In previous work, the author has shown that $\Pi ^1_1$ -induction along $\mathbb N$ is equivalent to a suitable formalization of the statement that every normal function on the ordinals has a fixed point. More precisely, this was proved for a representation of normal functions in terms of Girard’s dilators, which are particularly uniform transformations of well orders. The present paper works on the next type level and considers uniform transformations of dilators, which are called 2-ptykes. We show that (...) $\Pi ^1_2$ -induction along $\mathbb N$ is equivalent to the existence of fixed points for all 2-ptykes that satisfy a certain normality condition. Beyond this specific result, the paper paves the way for the analysis of further $\Pi ^1_4$ -statements in terms of well ordering principles. (shrink)

The larger project broached here is to look at the generally sentence “if X is well-ordered then f is well-ordered”, where f is a standard proof-theoretic function from ordinals to ordinals. It has turned out that a statement of this form is often equivalent to the existence of countable coded ω-models for a particular theory Tf whose consistency can be proved by means of a cut elimination theorem in infinitary logic which crucially involves the function f. To illustrate (...) this theme, we prove in this paper that the statement “if X is well-ordered then εX is well-ordered” is equivalent to . This was first proved by Marcone and Montalban [Alberto Marcone, Antonio Montalbán, The epsilon function for computability theorists, draft, 2007] using recursion-theoretic and combinatorial methods. The proof given here is principally proof-theoretic, the main techniques being Schütte’s method of proof search [Kurt Schütte, Proof Theory, Springer-Verlag, Berlin, Heidelberg, 1977] and cut elimination for a fragment of. (shrink)

In this note the proof-theoretic ordinal of the well-ordering principle for the normal functions \ on ordinals is shown to be equal to the least fixed point of \. Moreover corrections to the previous paper are made.

It is shown that the boldface maximality principle for subcomplete forcing,, together with the assumption that the universe has only set many grounds, implies the existence of a well‐ordering of definable without parameters. The same conclusion follows from, assuming there is no inner model with an inaccessible limit of measurable cardinals. Similarly, the bounded subcomplete forcing axiom, together with the assumption that does not exist, for some, implies the existence of a well‐ordering of which is (...) Δ1‐definable without parameters, and ‐definable using a subset of ω1 as a parameter. This well‐order is in. Enhanced versions of bounded forcing axioms are introduced that are strong enough to have the implications of mentioned above, and along the way, a bounded forcing axiom for countably closed forcing is proposed. (shrink)

We use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle ◊ $_{k^ - }^* $ at a proper class of cardinals k. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.

In this paper we make a proposal for reforming biomedical research that is aimed to align re-search more closely with the so-called fair-share principle according to which the proportions of global resources as-signed to different diseases should agree with the ratios of human suffering associated with those diseases.

The goal of this dissertation is to reconstruct, critically evaluate, and apply the pluralism of Paul Feyerabend. I conclude by suggesting future points of contact between Feyerabend’s pluralism and topics of interest in contemporary philosophy of science. I begin, in Chapter 1, by reconstructing Feyerabend’s critical philosophy. I show how his published works from 1948 until 1970 show a remarkably consistent argumentative strategy which becomes more refined and general as Feyerabend’s thought matures. Specifically, I argue that Feyerabend develops a persuasive (...) case against rationalism, or the thesis that there exist normative and exclusive rules of scientific rationality. In Chapter 2, I reconstruct Feyerabend’s pluralism and detail its relationship to his humanitarianism and epistemological anarchism. I understand Feyerabend’s pluralism as the combination of the principles of proliferation and tenacity. I show the evolution and justification of these principles from Feyerabend’s early papers until the late 1970s. In Chapter 3, I defend Feyerabend’s pluralism from its most prominent criticisms. I then clarify that Feyerabend’s pluralism amounts to a conception of the logic of theory pursuit and modify his view using insights from C.S. Peirce, Pierre Duhem, and Michael Polanyi. From Peirce, I show how economic, sociological, and value-laden features of theory pursuit may be used to constrain proliferation and tenacity. From Duhem and Polanyi, I try to show the proper role of tacit knowledge within a Feyerabendian framework. Finally, I show what implications Feyerabend’s pluralism has for models of distributing funds within scientific communities. I contend that it provides a more promising model that the ‘well-ordered science’ proposal advanced by numerous philosophers and social scientists. Specifically, I aim to understand what taking Feyerabend’s pluralism seriously entails for principles of balancing funding allocation decisions and the role of peer-review in evaluating the potential success of research proposals. I conclude by suggesting future lines of research for further analyzing and applying Feyerabend’s pluralism. (shrink)

In this paper we make a proposal for reforming biomedical research that is aimed to align re-search more closely with the so-called fair-share principle according to which the proportions of global resources as-signed to different diseases should agree with the ratios of human suffering associated with those diseases.

