing. They give particulars their “true nature”, and I call them “A-properties” (for “Analytical”). This article provides a defense of this second type of properties, in the particular case of sortals. To that end, a new fact is put forward: that sorts are classes which are natural not as a primitive feature, but in virtue of what the particulars which belong to them are, and which makes them _naturally belong_ to them. I then argue that this fact entails the existence of the desired type of properties, “sortal A-properties”, although leaving open the question of how they should be construed.

Julien Tricard criticizes the traditional formulation of the Problem of Induction, and offers to simplify it. Since Hume, he oughts to demonstrate that “the same causes always produce the same effects”, or that “the laws of nature cannot change over time” (uniformity of nature). First, an historical analysis shows, however, that the notion of causality is not needed to set the problem out. Second, the concept of “laws of nature” is analyzed, proving that laws cannot change over time: either there are unchanging laws in nature, or there is none. Therefore, it is necessary and plainly sufficient, in order to solve the Problem of Induction, to prove that laws of nature, governing natural phenomena, do exist.

Julien Tricard tackles the abductive solution to the problem of induction. In order to best explain the regularities that can be observed in nature, should one assume that they necessarily result from natural laws, without which they would be improbable cosmic coincidences? By examining David Armstrong's and John Foster's versions of this inference, Julien Tricard shows that it is based on the confusion of two incompatible concepts of “regularity”. From this he derives a conception of induction that is neither the empiricists’ factual generalization, nor the abduction of nomic necessities from observed regularities, but the operation of constituting particular facts as regular instances of laws.

By analyzing the successful prediction of the Ω− particle by M. Gell-Mann and Y. Ne'eman (in 1962), I bring to light a so far unexamined role of symmetries in physics. Symmetries within a family of objects or states (here, strongly interacting particles) may be used not only to classify the discovered ones, but also to predict the existence of unobserved ones, as instances of a nomological conjecture. To this end, I criticize previous accounts of Ω−’s episode as involving abductive reasoning or a very problematic, Pythagorean “Reification Principle” (Bangu, 2008), or as a case of heuristic reasoning (Ginammi, 2016; Bueno & French, 2018). I show that an adequate reconstruction of the episode relies on a principle according to which symmetric elements of a mathematical representation must be jointly interpreted, provided that a structuralist, background assumption is made on the represented physical system. I finally show that this rule reveals a nomological use of symmetries, which are used to bring together different states or objects as instances of the same law and to predict unobserved instances, such that mathematics—here, Group Theory—provides us with induction instruments to expand our knowledge of the physical world.

When Goodman put forward his “New Riddle of Induction”, he distinguished if from the old problem of justifying the so-called “Principle of Uniformity of Nature”: proving that the future will resemble the past, and that still standing lawful regularities will continue to hold. He intended to break with these ancient questions, while asking about lawlike generalizations and projectible predicates instead: how are we to separate those generalizations which are rightfully confirmed by their observed instances (i.e. nomological) and those accidental ones which are nonetheless empirically equivalent? One shall not seek a ground for induction anymore, but a criterion for nomological hypothesis. Therefore Goodman’s claim seems twofold: (A) one has to face a second problem of induction, which is distinct from the old one while genuinely being a problem about induction, and (B) this new problem is solvable by a criterion of empirical confirmability, which discriminates nomological from accidental generalizations. We claim that one cannot genuinely (A) face this new problem of induction while (B) looking for such a criterion. Indeed, we argue, when one compares several hypothesis or generalizations on the same observational basis, then they must appear as equally nomological. Conversely, if one is considering hypothesis or generalizations which are not equally nomological, then one is actually unable to compare them on the same observational basis, hence to formulate the “New Riddle”. Therefore the issue raised in (A) cannot be adequately solved in (B). Yet we do accept the claim (A) that a new and distinct problem of induction is to be confronted. Thus we deny that (B) offer an adequate type of solutions to this problem, which we shall finally formulate in a more suitable manner.