In this paper I develop a philosophical account of actual mathematical infinity that does not demand ontologically or epistemologically problematic assumptions. The account is based on a simple metaphor in which we think of indefinitely continuing processes as defining objects. It is shown that such a metaphor is valid in terms of mathematical practice, as well as in line with empirical data on arithmetical cognition.

In Tractatus, Wittgenstein held that there are null sentences – prominently including logical truths and the truths of mathematics. He says that such sentences are without sense (sinnlos), that they say nothing; he also denies that they are nonsensical (unsinning). Surely it is what a sentence says which is true or false. So if a sentence says nothing, how can it be true or false? The paper discusses the issue.

The meaning of an experimental result depends on the experiment's conceptual backdrop, particularly its null hypothesis. This observation provides the basis for a functional interpretation of belief in the base rate fallacy. On this interpretation, if the base rate fallacy is to be labelled a “myth,” then it should be recognized that this label is not necessarily a disparaging one.

If possible worlds are conjunctions of states of affairs, as in David Armstrong’s combinatorial theory, then is the empty world to be thought of as the null conjunction of states of affairs? The proposal seems plausible, and has received support from David Efird, Tom Stoneham, and Armstrong himself. However, in this paper, it is argued that the proposal faces a trilemma: either it leads to the absurd conclusion that the actual world is empty; or it reduces to a familiar (...) representation of the empty world in which the concept of a null conjunction plays no role; or it needs to make room for the null individual of certain non-classical mereologies. (shrink)

Algorithmic governmentality is a new form of political governance interconnected with technology and computation. By coining the term “algorithmic governmentality,” Antoinette Rouvroy argues that this mode of governance reduces everything to data, and people are no longer individuals but dividuals (able to be divided) or readable data profiles. Implementing the concept of algorithmic governmentality, the current study analyses Project Itoh’s award-winning novel Harmony in terms of such relevant concepts as “subjectivity,” “infra-individuality” and “control,” as suggested by Rouvroy and colleagues. The (...) analysis further draws on Foucault’s ideas of “governmentality” and “neoliberalism” and Deleuze’s concepts of “dividuality” and “society of control.” In Itoh’s fictional world, the entire society is subject to the new medical government, which replaced the chaotic world with a perfect but harrowing benevolent society, eradicating disease, suicide and crime. As elucidated in this paper, despite the dominant controlling government, there is a hope for humans to regain and reestablish their subjectivity and give meaning to their own personality by defying the nihilistic computational system. (shrink)

In this paper, I explore Bach’s idea (Bach, 2000) that null appositives, intended as expanded qua-clauses, can resolve the puzzles of belief reports. These puzzles are crucial in understanding the semantics and pragmatics of belief reports and are presented in a section. I propose that Bach’s strategy is not only a way of dealing with puzzles, but also an ideal way of dealing with belief reports. I argue that even simple unproblematic cases of belief reports are cases of pragmatic (...) intrusion, involving null appositives, or to use the words of Bach, ‘qua-clauses’. The main difference between my pragmatic approach and the one by Salmon (1986) is that this author uses the notion of conversational implicature, whereas I use the notion of pragmatic intrusion and explicature. From my point of view, statements such as ‘‘John believes that Cicero is clever’’ and ‘‘John believes that Tully is clever’’ have got distinct truth-values. In other words, I claim that belief reports in the default case illuminate the hearer on the mental life of the believer, that includes specific modes of presentation of the referents talked about. Furthermore, while in the other pragmatic approaches, it is mysterious how a mode of presentation is assumed to be the main filter of the believer’s mental life, here I provide an explanatory account in terms of relevance, cognitive effects, and processing efforts. The most important part of the paper is devoted to showing that null appositives are required, in the case of belief reports, to explain certain anaphoric effects, which would otherwise be mysterious. My examples show that null appositives are not necessitated at logical form, but only at the level of the explicature, in line with the standard assumptions by Carston and Recanati on pragmatic intrusion. I develop a potentially useful analysis of belief reports by exploiting syntactic and semantic considerations on presuppositional clitics in Romance. (shrink)

The authors propose a nested dissection approach to finding a fundamental cycle basis in a planar graph. The cycle basis corresponds to a fundamental null-space basis of the adjacency matrix. This problem is meant to model sparse null-space basis computations occurring in a variety of settings. An O(n3/2) bound is achieved on the nullspace basis size (i.e., the number of nonzero entries in the basis), and an O(n log n) bound on the size in the special case of (...) grid graphs. (shrink)