We gather the following miscellaneous results in proof theory from the attic.1. 1. A provably well-founded elementary ordering admits an elementary order preserving map.2. 2. A simple proof of an elementary bound for cut elimination in propositional calculus and its applications to separation problem in relativized bounded arithmetic below S21.3. 3. Equivalents for Bar Induction, e.g., reflection schema for ω logic.4. 4. Direct computations in an equational calculus PRE and a decidability problem for provable inequations in PRE.5. 5. (...) Intuitionistic fixed point theories which are conservative extensions of HA.6. 6. Proof theoretic strengths of classical fixed points theories.7. 7. An equivalence between transfinite induction rule and iterated reflection schema over IΣn.8. 8. Derivation lengths of finite rewrite rules reducing under lexicographic path orders and multiply recursive functions.Each section can be read separately in principle. (shrink)

Zermelo’s Theorem that the axiom of choice is equivalent to the principle that every set can be well-ordered goes through in third-order logic, but in second-order logic we run into expressivity issues. In this note, we show that in a natural extension of second-order logic weaker than third-order logic, choice still implies the well-ordering principle. Moreover, this extended second-order logic with choice is conservative over ordinary second-order logic with the well-ordering principle. We (...) also discuss a variant choice principle, due to Hilbert and Ackermann, which neither implies nor is implied by the well-ordering principle. (shrink)

In this paper we make a proposal for reforming biomedical research that is aimed to align research more closely with the so-called fair-share principle according to which the proportions of global resources assigned to different diseases should agree with the ratios of human suffering associated with those diseases.

This article improves two existing theorems of interest to neologicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved second-order logic. The improved theorem states that if an equivalence relation E is defined without nonlogical vocabulary, then the bicardinal slice of any equivalence class—those equinumerous elements of the equivalence class with equinumerous complements—can have one of only three profiles. The improvements to Fine’s theorem allow for an analysis (...) of the well-behaved models had by an abstraction principle, and this in turn leads to an improvement of Walsh and Ebels-Duggan’s relative categoricity theorem. (shrink)

Gilabert argues that the humanist conception of duties of global justice and the principle of cosmopolitan justifiability will lead us to accept an egalitarian definition of individual autonomy. Gilabert further argues that realizing conditions of individual autonomy can serve as the cut-off point to duties of global justice. I investigate his idea of autonomy, arguing that in order to make sense of this claim, we need a concept of autonomy. I propose 4 possible definitions of autonomy, none of which (...) seem to necessitate Gilabert’s duties of egalitarian global justice. Instead, I propose that he may have in mind Autonomy 5, which requires that individuals have access to a maximum number of options and not simply a sufficient range of options to choose from. I criticize this premise as too demanding in the global world characterized by fundamental inequality. Second, I argue that if we were to endorse the preconditions for Autonomy 5, we would have to accept that Gilabert’s theory of global justice doesn’t provide for a cut-off point of duties of global justice. (shrink)

Various forms of mathematical induction are applicable to domains with some kinds of order. This naturally leads to the questions about the possibility of unification of different inductions and their generalization to wider classes of ordered domains. In the paper we propose a common framework for formulating induction proof principles in various structures and apply it to partially ordered sets. In this framework we propose a fixed induction principle which is indirectly applicable to the class of all posets. In (...) a certain sense, this result provides a solution to the problem of formulating a common generalization of a number of well-known induction principles for discrete and continuous ordered structures. (shrink)

The weakly compact reflection principle\\) states that \ is a weakly compact cardinal and every weakly compact subset of \ has a weakly compact proper initial segment. The weakly compact reflection principle at \ implies that \ is an \-weakly compact cardinal. In this article we show that the weakly compact reflection principle does not imply that \ is \\)-weakly compact. Moreover, we show that if the weakly compact reflection principle holds at \ then there is (...) a forcing extension preserving this in which \ is the least \-weakly compact cardinal. Along the way we generalize the well-known result which states that if \ is a regular cardinal then in any forcing extension by \-c.c. forcing the nonstationary ideal equals the ideal generated by the ground model nonstationary ideal; our generalization states that if \ is a weakly compact cardinal then after forcing with a ‘typical’ Easton-support iteration of length \ the weakly compact ideal equals the ideal generated by the ground model weakly compact ideal. (shrink)

