This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential account of conditionals offered by Crupi and Iacona. As will be shown, in a first-order language that contains a naïve truth predicate and a suitable conditional, one can define a validity predicate in accordance with the thesis that the inference from a conjunction of premises to a conclusion is valid when the corresponding conditional is true. The validity (...) predicate so defined significantly increases our expressive resources and provides a coherent formal treatment of paradoxical arguments. (shrink)

This paper investigates Ockhamism from a metaphysical point of view. Its main point is that the claim that future contingents are true or false is less demanding than usually expected, as it does not require particularly contentious assumptions about the future. First it will be argued that Ockhamism is consistent with a wide range of metaphysical views. Then it will be shown that each of these views leaves room for the claim that the future is open, at least on some (...) plausible interpretations of that claim. (shrink)

This paper discusses some key connexive principles construed as principles about reasons, that is, as principles that express logical properties of sentences of the form ‘_p_ is a reason for _q_’. Its main goal is to show how the theory of reasons outlined by Crupi and Iacona, which is based on their evidential account of conditionals, yields a formal treatment of such sentences that validates a restricted version of the principles discussed, overcoming some limitations that affect most extant accounts (...) of conditionals. (shrink)

This paper explores an idea of Stoic descent that is largely neglected nowadays, the idea that an argument is valid when the conditional formed by the conjunction of its premises as antecedent and its conclusion as consequent is true. As it will be argued, once some basic features of our naıve understanding of validity are properly spelled out, and a suitable account of conditionals is adopted, the equivalence between valid arguments and true conditionals makes perfect sense. The account of validity (...) outlined here, which displays one coherent way to articulate the Stoic intuition, accords with standard formal treatments of deductive validity and encompasses an independently grounded characterization of inductive validity. (shrink)

In some recent works, Crupi and Iacona have outlined an analysis of ‘if’ based on Chrysippus’ idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic.

.This paper discusses Aristotle’s thesis and Boethius’ thesis, the most distinctive theorems of connexive logic. Its aim is to show that, although there is something plausible in Aristotle’s thesis and Boethius’ thesis, the intuitions that may be invoked to motivate them are consistent with any account of indicative conditionals that validates a suitably restricted version of them. In particular, these intuitions are consistent with the view that indicative conditionals are adequately formalized as strict conditionals.

This paper addresses the question whether future contingents are knowable, that is, whether one can know that things will go a certain way even though it is possible that things will not go that way. First I will consider a long-established view that implies a negative answer, and draw attention to some endemic problems that affect its credibility. Then I will sketch an alternative line of thought that prompts a positive answer: future contingents are knowable, although our epistemic access of (...) them is limited in some important respects. (shrink)

This paper outlines an account of conditionals, the evidential account, which rests on the idea that a conditional is true just in case its antecedent supports its consequent. As we will show, the evidential account exhibits some distinctive logical features that deserve careful consideration. On the one hand, it departs from the material reading of ‘if then’ exactly in the way we would like it to depart from that reading. On the other, it significantly differs from the non-material accounts which (...) hinge on the Ramsey Test, advocated by Adams, Stalnaker, Lewis, and others. (shrink)

This paper articulates in formal terms a crucial distinction concerning future contingents, the distinction between what is true about the future and what is reasonable to believe about the future. Its key idea is that the branching structures that have been used so far to model truth can be employed to define an epistemic property, credibility, which we take to be closely related to knowledge and assertibility, and which is ultimately reducible to probability. As a result, two kinds of claims (...) about future contingents—one concerning truth, the other concerning credibility—can be smoothly handled within a single semantic framework. (shrink)

This paper claims that there is no such thing as the correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and semantics. The first part of the paper outlines the thesis that a unique notion of logical form fulfils both roles, and argues that the alleged best candidate for making it true is unsuited for one of the two roles. (...) The second part spells out a considerably different notion which is free from that problem, although it does not fit the other role. As it will be suggested, each of the two notions suits at most one role, so the uniqueness thesis is ungrounded. (shrink)

This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.

