In a recent article, Azzouni has argued in favor of a version of formalism according to which ordinary mathematical proofs indicate mechanically checkable derivations. This is taken to account for the quasi-universal agreement among mathematicians on the validity of their proofs. Here, the author subjects these claims to a critical examination, recalls the technical details about formalization and mechanical checking of proofs, and illustrates the main argument with aanalysis of examples. In the author's view, much of mathematical reasoning presents genuine (...) meaning-dependent mathematical characteristics that cannot be captured by formal calculi. ‘…there is a conflict between mathematical practice and the formalist doctrine.’ [Kreisel, 1969, p. 39]. (shrink)

In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that (...) by 1676 Leibniz had already developed an interpretation from which he never wavered, according to which infinitesimals, like infinite wholes, cannot be regarded as existing because their concepts entail contradictions, even though they may be used as if they exist under certain specified conditions—a conception he later characterized as “syncategorematic”. Thus, one cannot infer the existence of infinitesimals from their successful use. By a detailed analysis of Leibniz’s arguments in his De quadratura of 1675–1676, we show that Leibniz had already presented there two strategies for presenting infinitesimalist methods, one in which one uses finite quantities that can be made as small as necessary in order for the error to be smaller than can be assigned, and thus zero; and another “direct” method in which the infinite and infinitely small are introduced by a fiction analogous to imaginary roots in algebra, and to points at infinity in projective geometry. We then show how in his mature papers the latter strategy, now articulated as based on the Law of Continuity, is presented to critics of the calculus as being equally constitutive for the foundations of algebra and geometry and also as being provably rigorous according to the accepted standards in keeping with the Archimedean axiom. (shrink)

I examine several alleged grounds of the principle of sufficient reason in Leibniz’s philosophy. These include the nature of a requisite and a sufficient condition, the nature of truth, and the nature of harmony. I argue that Leibniz does not ground the PSR in any of these ways. Instead, he is committed to a value-based grounds of the PSR: God creates the best possible world, and the fact that the PSR obtains in this world contributes to it being the best. (...) I conclude by considering some objections to this way of grounding the PSR. (shrink)

Editor’s Choice for 21st Anniversary Special Edition. Originally published in British Journal for the History of Philosophy, 7(1) (1999), 57-78.

Leibniz is unclear about the nature of pleasure. In some texts, he describes pleasure as a perception of perfection, while in other texts he describes pleasure as being caused by a perception of perfection. In this article, I disambiguate two senses of “perception of perfection”, which clarifies Leibniz’s considered position. I argue that pleasure is a perception of an increase in a substance’s power which is caused by a substance’s knowledge of a perfection of the universe or God. This reading (...) helps clarify the nature of Leibnizian happiness. Happiness is a cognitive process (akin to a mood), constituted fundamentally out of pleasure, which is grounded in increases in a substance’s power. A rational substance will sustain its happiness so long as it is more powerful than it is weak, and it is engaging in activities that increase its power. (shrink)

Cet article propose une reconstruction du débat wolffien sur l'idéalisme de Leibniz autour de la première réception de la Monadologie de Leibniz. Cette reconstruction impose une relecture de quelques problèmes centraux à ce débat: traduction infidèle d'un terme dans la Monadologie latine ( « le composé » est traduit par « substantia composita »); statut du corps en tant que substance composée; statut des éléments en tant que substances simples dont résultent les corps (et cela contre la conception cartésienne de (...) la substance); statut des notions leibniziennes de perception, force et harmonie préétablie; statut de l'expérience comme procédé ho liste et systématique (contre sa conception et la tabula rasa chez Locke) dans la réception et le système wolffiens. Un examen approfondi des textes fondateurs de cette réception (Bilfinger et Wolff) nous permet de reconsidérer sous un nouvel angle le rapport entre Leibniz et Wolff. (shrink)