We introduce the notion of constructive suprema and of constructively directed sets. The Axiom of Choice turns out to be equivalent to the postulate that every supremum is constructive, but also to the hypothesis that every directed set admits a function assigning to each finite subset an upper bound. The Axiom of Multiple Choice implies a simple set-theoretical induction principle , stating that any system of sets that is closed under unions of well-ordered subsystems and contains all finite (...) subsets of a given set must also contain that set itself. This is not provable without choice principles but equivalent to the statement that the existence of joins for constructively directed subsets of a poset follows from the existence of joins for nonempty well-ordered subsets. Moreover, we establish the equivalence of SIP with several other fundamental statements concerning inductivity, compactness, algebraic closure systems, and the exchange between chains and directed sets. (shrink)

In this article I investigate the phenomenon of minimum and minimal models of second-order set theories, focusing on Kelley–Morse set theory KM, Gödel–Bernays set theory GB, and GB augmented with the principle of Elementary Transfinite Recursion. The main results are the following. (1) A countable model of ZFC has a minimum GBC-realization if and only if it admits a parametrically definable global well order. (2) Countable models of GBC admit minimal extensions with the same sets. (3) There is (...) no minimum transitive model of KM. (4) There is a minimum β-model of GB+ETR. The main question left unanswered by this article is whether there is a minimum transitive model of GB+ETR. (shrink)

This article is concerned with the selection of an appropriate model of choice to underlie Rawls' two principles of justice. Rawls' first principle of justice states that basic liberty is not to be sacrificed for other objectives, including wealth. His second principle of justice suggests that even a minute decrease in the well-being of the least prosperous classes should not be accepted in exchange for an increase, no matter how large, in the well-being of more (...) class='Hi'>well-to-do citizens. (shrink)

Even though social engineering has gained a bad reputation, due to new possibilities in the information age, it may be time to reconsider Karl Popper’s conception of “piecemeal social engineering.” Piecemeal social engineering is not only an element within Popper’s open society. It also connects his political philosophy to his philosophy of science and his evolutionary epistemology. Furthermore, it seems to fit well into the search for implementation strategies for policies and social actions in the context of nonideal theory. (...) Nevertheless, this does not necessarily undermine the need for political ideals and first-order principles, which are inhabitants of “World 3.”. (shrink)

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for (...) categorial languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

The Axiom of Choice implies the Partition Principle and the existence, uniqueness, and monotonicity of (possibly infinite) sums of cardinal numbers. We establish several deductive relations among those principles and their variants: the monotonicity follows from the existence plus uniqueness; the uniqueness implies the Partition Principle; the Weak Partition Principle is strictly stronger than the Well-Ordered Choice.

Vopěnka’s Principle is a natural large cardinal axiom that has recently found applications in category theory and algebraic topology. We show that Vopěnka’s Principle and Vopěnka cardinals are relatively consistent with a broad range of other principles known to be independent of standard (ZFC) set theory, such as the Generalised Continuum Hypothesis, and the existence of a definable well-order on the universe of all sets. We achieve this by showing that they are indestructible under a broad class (...) of forcing constructions, specifically, reverse Easton iterations of increasingly directed closed partial orders. (shrink)

We show that many principles of first-order arithmetic, previously only known to lie strictly between [Formula: see text]-induction and [Formula: see text]-induction, are equivalent to the well-foundedness of [Formula: see text]. Among these principles are the iteration of partial functions of Hájek and Paris, the bounded monotone enumerations principle by Chong, Slaman, and Yang, the relativized Paris–Harrington principle for pairs, and the totality of the relativized Ackermann–Péter function. With this we show that the well-foundedness of [Formula: (...) see text] is a far more widespread than usually suspected. Further, we investigate the [Formula: see text]-iterated version of the bounded monotone iterations principle, and show that it is equivalent to the well-foundedness of the -height [Formula: see text]-tower [Formula: see text]. (shrink)

“Those are my principles, and if you don’t like them...well, I have others.”Groucho MarxWe also know of another superstition of that time: that of the Man of the Book. On some shelf in some hexagon (men reasoned) there must exist a book which is the formula and perfect compendium of all the rest: some librarian has gone through it and he is analogous to a god.... How could one locate the venerated and secret hexagon which housed Him? Someone proposed (...) a regressive method: To locate book A, consult first book B which indicates A’s position; to locate book B, consult first a book C, and so on to infinity... In adventures such as these, I have squandered and wasted my years.2 J.L. Borges, The Library of Babel. (shrink)