This paper investigates the logic of Ockhamism, a view according to which future contingents are either true or false. Several attempts have been made to give rigorous shape to this view by defining a suitable formal semantics, but arguably none of them is fully satisfactory. The paper draws attention to some problems that beset such attempts, and suggests that these problems are different symptoms of the same initial confusion, in that they stem from the unjustified assumption that the actual course (...) of events must be represented in the semantics as a distinguished history, the Thin Red Line. (shrink)

According to the analysis of concessive conditionals suggested by Crupi and Iacona, a concessive conditional \(p{{\,\mathrm{\hookrightarrow }\,}}q\) is adequately formalized as a conjunction of conditionals. This paper presents a sound and complete axiomatic system for concessive conditionals so understood. The soundness and completeness proofs that will be provided rely on a method that has been employed by Raidl, Iacona, and Crupi to prove the soundness and completeness of an analogous system for evidential conditionals.

Among the various motivations that may lead to the idea that truth is relative in some non-conventional sense, one is that the idea helps explain how there can be ‘‘ faultless disagreements’’, that is, situations in which a person A judges that p, a person B judges that not-p, but neither A nor B is at fault. The line of argument goes as follows. It seems that there are faultless disagreements. For example, A and B may disagree on culinary matters (...) without either A or B being at fault. But standard semantics has no room for such a case, so there is something wrong with standard semantics. The best way to amend it is to add a new parameter that is relevant to the truth or falsity of what A and B judge, presumably, something related to personal taste. The aim of the paper is to show that this line of argument is flawed. It is true that standard semantics has no room for faultless disagreements. But there is nothing wrong with this, for it should not be assumed that such disagreements exist. (shrink)

This paper raises some questions about the formalization of sentences containing ‘if’ or similar expressions. In particular, it focuses on three kinds of sentences that resemble conditionals in some respects but exhibit distinctive logical features that deserve separate consideration: whether-or-not sentences, biscuit conditionals, and concessive conditionals. As will be suggested, the examples discussed show in different ways that an adequate formalization of a sentence must take into account the content expressed by the sentence. This upshot is arguably what one should (...) expect on the view that logical form is determined by truth conditions. (shrink)

In the intriguing article The puzzle of the changing past, Barlassina and Del Prete argue that, if one grants a platitude about truth and accepts a simple story that they tell, one is forced to conclude that the past has changed. I will suggest that there is a coherent way to resist that conclusion. The platitude about truth is in fact a platitude, but the story is not exactly as they tell it.

This paper defends the thesis that counterfactuals are strict conditionals. Its purpose is to show that there is a coherent view according to which counterfactuals are strict conditionals whose antecedent is stated elliptically. Section 1 introduces the view. Section 2 outlines a response to the main argument against the thesis that counterfactuals are strict conditionals. Section 3 compares the view with a proposal due to Aqvist, which may be regarded as its direct predecessor. Sections 4 and 5 explain how the (...) view di ers from the theories of counterfactuals advocated by Stalnaker and Lewis, and from some contextualist strict conditional accounts of counterfactuals that have emerged recently. Finally, section 6 addresses the thorny issue of disjunctive antecedents. (shrink)

This paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging (...) puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences. (shrink)

This paper is intended to show that, at least in a considerably wide class of cases, indicative conditionals are adequately formalized as strict conditionals. The first part of the paper outlines three arguments that support the strict conditional view, that is, three reasons for thinking that an indicative conditional is true just in case it is impossible that its antecedent is true and its consequent is false. The second part of the paper develops the strict conditional view and defends it (...) from some foreseeable objections. (shrink)

A fairly simple theory of the semantics of tense is obtained by combining three claims: (i) for any time t, a present-tense sentence `p' is either true or false at t; (ii) for any time t0 earlier than t, the future-tense sentence `It will be the case that p at t' is true at t0 if `p' is true at t, false otherwise; (iii) for any time t0 later than t, the past-tense sentence `It was the case that p at (...) t' is true at t0 if `p' is true at t, false otherwise. This theory, which has been called the theory of timeless truth, is often dismissed on the basis of its alleged incapacity to comply with indeterminism. Here, instead, it will be suggested that there is no reason to be dismissive. Section 1 provides some elucidations about the theory. Sections 2 and 3 explain how a foregone objection to it can be resisted. Sections 4 and 5 show that there is a plausible sense in which (i)-(iii) are compatible with indeterminism. Sections 6 and 7 dispel some misunderstandings that may lead to think that indeterminism is not vindicated in some important sense other than that outlined. (shrink)

