Justice Across Ages offers an attractive account of justice between the young and the old that brings together three notable principles of age-group justice: complete-lives equality, relational equality, and prudence. Yet, the book says little about the fact that many of us live longer than others, and the little it does say casts doubt on whether lifespan inequality threatens justice as construed by the three principles. This essay argues, instead, that theories of justice between the young and the old should (...) not dispense with a conception of justice between different longevity groups. It concludes that we must be sensitive to lifespan variations when designing policies to promote justice across age groups. (shrink)

The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric figures of ancient Greek practical (...) geometry. Then, we propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of the geometric objects of Euclidean geometry. The models are based on the hub-and-spoke theory. In our view, the existence of specific models opens the possibility of addressing the relationship between geometric figures and geometric objects, in a novel way, in terms of their neural representation. (shrink)

It seems plausible that successfully communicating with our peers requires entertaining the same thoughts as they do. We argue that this view is incompatible with other, independently plausible principles of thought individuation. Our argument is based on a puzzle inspired by the Kripkean story of Peter and Paderewski: having developed several variations of the original story, we conclude that understanding and communication cannot be modeled as a process of thought transfer between speaker and hearer. While we are not the first (...) to reach this conclusion, the significance of our argument lies in the fact that it only relies on widely accepted premises, without depending on any especially controversial theory of mental and linguistic content. We conclude by drawing out the implications of that conclusion: if communication and understanding do not require thought identity, then one important motivation for the postulation of inter-personally shared thoughts is undercut. (shrink)

In recent years, the biomedical field has witnessed the emergence of novel tools and modelling techniques driven by the rise of the so-called Big Data. In this paper, we address the issue of predictability in biomedical Big Data models of cancer patients, with the aim of determining the extent to which computationally driven predictions can be implemented by medical doctors in their clinical practice. We show that for a specific class of approaches, called k-Nearest Neighbour algorithms, the ability to draw (...) predictive inferences relies on a geometrical, or topological, notion of similarity encoded in a well-defined metric, which determines how close the characteristics of distinct patients are on average. We then discuss the conditions under which the relevant models can yield reliable and trustworthy predictive outcomes. (shrink)

This chapter discusses what maximin egalitarians should think about two types of age-sensitive taxation. One is a form of cumulative income taxation, which taxes yearly incomes taking into account all earlier income years instead of only the last one. The second is age-differentiated taxation, which taxes yearly incomes adjusting the rate to the taxpayer’s age. The chapter first presents the main reasons supporting cumulative income taxation and then proceeds to look at how it affects fiscal obligations across life. Then it (...) argues that egalitarians should aim at a fiscal reform that benefits the young and the elderly but not the middle-aged. Finally, it questions whether cumulative income taxes can deliver this without resorting to age-differentiated taxes. The chapter shows that while cumulative income taxation can benefit the young, age-differentiated taxes are necessary to benefit the elderly. (shrink)

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)

Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as a more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena (...) that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory. (shrink)

I discuss a criterion for successful communication between a speaker and a hearer put forward by Buchanan according to which there is communicative success only if the hearer entertains, as a result of interpreting the speaker's utterance, a thought that has the same truth conditions as the thought asserted by the speaker and, furthermore, does so in virtue of recognizing the speaker's communicative intentions. I argue, against Buchanan, that the data on which it is based are compatible with a view (...) involving Fregean modes of presentation. In the second part of the article I critically discuss Unnsteinsson's claim that communicative success depends on the absence of contextually salient false distinctness beliefs about the subject matter of the conversation. I argue that this thesis leads to clearly counterintuitive consequences and that no fundamental role must be given to the presence or absence of false distinctness beliefs in one's account of successful communication. The upshot is that we should stick with Buchanan's criterion. I conclude by employing Strawson and Recanati's concepts of linking and merging to show how the criterion I favour is compatible with the fact that, when subjects hold no relevant false distinctness beliefs, communicative success does not seem to be disrupted by the hearer seemingly failing to recognize the speaker's intentions. (shrink)