One widely-endorsed argument in the experimental philosophy literature maintains that intuitive judgments are unreliable because they are influenced by the order in which thought experiments prompting those judgments are presented. Here, we explicitly state this argument from ordering effects and show that any plausible understanding of the argument leads to an untenable conclusion. First, we show that the normative principle is ambiguous. On one reading of the principle, the empirical observation is well-supported, but the normative (...) class='Hi'>principle is false. On the other reading, the empirical observation has only weak support, and the normative principle, if correct, would impugn the reliability of deliberative reasoning, testimony, memory, and perception, since judgments in all these areas are sensitive to ordering in the relevant sense. We then reflect on what goes wrong with the argument. (shrink)

One well known problem regarding quantifiers, in particular the 1st order quantifiers, is connected with their syntactic categories and denotations.The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for (...) categorial languages generated by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functor-function defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

This paper develops a full account of Rawls's notion of a well-ordered society and uses it to address two luck egalitarian objections to his principles of justice. The first is an internal criticism which claims that Rawls's account of justice is better captured by a responsibility-sensitive egalitarian account. The second is an external objection according to which, regardless of the alleged inconsistency between Rawls's principles and his account of justice, we should reject those principles in favour of a responsibility-sensitive (...) criterion because it better captures our moral intuitions about distributive justice. The argument presented answers both objections by defending the value of well-orderedness and showing the difficulties of responsibility-sensitive egalitarian conceptions in realizing this ideal. (shrink)

It has recently been argued that a sensitivity theory of knowledge cannot account for intuitively appealing instances of higher-order knowledge. In this paper, we argue that it can once careful attention is paid to the methods or processes by which we typically form higher-order beliefs. We base our argument on what we take to be a well-motivated and commonsensical view on how higher-order knowledge is typically acquired, and we show how higher-order knowledge is possible in a sensitivity theory once (...) this view is adopted. (shrink)

The rigid relation principle, introduced in this article, asserts that every set admits a rigid binary relation. This follows from the axiom of choice, because well-orders are rigid, but we prove that it is neither equivalent to the axiom of choice nor provable in Zermelo-Fraenkel set theory without the axiom of choice. Thus, it is a new weak choice principle. Nevertheless, the restriction of the principle to sets of reals is provable without the axiom of choice.

For every$n\in \omega \setminus \{0,1\}$we introduce the following weak choice principle:$\operatorname {nC}_{<\aleph _0}^-:$For every infinite family$\mathcal {F}$of finite sets of size at least n there is an infinite subfamily$\mathcal {G}\subseteq \mathcal {F}$with a selection function$f:\mathcal {G}\to \left [\bigcup \mathcal {G}\right ]^n$such that$f(F)\in [F]^n$for all$F\in \mathcal {G}$.Moreover, we consider the following choice principle:$\operatorname {KWF}^-:$For every infinite family$\mathcal {F}$of finite sets of size at least$2$there is an infinite subfamily$\mathcal {G}\subseteq \mathcal {F}$with a Kinna–Wagner selection function. That is, there is a (...) function$g\colon \mathcal {G}\to \mathcal {P}\left (\bigcup \mathcal {G}\right )$with$\emptyset \not =f(F)\subsetneq F$for every$F\in \mathcal {G}$.We will discuss the relations between these two choice principles and their relations to other well-known weak choice principles. Moreover, we will discuss what happens when we replace$\mathcal {F}$by a linearly ordered or a well-ordered family. (shrink)

Aristotle shares with Plato the attitude that the world, ‘the all,’ is a kosmos, a well-ordered and beautiful whole which, as such, can be rendered intelligible, or understood, by the intellect. One understands things, generally speaking, by tracing them back to their sources, origins or principles and causes or explanatory factors, and seeing in what manner they are related to these principles. We know, or understand, a thing when we grasp ‘the why’ or cause. Consequently, understanding is systematic. Some (...) things we understand through themselves - these are the first principles and as such are not understood by tracing them back to causes. We understand other things by systematically relating them in appropriate ways to what is known through itself. These other things are known through, or by means of, their causes and principles. (shrink)

We investigate computability theoretic and descriptive set theoretic contents of various kinds of analytic choice principles by performing a detailed analysis of the Medvedev lattice of $\Sigma ^1_1$ -closed sets. Among others, we solve an open problem on the Weihrauch degree of the parallelization of the $\Sigma ^1_1$ -choice principle on the integers. Harrington’s unpublished result on a jump hierarchy along a pseudo-well-ordering plays a key role in solving this problem.