El presente trabajo pretende entablar un diálogo crítico entre la historia conceptual y la filosofía de la historia. Por una parte, en lo tocante al supuesto inicio de la “identidad semántica” de la modernidad; por otra, en la propia noción de “saber histórico” y con ella las experiencias históricas colectivas e individuales que lo conforman: no podemos olvidar que el sujeto del saber histórico no es sólo –o fundamentalmente- el estudioso de la historia, sino también quienes “hacen” esa historia o (...) la “padecen” y que también contribuyen a gestar el humus conceptual de una experiencia que se traduce –o debería traducirse- en responsabilidad ética por esos mismos conceptos. La crítica a la filosofía clásica de la historia tiende así la mano a la propuesta de la rehabilitación de una filosofía crítica de la historia, aspectos ambos en los que se presentan como antecedentes diferentes conceptos leibnizianos, como no podía ser de otra manera en un trabajo dedicado a mi querido y extrañado amigo Quintín Racionero –que ya no será lo mismo sin poder discutirlo con él. (shrink)

This article addresses the topic of death and immortality in Leibniz and Diderot. The plaisanterie by Diderot that perception continues after death is compared to Leibniz’ position regarding monad incessancy. This will lead to an analysis of Leibniz’ reasons to defend not only the incessancy, but even the immortality of certain monads.

Hans Jonas developed in ‘Past and Truth’ (1991) a demonstration of the existence of God based on the ‘truth of past things’. And in ‘The Concept of God after Auschwitz’ (1984) he created a new myth of divine self-alienation in order to take away God’s responsibility for human misery. Both these texts were conceived as an alternative to a more Hegelian, objective idealist perspective on theology. This article shows that Jonas’s alternative does not fully succeed in this respect because his (...) arguments bring him back to an idealist perspective. His proof of God is revisited and explained using new insights recently developed by Robert Spaemann, whose interpretation of the proof makes it clear that many important critics of Jonas are too quick to reject his claims. The arguments of Jonas now seem to show a new strength even though they still fail to give an alternative to an objective idealist theological framework. (shrink)

InLeibniz: Perception, Apperception, and Thought, Robert McRae alleges a flat “contradiction” at the heart of Leibniz's doctrine of three grades of monads: bare entelechies characterized by perception; animal souls capable both of perception and of sensation; and rational souls, minds or spirits endowed not only with capacities for perception and sensation but also with consciousness of self or what Leibniz calls “apperception.” Apperception is a necessary condition of those distinctively human mental processes associated with understanding and with reason. Insofar as (...) it is also a sufficient condition of rationality, it is not ascribable to animals. But apperception is a necessary condition of sensation or feeling as well; and animals are capable of sensation, according to Leibniz, who decisively rejected the Cartesian doctrine that beasts are nothing but material automata. “On the one hand,” writes McRae, “what distinguishes animals from lower forms of life is sensation or feeling, but on the other hand apperception is a necessary condition of sensation, and apperception distinguishes human beings from animals”. “We are thus left with an unresolved inconsistency in Leibniz's account of sensation, so far as sensation is attributable both to men and animals”. (shrink)

ABSTRACT: The analytic method by which Descartes established the first principle of his philosophy is a unique cognitive process of direct insight and non-logical inference that differs markedly from the deductive model of noetic apprehension long associated with seventeenth-century rationalism. In this paper, it is shown that the same analytic process is at work in the Third Meditation proof of the innateness of the idea of God, where, however, there are serious doubts about its legitimacy.

This book is an expanded version of Joan Weiner's introduction to Frege's work in the Oxford University Press ‘Past Masters’ series published in 1999. The earlier book had chapters on Frege's life and character, his basic project, his new logic, his definitions of the numbers, his 1891 essay ‘Function and concept’, his 1892 essays ‘On Sinn and Bedeutung’ and ‘On concept and object’, the Grundgesetze der Arithmetik and the havoc wreaked by Russell's paradox, and a final brief chapter on Frege's (...) influence. To this, Weiner has added two further chapters on Frege's dispute with Hilbert on the foundations of geometry and on the three late essays of his ‘Logical investigations’. There is little change to the content of the earlier chapters, but they have been divided into sections, each with its own heading, which makes it easier to find one's way around.With the two additional chapters, the book provides an excellent introduction to Frege's work from his earliest Begriffsschrift , which gives the first presentation of his new logic, to his three late essays , which expound his views on logic, truth, and thought. As in the earlier version, the focus is on the logicist project that dominated Frege's career: the attempt to demonstrate that arithmetic is reducible to logic. In all her writings on Frege, Weiner has been particularly sensitive to the philosophical …. (shrink)

