Invariance as a basis for necessity and laws

Australasian Journal of Philosophy, 2004

Journal of Philosophical Theological Research, 2023

Avicenna has aimed to establisha harmonized philosophical system that incorporates logic, epistemology, metaphysics, natural philosophy, and other types of knowledge. Although he has not directly written anything about the metaphysical foundations of science, we believe that there are some implications in his philosophy that could be considered astruthmakers of scientific propositions. As natural law is significantly correlated to "experiment", we will first discuss the epistemological aspect of experiments in Avicennian philosophy. He believes that the observation of a repeated event could lead us to a causal relationship due to the fact that accidental events are neither permanent nor frequent. Following that, the logical approach which corresponds to this epistemology will be introduced. As Avicenna's logic does not directly consider such an approach, we are to derive it from apparently disconnected chapters and then formulate them. It will be indicated that Avicenna has been aware of the differences between propositions that merely refer to existent instances and ones that consider the nature of instances. The latter obviously could refer to both existent instances and hypothetical instances. Finally, we present some points in his metaphysics that could establisha metaphysical basis for propositions concerning natural law. In addition, we will indicate that Avicenna's system is able to justify the counterfactual conditionals that relate to laws of nature.

Metascience: A Journal for history, Philosophy and Social Studies of Science

Synthese

A common feature of all standard theories of the laws of nature is that they are ‘absolutist’: They take laws to be either all metaphysically necessary or all contingent. Science, however, gives us reason to think that there are laws of both kinds, suggesting that standard theories should make way for ‘non-absolutist’ alternatives: theories which accommodate laws of both modal statuses. In this paper, we set out three explanatory challenges for any candidate non-absolutist theory, and discuss the prospects of the two extant candidates in light of these challenges. We then develop our own non-absolutist theory, the essentialist DTA account, which combines the nomic-necessitation or DTA account with an essentialist approach to metaphysical modality in order to meet the three explanatory challenges. Finally, we argue that the distinction between kinematical and dynamical laws found in physical theories supports both non-absolutism in general and our proposed essentialist DTA view in pa...

Ratio, 2005

Those who favour an ontology based on dispositions are thereby able to provide a dispositional essentialist account of the laws of nature. In part 1 of this paper I sketch the dispositional essentialist conception of properties and the concomitant account of laws. In part 2, I characterise various claims about the modal character of properties that fall under the heading 'quidditism' and which are consequences of the categoricalist view of properties, which is the alternative to the dispositional essentialist view. I argue that quidditism should be rejected. In part 3, I address a criticism of a strong dispositional essentialist view, viz. that 'structural' (i.e. geometrical, numerical, spatial and temporal) properties must be regarded as categorical.

PROBLEMS FROM ARMSTRONG, Acta Philosophica Fennica 84, Helsinki 2008. Eds. Tim De Mey and Markku Keinänen.

Journal of Philosophy, 2015

The essay discusses a recurrent criticism of the isomorphism-invariance criterion for logical terms, according to which the criterion pertains only to the extension of logical terms, and neglects the meaning, or the way the extension is fixed. A term, so claim the critics, can be invariant under isomorphisms and yet involve a contingent or a posteriori component in its meaning, thus compromising the necessity or apriority of logical truth and logical consequence. This essay shows that the arguments underlying the criticism are flawed since they rely on an invalid inference from the modal or epistemic status of statements in the metalanguage to that of statements in the object-language. The essay focuses on McCarthy’s version of the argument, but refers to Hanson and McGee’s versions as well.

This work discusses the relevance of transcendent universals for different non-Humean theories on natural laws. These theories are: (i) theories that consider natural laws to be either ontologically dependent on primitive counterfactual facts, or theories that consider natural laws as themselves ontologically primitive; and (ii) theories that consider natural laws to be dependent on universals. In both cases (i) and (ii), laws are supposed to have a specific modal character. It is contended that in case (i) this modal character requires a connection with complexions of universals, as modal facts require universals (or so it is maintained). Thus it is more plausible to think of laws as dependent on universals, as in theories of type (ii). In theories of type (ii), furthermore, modal facts seem to require the acceptance of non-instantiated universals. In effect, the existence of a law implies the existence of the universals that are connected within it. As laws seem to exist in possible worlds where the universals that appear therein are not instantiated, non-instantiated universals seem to exist.