In this note the well-ordering principle for the derivative \ of normal functions \ on ordinals is shown to be equivalent to the existence of arbitrarily large countable coded \-models of the well-ordering principle for the function \.

Sensitivity is a modal epistemic principle. Modal knowledge accounts are externalist in nature and claim that the knowledge yielding connection between a true belief and the truthmaker must be spelled out in modal terms. The sensitivity condition was introduced by Robert Nozick. He suggests that if S knows that p, then S’s belief that p tracks truth. Nozick argues that this truth-tracking relation can be captured by subjunctive conditionals. As a first approximation, he provides the following modal analysis of (...) knowledge: S knows that p iff (1) p is true; (2) S believes that p; (3) if p were false, S wouldn’t believe that p and (4) if p were true, S would believe that p. The dominant terminology in the literature, also adopted here, is to call condition (3) the sensitivity condition and condition (4) the adherence condition. The sensitivity condition is intuitively appealing since it states that a subject does not know that p if she would believe that p even if p were false. Nozick used the sensitivity condition to accomplish two major tasks. First, he provided a solution to the Gettier problem by arguing that in Gettier cases subjects do not know since the sensitivity condition is violated. Second, he presented a controversial solution to the skeptical problem according to which we have external world knowledge but do not know that the skeptical hypothesis is false. This solution is available because sensitivity is not closed under known entailment. Quickly, criticism of the sensitivity condition emerged. First, most epistemologists regarded the price of abandoning knowledge closure as a price too high to pay. Second, it was noted that sensitivity leads to the counterintuitive consequence of precluding us from inductive knowledge since induction typically yields insensitive beliefs. The most dominant reaction to these problems was to replace sensitivity by the modal principle of safety, nowadays the most popular modal principle. However, sensitivity is not only important as a starting point of modal epistemology. Because of its intuitive attractiveness, many authors aimed at refining the original sensitivity account in order to avoid well-known problems. This has led to a second wave of sensitivity accounts. As of today, various sensitivity-based theories are on the market, including accounts that avoid closure failure, probabilistic interpretations of sensitivity and adherence, and contextualist approaches. There is thus a vivid and ongoing debate about the sensitivity principle in epistemology. (shrink)

George Boolos has described an interpretation of a fragment of ZFC in a consistent second-order theory whose only axiom is a modification of Frege's inconsistent Axiom V. We build on Boolos's interpretation and study the models of a variety of such theories obtained by amending Axiom V in the spirit of a limitation of size principle. After providing a complete structural description of all well-founded models, we turn to the non-well-founded ones. We show how to build models (...) in which foundation fails in prescribed ways. In particular, we obtain models in which every relation is isomorphic to the membership relation on some set as well as models of Aczel's anti-foundation axiom (AFA). We suggest that Fregean extensions provide a natural way to envisage non-well-founded membership. (shrink)

Among theories of human language comprehension, cue‐based memory retrieval has proven to be a useful framework for understanding when and how processing difficulty arises in the resolution of long‐distance dependencies. Most previous work in this area has assumed that very general retrieval cues like [+subject] or [+singular] do the work of identifying (and sometimes misidentifying) a retrieval target in order to establish a dependency between words. However, recent work suggests that general, handpicked retrieval cues like these may not be enough (...) to explain illusions of plausibility (Cunnings & Sturt, 2018), which can arise in sentences like The letter next to the porcelain plate shattered. Capturing such retrieval interference effects requires lexically specific features and retrieval cues, but handpicking the features is hard to do in a principled way and greatly increases modeler degrees of freedom. To remedy this, we use well‐established word embedding methods for creating distributed lexical feature representations that encode information relevant for retrieval using distributed retrieval cue vectors. We show that the similarity between the feature and cue vectors (a measure of plausibility) predicts total reading times in Cunnings and Sturt’s eye‐tracking data. The features can easily be plugged into existing parsing models (including cue‐based retrieval and self‐organized parsing), putting very different models on more equal footing and facilitating future quantitative comparisons. (shrink)