The category of sympathy marks a number of basic divisions in early modern approaches to action explanations, whether for human agency or for change in the wider natural world. Some authors were critical of using sympathy to explain change. They call such principles “unintelligible” or assume they involve “mysterious” action at a distance. Others, including Margaret Cavendish, Anne Conway, and Gottfried Wilhelm Leibniz, appeal to sympathy to capture natural phenomena, or to supply a backbone to their metaphysics. Here I discuss (...) how concerns about sympathetic actions form at least a partial background for differing seventeenth-century conceptions of what it is to explain action. I argue that critics of sympathy generally insist on an “atomistic” approach to action explanation, which makes primitively relational phenomena come out as problematic. Proponents of sympathy, by contrast, allow for a more holistic approach to action explanation, which allows for such basic connections. Hence, divergent attitudes toward sympathetic action in part explain differences in approaches to explanation. I conclude by showing how some of these core concerns fade into the background when in the eighteenth-century sympathy gets psychologised and individualised. (shrink)

Leibniz's well-known thesis that the actual world is just one among many possible worlds relies on the claim that some possibles are incompossible , meaning that they cannot belong to the same world. Notwithstanding its central role in Leibniz's philosophy, commentators have disagreed about how to understand the compossibility relation. We examine several influential interpretations and demonstrate their shortcomings. We then sketch a new reading, the cosmological interpretation, and argue that it accommodates two key conditions that any successful interpretation must (...) satisfy. (shrink)

O autor estuda a noção de liberdade como milagre privado, segundo Leibniz. O homem é capaz de milagres, isto é, ser-se humano é ser-se capaz de liberdade. A vontade livre está sempre inclinada e essa inclinação é justamente a marca da sua indiferença. Nenhuma lei vincula o humano, e por isso é capaz de ser excepcional e de se soltar das amarras que o escravizam às coisas exteriores. A mente humana é capaz de produzir o imprevisível. O humano é, por (...) princípio, capaz de se assenhorear de si e de se determinar ao que de melhor lhe é possível, ainda que na maioria das vezes se deixe afundar no mar das paixões. (shrink)

In his groundbreaking work of 1969, Spinoza's Metaphysics: An Essay in Interpretation, Edwin Curley attacked the traditional understanding of the substance-mode relation in Spinoza, according to which modes inhere in substance. Curley argued that such an interpretation generates insurmountable problems, as had already been claimed by Pierre Bayle in his famous Dictionary entry on Spinoza. Instead of having modes inhere in substance Curley suggested that the modes’ dependence upon substance should be interpreted in terms of (efficient) causation, i.e., as committing (...) Spinoza to nothing over and above the claim that substance is the (efficient) cause of the modes. These bold and fascinating claims generated one of the most important scholarly controversies in Spinoza scholarship of the past thirty-five years. In this paper I argue against Curley’s interpretation and attempt to reestablish the traditional understanding of Spinozistic modes as inhering in God and as predicated of God. I also criticize Curley’s philosophical motivation for suggesting this interpretation. In order to show that, for Spinoza, modes are predicated of - and inhere in - substance, I will proceed in the following manner. First, I will summarize Curley’s arguments against substance-mode inherence and present his alternative interpretation of the substance-mode relation. I will then present what I consider to be the most compelling arguments against Curley’s interpretation. Some of these arguments have already been suggested in the literature of the past thirty years (and by Bayle); however, as far as I know, most of the arguments I will be making are new. In the subsequent section I will respond to objections that Curley and Bayle advance against Spinoza’s view of God as the substratum in which all things inhere. Finally, I will address whether Spinozistic modes are predicated of (and not only inhere in) substance, and whether Spinoza considered modes to be particular properties (or “tropes,” in the jargon of contemporary metaphysics). Since Bayle’s claims will be used both in support of and against Curley’s interpretation, it would be appropriate to say a few introductory words on Bayle’s stance. In his Spinoza entry, Bayle criticizes Spinoza’s claim that all things are modes of God, claiming that it “is the most monstrous hypothesis that could be imagined, the most absurd, and the most diametrically opposed to the most evident notions of our mind.” Bayle, however, has no doubt that when Spinoza claims that all things are modes of God, Spinoza means that all things inhere in God. Curley embraces Bayle’s arguments against Spinoza, but uses them in order to claim that we should not ascribe to Spinoza a view which is allegedly shown by Bayle to be absurd. What we should do, Curley argues, is to reinterpret the substance-mode relation as a relation of causal dependence, which would set Spinoza free from Bayle’s hook. Interestingly, as we shall soon see, Bayle himself discusses and rejects a very similar revisionary interpretation of the substance-mode relation. (shrink)