In this article I give a critical evaluation of the use and limitations of null-model-based hypothesis testing as a research strategy in the biological sciences. According to this strategy, the null model based on a randomization procedure provides an appropriate null hypothesis stating that the existence of a pattern is the result of random processes or can be expected by chance alone, and proponents of other hypotheses should first try to reject this null hypothesis in order (...) to demonstrate their own hypotheses. Using as an example the controversy over the use of null hypotheses and null models in species co-occurrence studies, I argue that null-model-based hypothesis testing fails to work as a proper analog to traditional statistical null-hypothesis testing as used in well-controlled experimental research, and that the random process hypothesis should not be privileged as a null hypothesis. Instead, the possible use of the null model resides in its role of providing a way to challenge scientists’ commonsense judgments about how a seemingly unusual pattern could have come to be. Despite this possible use, null-model-based hypothesis testing still carries certain limitations, and it should not be regarded as an obligation for biologists who are interested in explaining patterns in nature to first conduct such a test before pursuing their own hypotheses. (shrink)

According to the cliché a picture is worth a thousand words. But this is a canard, for it vastly underestimates the expressive power of many pictures and diagrams. In this note we show that even a simple map such as the outline of Manhattan Island, accompanied by a pointer marking North, implies a vast infinity of statements—including a vast infinity of true statements.

Celem artykułu jest ogólna analiza alternacji z zerem, zachodzących w języku niemieckim i polskim. Alternacje te, występujące zarówno we fleksji, jak też i w słowotwórstwie, służą w obu konfrontowanych językach, a szczególnie w znacznie szerszym stopniu w języku polskim sygnalizowaniu klas i kategorii gramatycznych. Wnioskiem wynikającym z konfrontacji jest stwierdzenie różnic systemowych, związanych z dyslrybucją w sferze używalności alternacji oraz w planie funkcjonalnym. Autor ukazuje w artykule całą złożoność problematyki alternacji z zerem, uwarunkowaną różnicami strukturalnymi badanych języków.

In this paper, I develop an essentialist model of the semantics of slurs. I defend the view that slurs are a species of kind terms: Slur concepts encode mini-theories which represent an essence-like element that is causally connected to a set of negatively-valenced stereotypical features of a social group. The truth-conditional contribution of slur nouns can then be captured by the following schema: For a given slur S of a social group G and a person P, S is true of (...) P iff P bears the “essence” of G—whatever this essence is—which is causally responsible for stereotypical negative features associated with G and predicted of P. Since there is no essence that is causally responsible for stereotypical negative features of a social group, slurs have null-extension, and consequently, many sentences containing them are either meaningless or false. After giving a detailed outline of my theory, I show that it receives strong linguistic support. In particular, it can account for a wide range of linguistic cases that are regarded as challenging, central data for any theory of slurs. Finally, I show that my theory also receives convergent support from cognitive psychology and psycholinguistics. (shrink)

The ecologist today finds scarce ground safe from controversy. Decisions must be made about what combination of data, goals, methods, and theories offers them the foundations and tools they need to construct and defend their research. When push comes to shove, ecologists often turn to philosophy to justify why it is their approach that is scientific. Karl Popper’s image of science as bold conjectures and heroic refutations is routinely enlisted to justify testing hypotheses over merely confirming them. One of the (...) most controversial theories in contemporary science is the Neutral Theory of Ecology. Its chief developer and proponent, Stephen Hubbell, presents the neutral theory as a bold conjecture that has so far escaped refutation. Critics of the neutral theory claim that it already stands refuted, despite what the dogmatic neutralists say. We see the controversy through a Popperian lens. But Popper’s is an impoverished philosophy of science that distorts contemporary ecology. -/- The controversy surrounding the neutral theory actually rests on a methodological fault. There is a strong but messy historical link between the concepts of being neutral and being null in biology, and Hubbell perpetuates this when he claims that the neutral theory is supplies the appropriate null for testing alternative theories. What method is being followed here? There are three contenders: -/- Null hypothesis testing tests for whether a there is a pattern to be explained. Null modeling tests for whether a process is causally relevant to a pattern. Baseline modeling apportions relative responsibility to multiple processes each relevant to a pattern. -/- Whether the neutral theory supplies an appropriate “null” depends upon whether null hypothesis, null modeling, or baseline model is intended. These methods prescribe distinct inference patterns. If they are null hypothesis testing or null modeling, the neutralists’s reasoning is invalid. If they are baseline modeling, the justification of a crucial assumption remains opaque. Either way, the neutral-null connection is being exploited rhetorically to privilege the neutral theory over its rivals. Clarifying the reasoning immunizes us against the rhetoric and foregrounds the underlying virtues of the neutralist approach to ecology. -/- The Popperian lens distorts theoretical development as dogmatism. Lakatos’s view of science as the development of research programmes clarifies the epistemology of the neutral theory. Focusing philosophical attention on the neutralist research programme illuminates (1) the synchronic uses of the neutral theory to make predictions and give descriptions and explanations; (2) its diachronic development in response to theoretical innovation and confrontation with data; (3) its complex relationships to alternative theories. For example, baseline modeling is now seen to be its primary explanatory heuristic. The justification for baseline modeling with the neutral theory, previously hidden from view, is seen in the logic of in the neutralist research programme. (shrink)