A school that adopts a curriculum, that aims for a holistic understanding of technology, does so because it produces a better educated person than a curriculum which does not. How do we know when we are teaching technology holistically and why must we do so? Increasingly, more is asked of technology educators to be holistic in the understanding conveyed to learners of technology itself in order to make better informed technical and design decisions in a wider range of applied settings. (...) The ability of the learner to naturally consider social and environmental factors, for example, when seeking solutions is seen by some State education systems in Australia as fundamental to a genuine education in technology (New South Wales Board of Studies, 2000 & 2002). In philosophy, the holist position asserts that to understand the particular one must understand its relation to the whole and that only through reflection of one's sensation based applications can genuine knowledge be critically affirmed (Matthews, 1980, p.87 & p.93). The combined apparently independent paths of the State and the Holist positions set a compelling scene not only for the socio-economic necessity for holistic technology education in the curriculum but also for Technology's status as a key curriculum agent in the knowledge formation process of educated individuals. -/- This paper asserts that the general elements of Applied Setting (including Time), Human (as Agent), Tool and Environment are well placed to be the necessary basics to any holistic human technological activity. How and why these elements work together, their schema, will be referred to in this paper as the 'Basic Principles'. The paper presents the thesis that Technology cannot be reduced to less than these general elements and as such, Technology is their product. We therefore may need to understand and teach these elements and their relations to each other explicitly, in ways that reveal the utility of such understanding when making technical choices and design decisions for all the genres of technology and at all their scales of application and discovery. The case is made for technology to not merely be a 'know how' learning experience, but necessarily also a holistic 'know why' learning experience essential for developing and transferring technological knowledge. (shrink)

What challenges must a principle of need for prioritisations in health care meet in order to be plausible and practically useful? Some progress in answering this question has recently been made by Hope, Østerdal and Hasman. This article continue their work by suggesting that the characteristic feature of principles of needs is that they are sufficientarian, saying that we have a right to a minimally acceptable or good life or health, but nothing more. Accordingly, principles of needs must answer (...) two distributive questions: when do we have sufficient and how should we prioritise among those who do not yet have a sufficiency? Furthermore, it is argued that Roger Crisp’s theory of need, which combines sufficientarianism with prioritarianism below the threshold of need, is better equipped than alternatives to answer these questions as well as meeting the challenges formulated by Hope, Østerdal and Hasman. However, Crisp’s theory faces two major challenges. First, it has to say something about the currency of distribution: a principle of need must be complemented either with a theory on the human good or a theory about the proper goals of health care. Second, it has to say something about where the threshold should be set. However, any attempt to set a threshold seems morally arbitrary in the light of the sufficientarian idea that those just above the threshold never should be given priority over those just below the threshold. (shrink)

Two well-known ancient witnesses report that Aristophanes of Byzantium was responsible for the arrangement of Pindar's poems into seventeen book-rolls according to lyric genres. These witnesses form fr. 381 in the edition of Aristophanes’ fragments by W.J. Slater : Vit. Pind. P.Oxy. 2438.35–9 δ]ιῄρητα̣ι̣ δὲ α̣ὐ̣τ̣[ο]ῦ̣ τ̣[ὰ ποιήματα ὑπ’ Ἀριστοφάν]ους εἰς βιβλία ιζˊ· διθ̣[υ]ρά̣[μ]βων βˊ [προσοδίω]ν̣ βˊ παιάνων αˊ πα[ρ]θεν[εί]ων γ̣ˊ [ἐπινικίω]ν̣ δˊ ἐγκωμίων αˊ ἐν [ᾧ] κα̣ὶ [σκ]όλ̣[ια ±4 ὕμ]ν̣ων αˊ ὑ[π]ορχημάτων αˊ θρ̣[ήνων.| nisi aliter ind., omnia suppl. (...) Lobel | 2 Ἀριστοφάν]ους Lobel e Vit. Pind. Vat. | 3 ἐν [ᾧ] κα̣ὶ [σκ]όλ̣[ια …. de Kreij : ἐν [ᾧ] κ[αὶ σκόλιά τινα vel ἐν [ᾧ] κ[αὶ σκόλιά ἐστι Gallo : ἐν [ᾧ] καὶ [παροίνια D'Alessio | 4 αˊ post θρ̣[ήνων coni. edd., fort. recte; an θρ̣[- βˊ?Vit. Pind. Vat. page 7.14–17 Dr. ὁ δὲ ἐπινίκιος οὗ ἡ ἀρχὴ “Ἄριστον μὲν ὕδωρ” προτέτακται ὑπὸ Ἀριστοφάνους τοῦ συντάξαντος τὰ Πινδαρικὰ διὰ τὸ περιέχειν τοῦ ἀγῶνος ἐγκώμιον καὶ τὰ περὶ τοῦ Πέλοπος, ὃς πρῶτος ἐν ῎Ηλιδι ἠγωνίσατο.A much-debated question is whether the order of the poems attested by the papyrus can be credited to Aristophanes, since an ordering principle is apparently not to be found in the list transmitted by it. Moreover, there are some disagreements with the list of Pindar's works transmitted by the Vita Ambrosiana, which is generally deemed the most authoritative catalogue of the poet's corpus, on account of its well-recognized criterion of classification: the poems are divided between those for gods and those for men, and both of these categories of songs are arranged from the most general to the most specific. This catalogue has been thought to reproduce the order established by Aristophanes in his edition of Pindar. (shrink)