The paper discusses Leibniz's theory of denominations, expression, and individual notions, the central claim being that the key to many of Leibniz's fundamental theses is to consider his argument, starting from his predicate-in-subject account of truth (that in a true statement the notion of the predicate is contained in that of the subject), against purely extrinsic denominations: this argument shows why there is an internal foundation for all denominations, why everything in the world is interconnected, why each substance expresses all (...) the others, and why every change in the world is reflected as a real, internal change in every substance. (shrink)

In his recent paper, Winch attacks a group of theories he calls cognitivism. These theories agree in holding that ‘the ability to think, both consciously and subconsciously, amounts to an ability to internally manipulate symbolic representations of that which we think about.The relevance of this attack to education is that ‘Cognitivism’ supplies plausible‐looking reasons for thinking that learning can take place without instruction, practice, memorisation or training and its prestige as a theory of learning devalues those activities within education.Its rejection (...) should therefore lead us to re‐examine our need for explicit teacher‐oriented pedagogies’.Cognitivism has led to an emphasis on autonomous learning and a consequent devaluing of the role of overt teaching, ‘the active transmission of knowledge and technique by an authoritative figure’. (shrink)

This article is about Gilles Deleuze's book Le Pli. Leibniz et le Baroque from 1988. It shows how Deleuze's notion of folding captures some basic intuitions in Leibniz and how they relate to each other. To this purpose, I propose five figures, all referring to the same basic fold, all illustrating how the consideration of such figures allows developing central elements of Leibniz's monadology. These figures can help, I hope, alleviate some of the fundamental difficulties in understanding Deleuze's approach to (...) the Monadology from the non-Deleuzian perspective of contemporary Leibniz scholarship and give a sense of the synthetic, explanatory force that Deleuze's notion of folding has in relation to Leibniz's monadological metaphysics. (shrink)

Leibniz is often cited as an authority when it comes to the formulation and answer strategy of the question “Why is there something rather than nothing?” Yet much current research assumes that Leibniz advocates an unambiguous question and strategy for the answer. In this respect, one repeatedly finds the argument in the literature that alternative explanatory approaches to this question violate Leibniz’s intention, since he derives the question from the principle of sufficient reason and also demands a causal explanation to (...) the question. In particular, the new research on non-causal explanatory strategies to the Leibniz question seems to concern this counter-argument. In this paper, however, I will argue that while Leibniz raises the question by means of the principle of sufficient reason, he even favours a non-causal explanatory strategy to the question. Thus, a more accurate Leibniz interpretation seems not only to legitimise but also to support non-causal explanations to the Leibniz question. (shrink)

Spinoza's remarks about consciousness in the Ethics constitute two theories about conscious experience and knowledge. Several remarks, including 3p9 and 4p8, make the point that self knowledge—an especially valuable good for Spinoza—is not available to introspection. We are, as a matter of course, conscious of ourselves, but we do not, as a matter of course, know ourselves. A second group of remarks, all of which occur in part 5 of the Ethics, emphasizes a different point about consciousness and knowledge: the (...) knowledge that distinguishes the minds of the most powerful or virtuous people is conscious. The characterization of human consciousness that underlies both theories is best understood as one on which a wide variety of ideas in human minds are conscious, and the intensity or degree of consciousness of a given idea is a function of its power. For human minds, because the power of any idea derives from the power of its causes and because many ideas have external causes, there are no grounds for taking the intensity of conscious experience to track a mind's power closely. Rather, as the second group of remarks suggests, power in a human mind tracks the degree to which knowledge characterizes a mind's conscious states. (shrink)

Gottfried Wilhelm Leibniz endorses a version of the guise of the good thesis: he holds that whenever we do something intentionally, we do it because it seems good to us. This paper explores Leibniz...

