This paper will look at three closely interrelated questions about necessary a posteriori identities, in particular concerning natural kinds. First-ly, what is the semantic phenomenon responsible for a posteriori necessities in general, and theoretical identity statements concerning natural kinds in particular? I will argue that (contrary to what is often assumed) rigidity, as it is usually defined, cannot do the job for theoretical identity statements. Rather, a posteriori necessities are grounded in a (meta)semantic phenomenon that I have in earlier work called actuality-dependence. Secondly, what is the basis for this semantic phenomenon? In other words, what makes a given expression actuality-dependent, and thereby fit for appearing in a posteriori necessities? I will argue that actuality-dependence is grounded in our linguistic patterns and dispositions of application and interpretation. Thirdly and finally, what does this tell us about what essences are, and how we possess knowledge of them? I will claim that the view I am proposing gives direct support to a conferralist view of essences, at least when it comes to natural kinds. Moreover, the explanation of a posteriori necessities does not rely on independent essentialist premises; however, it does rely on essentialist beliefs or expectations on the part of ordinary speakers.

There are several forms of four-dimensionalism. In this paper, I propose a version of four-dimensionalism called four-dimensional mereology (4DM). To investigate ontological problems, it is important to clarify epistemological problems that are closely related to ontological positions. According to the static view of time, change takes place within time, but time itself doesn’t change, and time merely separates events temporally, as space separates them spatially. However, according to the dynamic view of time, time really does pass, and the world is caught up in a process of purely temporal change. In this paper, I show that the static view of time is right from the ontological viewpoint (i.e. the external viewpoint), whereas the dynamic view of time is right from the epistemological viewpoint (i. e. the internal viewpoint). You may ask which of these two views are real. However, this question is misleading. The universe can be described from several different viewpoints. The internal and the external description give important information about certain parts of the universe and these two descriptions can be correlated and combined. They do not conflict each other, when we compare them in a proper manner. Both descriptions help us to understand the reality of the universe and to interpret ourselves as parts of the universe.

In his recent book Peirce and the Threat of Nominalism, Paul Forster (2011) presented how Peirce understood the nominalist scruple to individualise concepts for collections at the cost of denying properties of true continua. In that process Peirce showed some vibrant problems, as for example, the classic one of universals. Nonetheless that work is still incomplete; as long as that should be adequately related with what Peirce called his ‘scholastic realism’. Continuity is started by the theory of multitude and frees his analysis from any constraints of the nominalist theories of reality as integrated by incognizable things-in-themselves. His theory of multitude, instead, can be derived with mathematics: By drawing in the work of the ways of abstraction in diagrammatic reasoning made by Sun Jo Shin (2010) and in continuum theories by Cathy Legg (2010) I will show the device of diagrammatic reasoning as a plausible pragmatic tool to represent those continua and make sense of his scholastic realism. The analysis of continuity is a perfect example of how the method of diagrammatic reasoning helps unblock the road of philosophical inquiry and also helps to clarify other problems as, for example, the applicability of Mathematics. General concepts define continua, and, while the properties of true continua are not reducible to properties of the individuals they comprise, they are still intelligible and necessary to ground any science of inquiry.

During the 9th century Aristotle’s Metaphysics was translated for the first time from Greek into Arabic by Ustâth, at the request of al-Kindî and, afterwards, the interest of the Arab world in this oeuvre grew with the production of several translations, comments and paraphrases of the work. Among the books which compose the Metaphysics, one of the most studied was book Epsilon. In particular Arab philosophers focused their interest on the passage of Ε1, which contains a classification of the theoretical sciences (1026a13-1026a16), founded on the degree of immateriality and of separation from the matter of their object. Aristotle states: “Natural science deals with things which are inseparable from matter but not immovable, and some parts of mathematics deal with things which are immovable, but probably not separable, but are embodied in matter; while the first science deals with things which are both separable and immovable”. According to the Arab exegetes, Aristotle introduces here the doctrine of the three degrees of abstraction, on the base of which the object of first philosophy is the most abstract among the beings, both from the conceptual point of view and from the real one. This interpretation of the Aristotelian text – already present in Avicenna – had a huge influence on the Latin Middle Ages and on modern philosophy.

I have two main objectives in this paper. First, I attempt to make sense of the Aristotelian notion of infinity or the notion of potential infinity. I show that the so-called notion of “potential infinity” should be understood as the notion of infinite potentialities. Second, I consider how well different theories of modality may fare as accounts of the notion of potential infinity (i.e. the notion of infinite potentialities). I discuss well-known theories of modality such as genuine modal realism, ersatz modal realism, and modalism. Then I introduce my own theory of modality, modal quantificationalism. I argue that only modal quantificationalism offers an adequate formulation of the notion of potential infinity.

This article tries to establish the relevance of phenomenological analysis within the current epistemological edifice, in particular, with regard to certain key issues of the epistemology of our time, this last one meant as a philosophy of science. In doing so, it is primarily based, on the one hand, on certain Husserlian texts mainly those published in Logical Investigations, Formal and Transcendental Logic and the Phenomenology of Time Consciousness and, on the other, on certain developments, essentially running from the beginning of 20th century, in such diverse fields of positive science as logic and the foundations of mathematics as well as quantum mechanics. The overall argumentation serves to establish a holistic approach of the objects of knowledge, taken as material or mental ones, to the extent that they may be taken as objects in evident presentation in front of an embodied consciousness provided with certain a priori constitutional modes.