The concept of formal transcendentalism is utilized. The fundamental and definitive property of the totality suggests for “the totality to be all”, thus, its externality (unlike any other entity) is contained within it. This generates a fundamental (or philosophical) “doubling” of anything being referred to the totality, i.e. considered philosophically. Thus, that doubling as well as transcendentalism underlying it can be interpreted formally as an elementary choice such as a bit of information and a quantity corresponding to the number (...) of elementary choices to be defined. This is the quantity of information defined both transcendentally and formally and thus, philosophically and mathematically. If one defines information specifically, as an elementary choice between finiteness (or mathematically, as any natural number of Peano arithmetic) and infinity (i.e. an actually infinite set in the meaning of set theory), the quantity of quantum information is defined. One can demonstrate that the so-defined quantum information and quantum information standardly defined by quantum mechanics are equivalent to each other. The equivalence of the axiom of choice and the well-ordering “theorem” is involved. It can be justified transcendentally as well, in virtue of transcendental equivalence implied by the totality. Thus, all can be considered as temporal as far anything possesses such a temporal counterpart necessarily. Formally defined, the frontier of time is the current choice now, a bit of information, furthermore interpretable as a qubit of quantum information. (shrink)

A continuum is here a primitive notion intended to correspond precisely to a path-connected subset of the usual euclidean space. In contrast, however, to the traditional treatment, we treat here continua not as pointsets, but as irreducible entities equipped only with a partial ordering ≤ interpreted as parthood. Our aim is to examine what basic topological and geometric properties of continua can be expressed in the language of ≤, and what principles we need in order to prove elementary facts (...) about them. Surprisingly enough ≤ suffices to formulate the very heart of continuity (=jumpless and gapless transitions) in a general setting. Further, using a few principles about ≤ (together with the axioms of ZFC), we can define points, joins, meets and infinite closeness. Most important, we can develop a dimension theory based on notions like path, circle, line (=one-dimensional continuum), simple line and surface (=two-dimensional continuum), recovering thereby in a rigorous way Poincaré's well-known intuitive idea that dimension expresses the ways in which a continuum can be torn apart. We outline a classification of lines according to the number of circles and branching points they contain. The ordering (C,≤) is a topped and bottomed, atomic, almost dense and complete partial ordering, weaker than a lattice. Continuous transformations from C to C are also defined in a natural way and results about them are proved. (shrink)

We investigate the complexity of various combinatorial theorems about linear and partial orders, from the points of view of computability theory and reverse mathematics. We focus in particular on the principles ADS (Ascending or Descending Sequence), which states that every infinite linear order has either an infinite descending sequence or an infinite ascending sequence, and CAC (Chain-AntiChain), which states that every infinite partial order has either an infinite chain or an infinite antichain. It is well-known that Ramsey's Theorem for (...) pairs (RT₂²) splits into a stable version (SRT₂²) and a cohesive principle (COH). We show that the same is true of ADS and CAC, and that in their cases the stable versions are strictly weaker than the full ones (which is not known to be the case for RT₂² and SRT₂²). We also analyze the relationships between these principles and other systems and principles previously studied by reverse mathematics, such as WKL₀, DNR, and BΣ₂. We show, for instance, that WKL₀ is incomparable with all of the systems we study. We also prove computability-theoretic and conservation results for them. Among these results are a strengthening of the fact, proved by Cholak, Jockusch, and Slaman, that COH is Π₁¹-conservative over the base system RCA₀. We also prove that CAC does not imply DNR which, combined with a recent result of Hirschfeldt, Jockusch, Kjos-Hanssen, Lempp, and Slaman, shows that CAC does not imply SRT₂² (and so does not imply RT₂²). This answers a question of Cholak, Jockusch, and Slaman. Our proofs suggest that the essential distinction between ADS and CAC on the one hand and RT₂² on the other is that the colorings needed for our analysis are in some way transitive. We formalize this intuition as the notions of transitive and semitransitive colorings and show that the existence of homogeneous sets for such colorings is equivalent to ADS and CAC, respectively. We finish with several open questions. (shrink)