This paper explores the theory of freedom that Emilie du Châtelet advances in her essay “On Freedom.” Using contemporary terminology, we can characterize this theory as a version of agent-causal compatibilism. More specifically, the theory has the following elements: (a) freedom consists in the power to act in accordance with one’s choices, (b) freedom requires the ability to suspend desires and master passions, (c) freedom requires a power of self-motion in the agent, and (d) freedom is compatible with moral necessity (...) but not with physical necessity. While these elements may at first appear disparate, the paper shows that they fit together quite well. The resulting theory is a surprising combination of doctrines that appear to be based on Samuel Clarke’s libertarian account of free will and doctrines that are reminiscent of the compatibilist accounts of John Locke, Anthony Collins, Gottfried Leibniz, and Thomas Hobbes. (shrink)

(2013). Leibniz, Pufendorf, and the Possibility of Moral Self-Governance. British Journal for the History of Philosophy: Vol. 21, No. 2, pp. 281-301. doi: 10.1080/09608788.2012.693064.

Quine’s most important charge against second-, and more generally, higher-order logic is that it carries massive existential commitments. The force of this charge does not depend upon Quine’s questionable assimilation of second-order logic to set theory. Even if we take second-order variables to range over properties, rather than sets, the charge remains in force, as long as properties are individuated purely extensionally. I argue that if we interpret them as ranging over properties more reasonably construed, in accordance with an abundant (...) or deflationary conception, Quine’s charge can be resisted. This interpretation need not be seen as precluding the use of model-theoretic semantics for second-order languages; but it will preclude the use of the standard semantics, along with the more general Henkin semantics, of which it is a special case. To that extent, the approach I recommend has revisionary implications which some may find unpalatable; it is, however, compatible with the quite different special case in which the second-order variables are taken to range over definable subsets of the first-order domain, and with respect to such a semantics, some important metalogical results obtainable under the standard semantics may still be obtained. In my final section, I discuss the relations between second-order logic, interpreted as I recommend, and a strong version of schematic ancestral logic promoted in recent work by Richard Heck. I argue that while there is an interpretation on which Heck’s logic can be contrasted with second-order logic as standardly interpreted, when it is so interpreted, its differences from the more modest form of second-order logic I advocate are much less substantial, and may be largely presentational. (shrink)

This article examines Leibniz's philosophy of causation with the aim of clarifying how causes are related to their effects. I argue that, much like J. L. Mackie's INUS conditions, Leibnizian causes are members of complex causal conditions. More precisely, Leibniz identifies causes with elements of complex causal conditions, where the complex condition as a whole is sufficient for the effect, and the cause is a necessary part of that condition. This conception of causation is able to incorporate Leibniz's many other (...) definitions of ‘cause’, thereby resolving what appear to be internal inconsistencies in his philosophy of science. Introduction The ingredients of causation Causes and conditions Causes as INUS conditions Conclusion. (shrink)

Leibniz's philosophy of time, often seen as a precursor to current forms of relationalism and causal theories of time, has rightly earned the admiration of his more recent counterparts in the philosophy of science. In this article, I examine Leibniz's philosophy of time from a new perspective: the role that tense and non-tensed temporal properties/relations play in it. Specifically, I argue that Leibniz's philosophy of time is best (and non-anachronistically) construed as a non-tensed theory of time, one that dispenses with (...) tensed temporal properties such as past, present, and future. In arguing for this thesis, I focus on the three facets of Leibniz's philosophy most relevant for evaluating his commitment to a B-theory of time: (1) the nature of change, (2) the reality of the future, and (3) the truth-conditions for tensed temporal statements. Despite prima facie evidence to the contrary, I show that a close examination of Leibniz's views on these topics provides compelling evidence for interpreting his philosophy of time as a B-theory of time. (shrink)