In this paper, I assess whether indexical attitudes, e.g. beliefs and desires, have any special properties or present any special challenge to theories of propositional attitudes. I being by investigating the claim that allegedly problematic indexical cases are just instances of the familiar phenomenon of referential opacity. Regardless of endorsing that claim, I provide an argument to the effect that indexical attitudes do have a special property. My argument relies on the fact that one cannot account for what is it (...) to share someone else’s indexical attitudes without rejecting some plausible thesis about propositional attitudes. In the end, I assess Herman Cappelen and Josh Dever’s considerations on intentional action and extract an argument from them that could – if successful – neutralize my own. I finish by arguing that their argument has an important flaw, thus failing to convince us that indexical attitudes are just as ordinary as any other. (shrink)

Political egalitarians tend to defend equal distributions of voting power at specific times, as in ‘one election, one vote’. Appealing as it is, the principle seems incompatible with distributing power proportionally to the stakes voters have at different elections, as in ‘one stake, one vote’. This article argues that the tension above stems from the temporal scope ascribed to political equality, as at specific moments of democratic decision-making instead of over entire lives. More specifically, ascribing a lifetime view to political (...) equality renders equality compatible with proportionality at different elections. I first show that storable votes differ from standard votes in their distinctive commitment to lifetime political equality. I then argue that storable voting schemes are compatible with three key reasons to value political equality: equal consideration of interests, relational equality, and non-domination. Finally, storable votes are also consistent with proportionality at specific times. I conclude that the neglected idea of lifetime political equality can, through storable votes, deliver proportionality without inequality. (shrink)

Despite being increasingly available to us all, retirement pensions remain unequally distributed: between rich and poor, young and old, men and women, and possibly different generations. As this topic receives little attention in moral and political philosophy, the articles in this thesis aim to deliver an original account of justice in retirement pensions along liberal egalitarian lines. The first part defends retirement pensions as a distribution of free time. It shows that including free time in the list of goods that (...) liberal egalitarians prioritise is plausible and avoids problems that would otherwise arise with other candidates, most notably leisure. Retirement as free time is an essential feature of liberal egalitarian societies by (re)distributing the means to pursue any life project, and especially valuable for the poor who work and contribute the longest. The second part makes a case for 'libertirement', a proposal to increase the freedom to enjoy free time across life, as a matter of justice between those who live long and those who die early. Specifically, I propose adding reverse pensions and sabbaticals on top of old-age retirement. Besides showing the importance of longevity for age-group justice, I also draw implications for distributing unconditional basic income and income taxes across life, which I suggest may offer alternative paths to libertirement. Finally, the third part discusses the cases of pension inequality between genders and generations, pushing us to refine our account further. I conclude that there is often a mismatch between liberal egalitarian justice and the design of retirement schemes. The solution is often but not always to reform these systems. Sometimes, we have reasons to revise our very own principles of justice. (shrink)

There is a constructive method to define a structure of simple k-cyclic Post algebra of order p, L p,κ, on a given finite field F, and conversely. There exists an interpretation Ф₁ of the variety V generated by L p,κ into the variety V) generated by F and an interpretation Ф₂ of V) into V such that Ф₂Ф₁ = B for every B ϵ V and Ф₁₂ = R for every R ϵ V). In this paper we show how we (...) can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple. (shrink)

I suggest a solution to a conflict between semantic internalism – according to which the concepts one expresses are determined by one's use of representations – and publicity – according to which, if two subjects successfully communicate or are in genuine agreement, then they entertain thoughts constituted by the same concepts. My solution rests on the thesis that there can be successful communication and genuine agreement between thinkers employing distinct concepts as long as there is a certain relation (of conceptually (...) guaranteed sameness of extension) between them. In section 2, I motivate semantic internalism and show how it conflicts with publicity. In section 3, I carve the logical space of possible solutions to the conflict into liberal and conservative solutions. Section 4 assesses Wikforss's conservative solution to Burge's arthritis thought‐experiment and concludes that it fails for more than one reason. Section 5 introduces a new case study involving a deferential concept. This case serves as the backdrop for my positive account offered in section 6. The conclusion of the article is preceded by a comparison of my view with another recently proposed by Recanati (section 7) and some replies to possible objections (section 8). (shrink)