This paper outlines an account of concessive conditionals that rests on two main ideas. One is that the logical form of a sentence as used in a given context is determined by the content expressed by the sentence in that context. The other is that a coherent distinction can be drawn between a reading of ‘if’ according to which a conditional is true when its consequent holds on the supposition that its antecedent holds, and a stronger reading according to which (...) a conditional is true when its antecedent supports its consequent. As we will suggest, the logical form of concessive conditionals can be elucidated by relying on this distinction. (shrink)

There are essentially two ways to develop the Peircean idea that future contingents are all false. One is to provide a quantificational semantics for "will," as is usually done. The other is to define a quantificational postsemantics based on a linear semantics for "will." As we will suggest, the second option, although less conventional, is more plausible than the first in some crucial respects. The postsemantic approach overcomes three major troubles that have been raised in connection with Peirceanism: the apparent (...) scopelessness of "will" with respect to negation, the failure of Future Excluded Middle, and the so-called zero credence problem. (shrink)

This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinction which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it outlines some implications of the account provided (...) which bear on three debated issues concerning quantification. (shrink)

In a paper called 'Definiteness and Knowability', Tim Williamson addresses the question whether one must accept that vagueness is an epistemic phenomenon if one adopts classical logic and a disquotational principle for truth. Some have suggested that one must not, hence that classical logic and the disquotational principle may be preserved without endorsing epistemicism. Williamson’s paper, however, finds ‘no plausible way of substantiating that possibility’. Its moral is that ‘either classical logic fails, or the disquotational principle does, or vagueness is (...) an epistemic phenomenon’. The moral of this paper, on the contrary, is that there is a plausible way of substantiating that possibility. The option it contemplates looks like a view that Williamson dismisses at the beginning of his paper, and that others regard as unworthy of serious consideration. (shrink)

A widely accepted claim about counterfactuals is that they differ from strict conditionals, that is, there is no adequate representation of them as sentences of the form   . To justify this claim, Stalnaker and Lewis have argued that some fallacious inferences would turn out valid if counterfactuals were so represented. However, their argument has a flaw, as it rests on a questionable assumption about the relation between surface grammar and logical form. Without that assumption, no consequence of the (...) alleged kind is obtained, hence the claim may be rejected. (shrink)

This paper deals with the logical form of quantified sentences. Its purpose is to elucidate one plausible sense in which quantified sentences can adequately be represented in the language of first-order logic. Section 1 introduces some basic notions drawn from general quantification theory. Section 2 outlines a crucial assumption, namely, that logical form is a matter of truth-conditions. Section 3 shows how the truth-conditions of quantified sentences can be represented in the language of first-order logic consistently with some established undefinability (...) results. Section 4 sketches an account of vague quantifier expressions along the lines suggested. Finally, section 5 addresses the vexed issue of logicality. (shrink)

This paper deals with the problem of future contingents, and focuses on two classical logical principles, excluded middle and bivalence. One may think that different attitudes are to be adopted towards these two principles in order to solve the problem. According to what seems to be a widely held hypothesis, excluded middle must be accepted while bivalence must be rejected. The paper goes against that line of thought. In the first place, it shows how the rejection of bivalence leads to (...) implausible consequences if excluded middle is accepted. In the second place, it addresses the question of why one should reject bivalence, and finds no satisfactory answer. /// Este artículo trata el problema de los futuros contingentes, y se enfoca en dos principios lógicos clásicos: el tercero excluido y la bivalencia. Se podría pensar que una solución del problema requiere actitudes diferentes hacia estos dos principios. Según una hipótesis que parece ampliamente compartida, el tercero excluido debe ser aceptado, mientras que la bivalencia debe ser rechazada. Este artículo argumenta en contra de esta línea de pensamiento. En primer lugar, se aborda cómo el rechazo de la bivalencia lleva a consecuencias poco plausibles si el tercero excluido es aceptado. En segundo lugar, se enfrenta la cuestión de por qué se debería rechazar la bivalencia, sin encontrar una respuesta satisfactoria. (shrink)