The Philosophical Quarterly, 2021

This paper shows how a niche account of the metaphysics of laws of nature and physical properties—the Powers-BSA—can underpin both a sense in which the laws are metaphysically necessary and a sense in which it is true that the laws could have been different. The ability to reconcile entrenched disagreement should count in favour of a philosophical theory, so this paper constitutes a novel argument for the Powers-BSA by showing how it can reconcile disagreement about the laws’ modal status. This paper also constitutes a defence of modal necessitarianism, the interesting and controversial view according to which all worlds are nomologically identical, because it shows how the modal necessitarian can appease the orthodox contingentist about laws.

Analysis, 2005

I show that Armstrong's view of laws as second-order contingent relations of 'necessitation' among categorical properties faces a dilemma. The necessitation relation confers a relation of extensional inclusion ('constant conjunction') on its relata. It does so either necessarily or contingently. If necessarily, it is not a categorical relation (in the relevant sense). If contingently, then an explanation is required of how it confers extensional inclusion. That explanation will need to appeal to a third-order relation between necessitation and extensional inclusion. The same dilemma reappears at this level. Either Armstrong must concede that some properties are not categorical but have essential powers -or he is faced with a regress.

2019

Properties and relations in general have a certain degree of invariance, and some types of properties/relations have a stronger degree of invariance than others. In this paper I will show how the degrees of invariance of different types of properties are associated with, and explain, the modal force of the laws governing them. This explains differences in the modal force of laws/principles of different disciplines, starting with logic and mathematics and proceeding to physics and biology.

1. The problem of identii cation and the problem of inference A main issue in the literature on laws is to dee ne criteria which would permit to distinguish genuine lawlike propositions from universally true propositions which describe merely accidental or fortuitous regularities in the world, such as all gold objects have a mass inferior to fty tons, to reformulate a well-known example due to Hans Reichenbach. This is the epistemological problem of identii cation. The challenge here is to formulate criteria, in the sense of suff cient conditions at least, which would justify attributing the title of law to a universally true proposition. If those criteria are satiss ed by the proposition, then we know that it is a law and that it does not just happen to be accidentally true. This is the task that Humean regularists set to themselves. Since, for them, lawlike propositions describe worldly regularities, their aim is to nd criteria which are consistent with their empiricist position and to refrain from introducing ingredients which would go beyond the realm of what is empirically accessible. In other words, serious empiricists are required to shun any kind of metaphysics. As we will see such endeavor is fraught with all sorts of diff culties. On this I agree with van Fraassen who is, in his own words, a " immoderate empiricist " (2000, 1660) and consistently sustains that there are no laws, in the sense that the search for empirically satisfactory criteria which would divide regularities into two distinct classes, lawful and unlawful, is bound to fail. Simply because there is no empirical fact, that is, some empirically detectable special kind of regularities, which would legitimate endowing the propositions which describe them with the title of law. Surely, some regularities are more general than others, but they all are regularities in the rst place and no empirical feature is available which would permit to single out some regularities and endow them with some privileged status. This is why the empiricists who would like to retain the distinction between laws and non-laws, just as scientists do, attempted to devise criteria which are internal to

The Semantic Conception of Logic: Essays on Consequence, Invariance, and Meaning. Eds. G. Sagi & J. Woods. Cambridge University Press, 2020

Although the invariance criterion of logicality first emerged as a criterion of a purely mathematical interest, it has developed into a criterion of considerable linguistic and philosophical interest. In this paper I compare two different perspectives on this criterion. The first is the perspective of natural language. Here, the invariance criterion is measured by its success in capturing our linguistic intuitions about logicality and explaining our logical behavior in natural-linguistic settings. The second perspective is more theoretical. Here, the invariance criterion is used as a tool for developing a theoretical foundation of logic, focused on a critical examination, explanation, and justification of its veridicality and modal force.

Mind, 2009

In philosophical logic necessity is usually conceived as a sentential operator rather than a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalised if necessity is formalised by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds-semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. * We thank Raf De Clercq, Leon Horsten, Hannes Leitgeb, Tim Williamson and two anonymous referees of Mind for useful comments and suggestions.