The paper investigates possible readings of the later Heisenberg's remarks on the nature of quantum states. It discusses, in particular, whether Heisenberg should be seen as a proponent of the epistemic conception of states – the view that quantum states are not descriptions of quantum systems but rather reflect the state assigning observers' epistemic relations to these systems. On the one hand, it seems plausible that Heisenberg subscribes to that view, given how he defends the notorious "collapse of the wave (...) function" by relating it to a sudden change in the epistemic situation of the observer registering a measured result. On the other hand, his remarks on quantum probabilities as "potentia" or "objective tendencies" are difficult to reconcile with such a reading. The accounts that are attributed to Heisenberg by the different possible readings considered are subjected to closer scrutiny; at the same time, their respective virtues and problems are discussed. _German_ Diese Arbeit untersucht mögliche Lesarten von Heisenbergs späten Bemerkungen über die Natur von Quantenzuständen. Insbesondere wird die Frage diskutiert, ob Heisenberg als Vertreter der epistemischen Auffassung von Quantenzuständen gelten kann – der Idee, dass Quantenzustände nicht Beschreibungen der objektiven Eigenschaften von Quantensystemen sind sondern die epistemischen Beziehungen von Beobachtern zu diesen Systemen widerspiegeln. Einerseits erscheint es plausibel, dass Heisenberg dieser Sichtweise zustimmt, wenn man sich ansieht, wie er den berüchtigten,,Kollaps der Wellenfunktion" verteidigt, indem er ihn mit einer plötzlichen Änderung in der Kenntnis des ein Messergebnis registrierenden Beobachters in Zusammenhang bringt. Andererseits sind seine Bemerkungen über quantenmechanische Wahrscheinlichkeiten als,,Potentia" oder,,objektive Tendenzen" mit einer solchen Lesart nur schwer in Einklang zu bringen. Die Positionen, die Heisenberg den verschiedenen möglichen Lesarten zufolge vertritt, werden eingehenden Untersuchungen unterzogen; gleichzeitig werden ihre jeweiligen Vorzüge und Probleme diskutiert. (shrink)

‘Controversy’ is here introduced as a technical term referring to one aspect of dispute. ‘Controversy’ is here understood as referring to an ongoing antagonistic exchange over a disagreement that cannot be readily resolved by the means at hand. However, the issue is being discussed because the participants believe that the controversy will be resolveable in the framework of a more advanced view which will be generated by the dispute. It is claimed that this ‘controversy’ merits study; it is not claimed (...) that a dispute can be reduced to this aspect. In fact, it is shown that the dispute studied here involved intrigues in which personal and national prejudices served as weapons.The historical case study is a controversy conducted between G. W. Leibniz and Denis Papin. The first topic of the controversy, which began in 1689 and ended in 1691, was the ‘measure of force’, but it soon extended also to fundamental issues of mechanics and science in general: to the epistemological status of conservation laws, to the nature of abstractions in science etc.The study shows that far from being a ‘logomachia’, the ‘vis viva controversy’ reflected two exclusive legitimate interpretations of the conceptual system involved and enhanced both of them, preparing their ‘Aufhebung’ in a more elaborate and comprehensive system.An English translation of a not-yet published ‘Synopsis Controversiae’ by Denis Papin with annotations by Leibniz is attached as an appendix.Author Keywords: Conservation laws; Controversy; G. W. Leibniz; D. Papin; Vis viva. (shrink)

For Kant, the moral law is the causal law of freedom. However, it is not an explanatory causal law. It is instead a causal law of imputation: it is a law according to which we can be held responsible for the actions the law declares necessary; that is, it is a law according to which we can be considered the causes of whether or not we act lawfully. In this way, the moral law makes possible a kind of causality that (...) is a “third thing” between natural necessity and blind chance. This essay traces the origins of this view to the Antinomy of Pure Reason of the first Critique and shows how it is refined in Kant’s foundational texts in practical philosophy of the 1780s and in his reflections on the nature of human evil from the 1790s. (shrink)

The thesis that existence is radically different from the determinacy of an actually existing thing –Kant considers this thesis to be the unsurmountable objection against the cosmological and the ontological argument– is the same thesis that demands a specific explanation of the existence of that actually existing thing. The notion of existence that results from its complete exclusion from the realm of the contents thoroughgoing determined by real predicates requires, thus, precisely because this thoroughness excludes it, a specific reason that (...) explains that in the actually existing thing its own actual existence is in fact united with its own determinacy; that notion of existence, however, cancels at the same time the requirement of a sufficient reason of the existence of what actually exists, and again for the same reason, namely, because since existence is as such excluded from the determinacy of the existing things, it radically differs from the specific realm where determinacy is constituted (that is why existing things are thoroughgoing determined as possible), and, therefore, it invalidates any application to itself of the logical laws that are valid only for the merely possible domain of determinacy. (shrink)