Once upon a time, some thought that indicative conditionals could be effectively analyzed as material conditionals. Later on, an alternative theoretical construct has prevailed and received wide acceptance, namely, the conditional probability of the consequent given the antecedent. Partly following critical remarks recently ap- peared in the literature, we suggest that evidential support—rather than conditional probability alone—is key to understand indicative conditionals. There have been motivated concerns that a theory of evidential conditionals (unlike their more tra- ditional counterparts) cannot generate (...) a sufficiently interesting logical system. Here, we will describe results dispelling these worries. Happily, and perhaps surprisingly, appropriate technical variations of Ernst Adams’s classical approach allow for the construction of a logic of evidential conditionals with distinctive fea- tures, which is also well-behaved and reasonably strong. (shrink)

In my book Logical Form I outline some reasons for thinking that, in the sense of «logical form» that matters to logic, logical form is determined by truth conditions. This paper compares three theories of propositions that might be employed to substantiate the underlying notion of truth conditions: the naturalized propositions theory, the truthmaker theory, and the classificatory theory. Its aim is to show that, while the naturalized propositions theory and the truthmaker theory accord equally well with the idea that (...) logical form is determined by truth conditions, the classificatory theory is more problematic in some respects. (shrink)

This paper outlines a formal account of tensed sentences that is consistent with Ockhamism, a view according to which future contingents are either true or false. The account outlined substantively differs from the attempts that have been made so far to provide a formal apparatus for such a view in terms of some expressly modified version of branching time semantics. The system on which it is based is the simplest quantified modal logic.

Lovers typically entertain two sorts of thoughts about their beloveds. On the one hand, they think that some qualities of their beloveds provide reasons for loving them. Romeo would say that he loves Juliet in virtue of the way she is. On the other hand, they regard their beloveds as irreplaceable. Romeo would never be willing to exchange Juliet with another maiden. Yet it may be asked how these two sorts of thoughts can coherently coexist. If some qualities of Juliet (...) justify Romeo’s love for her, shouldn’t another maiden with the same qualities be equally lovable for him? This paper draws some distinctions that we take to be crucial to the understanding of reasons for love. Its aim is to show that, even though the claim that beloveds as irreplaceable is plausible to some extent, there is at least one interesting sense in which lovers are replaceable. (shrink)

Despite the wide acceptance of standard modal logic, there has always been a temptation to think that ordinary modal discourse may be correctly analyzed and adequately represented in terms of predicates rather than in terms of operators. The aim of the formal model outlined in this paper is to capture what I take to be the only plausible sense in which ‘possible’ and ‘necessary’ can be treated as predicates. The model is built by enriching the language of standard modal logic (...) with a quantificational apparatus that is “substitutional” rather than “objectual”, and by obtaining from the language so enriched another language in which constants for such predicates apply to singular terms that stand for propositions. (shrink)

In this paper I provide five separate responses, one for each of the contributed papers, in order to clarify some crucial aspects of the view defended in my book.

So far, T×W frames have been employed to provide a semantics for a language of tense logic that includes a modal operator that expresses historical necessity. The operator is defined in terms of quantification over possible courses of events that satisfy a certain constraint, namely, that of being alike up to a given point. However, a modal operator can as well be defined without placing that constraint. This paper outlines a T×W logic where an operator of the latter kind is (...) used to express the epistemic property of definiteness. Section 1 provides the theoretical background. Sections 2 and 3 set out the semantics. Sections 4 and 5 show, drawing on established results, that there is a sound and complete axiomatization of the logic outlined. (shrink)

What makes discrimination morally bad? In this paper, we discuss the putative badness of a case of consensual discrimination to show that prominent accounts of the badness of discrimination—appealing, inter alia, to harm, disrespect and inequality—fail to provide a satisfactory answer to this question. In view of this, we present a more promising account.