The conventionality of simultaneity thesis as established by Reichenbach and Grünbaum is related to the partial freedom in the definition of simultaneity in an inertial reference frame. An apparently altogether different issue is that of the conventionality of spatial geometry, or more generally the conventionality of chronogeometry when taking also into account the conventionality of the uniformity of time. Here we will consider Einstein’s version of the conventionality of geometry, according to which we might adopt a different spatial geometry and (...) a particular definition of equality of successive time intervals. The choice of a particular chronogeometry would not imply any change in a theory, since its “physical part” can be changed in a way that, regarding experimental results, the theory is the same. Here, we will make the case that the conventionality of simultaneity is closely related to Einstein’s conventionality of chronogeometry, as another conventional element leading to it. (shrink)

In a way similar to classical mechanics where we have the concept of inertial time as expressed in the motions of bodies, in the theory of relativity we can regard the inertial time as the only notion of time at play. The inertial time is expressed also in the propagation of light. This gives rise to a notion of clock—the light clock, which we can regard as a notion derived from the inertial time. The light clock can be seen as (...) a solution of the theory, which complies with the requirement that a clock to be so must have a rate that is independent from its past history. Contrary to Einstein’s view, we do not need the concept of “clock” as an independent concept. This implies, in particular, that we do not need to rely on the notions of atomic clock or atomic time in the theory of relativity. (shrink)

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we go (...) through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

This paper develops a philosophical investigation of the merits and faults of a theorem by Lanford , Lanford , Lanford for the problem of the approach towards equilibrium in statistical mechanics. Lanford’s result shows that, under precise initial conditions, the Boltzmann equation can be rigorously derived from the Hamiltonian equations of motion for a hard spheres gas in the Boltzmann-Grad limit, thereby proving the existence of a unique solution of the Boltzmann equation, at least for a very short amount of (...) time. We argue that, by establishing a statistical H-theorem, it offers a prospect to complete Boltzmann’s combinatorial argument, without running against the objections which plug other typicality-based approaches. However, we submit that, while recovering the irreversible approach towards equilibrium for positive times, it fails to predict a monotonic increase of entropy for negative times, and hence it yields the wrong retrodictions about the past evolution of a gas. (shrink)

Einstein's gravitational redshift derivation in his famous 1916 paper on general relativity seems to be problematic, being mired in what looks like conceptual difficulties or at least contradictions or gaps in his exposition. Was this derivation a blunder? To answer this question, we will consider Einstein’s redshift derivations from his first one in 1907 to the 1921 derivation made in his Princeton lectures on relativity. This will enable to see the unfolding of an interdependent network of concepts and heuristic derivations (...) in which previous ideas inform and condition later developments. The resulting derivations and views on coordinates and clocks are in fact not without inconsistencies. However, we can see these difficulties as an aspect of an evolving network understood as a “work in progress”. (shrink)

While Einstein considered that sub specie astern the correct philosophical position regarding geometry was that of the conventionality of geometry, he felt that provisionally it was necessary to adopt a non-conventional stance that he called practical geometry. here we will make the case that even when adopting Einstein’s views we must conclude that practical geometry is conventional after all. Einstein missed the fact that the conventionality of simultaneity leads to a conventional element in the chrono-geometry, since it corresponds to the (...) possibility of different space-time metrics. (shrink)

With special relativity, we seem to be facing a conundrum. It is a very well-tested theory; in this way, the Minkowski spacetime must be “capturing” essential features of space and time. However, its geometry seems to be incompatible with any sort of global notion of time. We might only have local notions of now (present moment) and time flow, at best. In this note, we will explore the possibility that a pretty much global notion of now (and time flow) might (...) be hiding in plain sight in the geometry of the Minkowski spacetime. (shrink)