According to an influential idea in the philosophy of set theory, certain mathematical concepts, such as the notion of a well-order and set, are indefinitely extensible. Following Parsons (1983), this has often been cashed out in modal terms. This paper explores instead an extensional articulation of the idea, formulated in higher-order logic, that flat-footedly formalizes some remarks of Zermelo. The resulting picture is incompatible with the idea that the entire universe can be well-ordered, but entirely consistent with the (...) idea that the sets of any set-theoretic universe can be. (shrink)

Philosophy of mind is, and for a long while has been, 99% metaphysics and 1% epistemology. Attention is lavished on the question of the nature of mind, but questions concerning how we know about minds are discussed much less thoroughly. University courses in philosophy of mind routinely devote a lot of time to dualism, logical behaviourism, the mind/brain identity theory, and functionalism. But what gets said about the kinds of evidence that help one determine what mental states, if any, an (...) individual occupies? Well, Skinner's puritanical disdain for postulating mental states gets raked over the coals, the problem of other minds gets solved by a perfunctory invocation of the principle of inference to the best explanation, and the Turing test gets discussed, mainly in order to emphasize that it can lead to mistaken answers. (shrink)

We show that the axiom of choice AC is equivalent to the Vector Space Kinna-Wagner Principle, i.e., the assertion: “For every family [MATHEMATICAL SCRIPT CAPITAL V]= {Vi : i ∈ k} of non trivial vector spaces there is a family ℱ = {Fi : i ∈ k} such that for each i ∈ k, Fiis a non empty independent subset of Vi”. We also show that the statement “every vector space over ℚ has a basis” implies that every infinite (...) well ordered set of pairs has an infinite subset with a choice set, a fact which is known not to be a consequence of the axiom of multiple choice MC. (shrink)

This paper aims to introduce, in the context of Latin America, the theoretical epistemic discussion regarding the theme of the ‘common’ as a political principle which substantiates instituting and autonomous processes of government, control and community regulation. The work seeks to relate a democratic scenario of the ‘common’ with the discourses of pluralist and decolonial normativity, in a way that would guarantee not only horizontal communal self-management, but also a legitimate ordering of forms of life, founded on common (...) interest, social relations and interconnected structures. For this purpose the instrument of critical-socio-legal analysis is applied at the intersections with the ‘participative-communitary’ type of legal pluralism. Our proposal is to combine the contemporary meaning of the ‘common’, its relation to the Latin American principles of ‘buen vivir’ (living well) and ‘interculturalidade’ (interculturality), as well as the instituting practice of the ‘common’, that engenders a normativity built ‘from below’, which is in opposition to the traditional positivist and state legal system imposed through colonization in Latin America. Such achievements that, although formalized, are not being successful against institutional ruptures, have ‘cloistered’ the practices of the ‘common’ and made the existence of legal pluralism invisible. (shrink)

Simon May has argued that the notion of a principled compromise is incoherent. Reasons to compromise are always in his view strategic: though we think that the position we defend is still the right one, we compromise on this view in order to avoid the undesirable consequences that might flow from not compromising. I argue against May that there are indeed often principled reasons to compromise, and that these reasons are in fact multiple. First, compromises evince respect for persons that (...) we have reason to think of as our epistemic peers, and acknowledgement of our own finitudes as moral reasoners. Second, compromises are often made morally necessary by the shortfalls that unavoidably separate democratic institutions from democratic ideals. Third, compromises express a desirable form of democratic community. And fourth, compromises are often justified from a consequentialist point of view, in that they allow for the realization of values that would not be realized as well by the failure to compromise. (shrink)

We establish the thesis that in moral education, particularly in the first years of the child’s development, unreflexive acts or unreflexiveness in certain behaviours of adults is a condition for the development of the personality structure and virtues that enable autonomous ethical reflection and a relation to the Other. With the notion of unreflexiveness we refer to resolvedness in the response of adults when it is necessary to establish a limit, or cut, in the child’s demand for pleasure, as (...) class='Hi'>well as to resolvedness as one of the structurally essential elements in behaviours with which the adult subordinates the child to the symbolic order or language. In philosophy, a symptomatic position in this context is represented by Kant’s theory of education. On the basis of the “traditional” concept of “negative education”, and through Freud’s and Lacan’s psychoanalytic concepts, we identify two principles that should, in contemporary times, be an essential part of the moral educational behaviours of adults: the principle of a delimited response to the child’s demand for the satisfaction of pleasure, and the principle of reasoned, reflected, but nevertheless certain, persevering, resolved unreflexiveness in the subordination of the child’s desire to the symbolic order . On the basis of the preceding analysis, we highlight certain consequences of this structure of the subject for the contexts of particular theoretical discussions and for school practice. (shrink)