Sartre’s account of the emotions presupposes a conception of human nature that is never fully articulated. The paper aims to render such conception explicit and to argue that frustration occupies a foundational place in Sartre’s picture of affective existence.

In this paper, we propose a regularity theory of causation. The theory aims to be reductive and to align with our pre‐theoretic understanding of the causal relation. We show that our theory can account for a wide range of causal scenarios, including isomorphic scenarios, omissions, and scenarios which suggest that causation is not transitive.

Human-centered explainable AI (HCXAI) advocates for the integration of social aspects into AI explanations. Central to the HCXAI discourse is the Social Transparency (ST) framework, which aims to make the socio-organizational context of AI systems accessible to their users. In this work, we suggest extending the ST framework to address the risks of social misattributions in Large Language Models (LLMs), particularly in sensitive areas like mental health. In fact LLMs, which are remarkably capable of simulating roles and personas, may lead (...) to mismatches between designers' intentions and users' perceptions of social attributes, risking to promote emotional manipulation and dangerous behaviors, cases of epistemic injustice, and unwarranted trust. To address these issues, we propose enhancing the ST framework with a fifth 'W-question' to clarify the specific social attributions assigned to LLMs by its designers and users. This addition aims to bridge the gap between LLM capabilities and user perceptions, promoting the ethically responsible development and use of LLM-based technology. (shrink)

Affirmative action is standardly pursued in relation to admissions to prestigious universities, in hiring for prestigious jobs, and when it comes to being elected to parliament. Central to these forms of affirmative action is that they have to do with competitive goods. A good is competitive when, if we improve A’s chances of getting the good, we reduce B’s chances of obtaining the good. I call this Competitive Affirmative Action. I distinguish this from Non-competitive Affirmative Action. The latter has to (...) do with non-competitive goods, e.g., being granted early parole or freedom from arbitrary arrest. I argue that some of the most prominent objections against affirmative action—in particular, the reverse discrimination objection and the merit objection—speak less against Non-competitive Affirmative Action. And that some of the most prominent arguments in favor of affirmative action, insofar as they justify Competitive Affirmative Action, also justify Non-competitive Affirmative Action. (shrink)

Research on the ethics of algorithms has grown substantially over the past decade. Alongside the exponential development and application of machine learning algorithms, new ethical problems and solutions relating to their ubiquitous use in society have been proposed. This article builds on a review of the ethics of algorithms published in 2016, 2016). The goals are to contribute to the debate on the identification and analysis of the ethical implications of algorithms, to provide an updated analysis of epistemic and normative (...) concerns, and to offer actionable guidance for the governance of the design, development and deployment of algorithms. (shrink)

The well-known formal semantics of conditionals due to Stalnaker Studies in logical theory, Blackwell, Oxford, 1968), Lewis, and Gärdenfors The logic and 1140 epistemology of scientific change, North-Holland, Amsterdam, 1978, Knowledge in flux, MIT Press, Cambridge, 1988) all fail to distinguish between trivially and nontrivially true indicative conditionals. This problem has been addressed by Rott :345–370, 1986) in terms of a strengthened Ramsey Test. In this paper, we refine Rott’s strengthened Ramsey Test and the corresponding analysis of explanatory relations. We (...) show that our final analysis captures the presumed asymmetry between explanans and explanandum much better than Rott’s original analysis. (shrink)

In this paper, we analyse actual causation in terms of production. The latter concept is made precise by a strengthened Ramsey Test semantics of conditionals: \ iff, after suspending judgement about A and C, C is believed in the course of assuming A. This test allows us to verify or falsify that an event brings about another event. Complementing the concept of production by a weak condition of difference-making gives rise to a full-fledged analysis of causation.

According to relational egalitarianism, justice requires equal relations. In this paper, I ask the question: can equal relations be unjust according to relational egalitarianism? I argue that while on some conceptions of relational egalitarianism, equal relations cannot be unjust, there are conceptions in which equal relations can be unjust. Surprisingly, whether equal relations can be unjust cuts across the distinction between responsibility-sensitive and non-responsibility-sensitive conceptions of relational egalitarianism. I then show what follows if one accepts a conception in which equal (...) relations can be unjust, including why it provides a reason to grant some people less political power than others. (shrink)

According to Arti Dhand, it can be argued that all Indian ethics have been primarily virtue ethics. Many have indeed jumped on the virtue bandwagon, providing prima facie interpretations of Hindu, Jain, and Buddhist canons in virtue terms. Others have expressed firm skepticism, claiming that virtues are not proven to be grounded in the nature of things and that, ultimately, the appeal to virtue might just well be a mere façon de parler. In this paper, we aim to advance the (...) discussion of Indian virtue ethics. Our intent is not to provide a catch-all interpretation of the different Indian schools. Our goal is, more modestly, to offer a theory of virtues in Indian philosophies, as a framework for theorists and interpreters who see these diverse traditions as amenable to systematic virtue analysis. Our theory grounds virtues in the reality of genuine moral dispositions and in a system of beliefs where morality is understood as transformative in nature. (shrink)

As Peter Niebyl has documented, one of the issues in which the Wittenberg-based physician and philosopher Daniel Sennert (1572–1637) departed from Paracelsus and his followers was the concept of disease. Paracelsus and some of his followers regarded diseases as real beings—so-called “disease-entities” (entia morbis) that can enter into the body of a living being and thereafter possess a clearly defined location in the affected organism. 1 For Sennert, such a view is a dangerous confusion between disease and its causes. According (...) to him, causes of disease can be present in an organism without actually causing a disease (Sennert 1629, p. 253). Moreover, he shares the traditional Christian doctrine .. (shrink)

Powers, capacities and dispositions (in what follows I will use these terms synonymously) have become prominent in recent debates in metaphysics, philosophy of science and other areas of philosophy. In this paper I will analyse in some detail a well-known argument from scientific practice to the existence of powers/capacities/dispositions. According to this argument the practice of extrapolating scientific knowledge from one kind of situation to a different kind of situation requires a specific interpretation of laws of nature, namely as attributing (...) dispositions to systems. My main interest will be to discuss what characteristics these dispositions need to have in order to account for the scientific practice in question. I will furthermore assess whether the introduction of dispositions in the context of the extrapolation argument can be described as a ‘revitalization’ or as a ‘return’ to those notions repudiated by early modern philosophers. More particularly I will argue for the following claims: I. In repudiating scholastic terminology, including substantial forms with their causal powers, post-cartesian philosophers focussed on a concept of causation that was much stronger than 21st century conceptions of causation. For this reason alone, whatever ‘causal’ is supposed to mean in today’s causal powers, embracing causal powers is not a simple return to a pre-cartesian notion. II. The dispositions presupposed in scientific practice need not (and should not) be construed in causal terms (whether strong or weak). III. While some early modern philosophers contrasted the characterisation of the natural world in terms of substantial forms (and their causal powers) on the one hand and a mathematical characterization on the other and suggested that these approaches are incompatible, the dispositions postulated by the extrapolation argument to account for scientific practice are themselves characterized in mathematical terms. More precisely: The behaviour the systems are disposed to display is – at least in physics – often characterized in mathematical terms. IV. The dispositions assumed in the law-statements in scientific practice are determinable rather than determinate properties. (shrink)

Andrea Cesalpino is an important figure in the history of science. He demonstrated that blood circulates into heart from veins and from the heart to arteries, paving the way to Harvey’s complete description of blood circulation. Moreover, he was the founder of botany as a systematic discipline, which he based, rather than on the observation of accidental similarities of plants, on the discovery of their vegetative-generative principle. In philosophy, he attempted to conciliate the immortality of the soul (i.e., the (...) form of the body) with the existence of a unique immaterial intellect, which is individuated and multiplied in the singular souls that participate to it. (shrink)