The purpose of this article is to present several immediate consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. The use of Lambda will appear natural thanks to its role of condition of possibility of sets. On a conceptual level, the use of Lambda leads to a legitimation of the empty set and to a redefinition of the notion of set. It lets also clearly appear (...) the distinction between the empty set, the nothing and the ur-elements. On a technical level, we introduce the notion of pre-element and we suggest a formal definition of the nothing distinct of that of the null-class. Among other results, we get a relative resolution of the anomaly of the intersection of a family free of sets and the possibility of building the empty set from ``nothing". The theory is presented with equi-consistency results . On both conceptual and technical levels, the introduction of Lambda leads to a resolution of the Russell's puzzle of the null-class. (shrink)

The significance and use of absence of a thing is highlighted as its presence. The role of absence in various disciplines of mathematics, physics, semi-conductor electronics, computing and cognitive sciences for ease in conceptualizing is discussed. The use of null set, null vector and null matrix are also presented.

This article consists in two parts that are complementary and autonomous at the same time. -/- In the first one, we develop some surprising consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. On a conceptual level, it allows to see sets in a new light and to give a legitimacy to the empty set. On a technical level, it leads to a relative resolution of (...) the anomaly of the intersection of a family free of sets. -/- In the second part, we show the interest of introducing an operator of potentiality into a standard set theory. Among other results, this operator allows to prove the existence of a hierarchy of empty sets and to propose a solution to the puzzle of "ubiquity" of the empty set. -/- Both theories are presented with equi-consistency results (model and interpretation). -/- Here is a declaration of intent : in each case, the starting point is a conceptual questionning; the technical tools come in a second time\\[0.4cm] \textbf{Keywords:} nothing, void, empty set, null-class, zero-order logic with quantifiers, potential, effective, empty set, ubiquity, hierarchy, equality, equality by the bottom, identity, identification. (shrink)

Los Alephs de Borges se distinguen de los Alefs de Cantor. ¿Qué son aparte de infinitud? ¿Dónde viven? ¿Qué hacen? Este escrito es una invitación a la imaginación ante la dialéctica entre la Teoría de Conjuntos cantarina y la Poesía Múltiple borgesiana. Enfrentaremos entonces lo profundo, el corazón, la invención en esos dos autores, revisando en particular ideas de densidad, asintoticidad, fractalidad. Nuestro pensamiento se expande a partir de la Teoría de Conjuntos, pero solo Borges puede distorsionar algo tan sublime, (...) con sus deformaciones del espacio, del tiempo, de lo real, donde inventa más infinitos de los que podemos imaginar. Estudiaremos cómo, en la matemática y en la literatura, la expansión de la imaginación es fundamental para crear, descubrir, ligar pensamientos y llegar a lo más verdadero y profundo. (shrink)

pronominal clitics, pragmatics and propositional attitudes.

K denotes both the knowledge predicate satisfied by every currently known theorem and the finite set of all currently known theorems. The set K is time-dependent, publicly available, and contains theorems both from formal and constructive mathematics. Any theorem of any mathematician from past or present forever belongs to K. Mathematical statements with known constructive proofs exist in K separately and form the set K_c⊆K. We assume that mathematical sets are atemporal entities. They exist formally in ZFC theory although their (...) properties can be time-dependent (when they depend on K) or informal. The true statement "K is non-empty" is outside K forever because K is not a formal set. Paul Cohen proved in 1963 that the equality 2^{\aleph_0}=\aleph_1 is independent of ZFC. Before 1963, the statement "There is a known constructively defined integer n⩾1 such that 2^{\aleph_0}=\aleph_n" was outside K. Since 1963, this statement is outside K forever. The true statement "There exists a set X⊆{1,...,49} such that card(X)=6 and X never occurred as the winning six numbers in the Polish Lotto lottery" refers to the current non-mathematical knowledge and is outside K forever. In Martin-Löf's terminology, every currently known theorem is actually true whereas every theorem (known or unknown) is potentially true. Actual truth is knowledge dependent and tensed. Potential truth is knowledge independent and tenseless. Algorithms always terminate. We explain the distinction between algorithms whose existence is provable in ZFC and constructively defined algorithms which are currently known. By using this distinction, we obtain non-trivially true statements on decidable sets X⊆N that belong to constructive and informal mathematics and refer to the current mathematical knowledge on X. For every such statement, its truth concerning the current mathematical knowledge is implied by a true statement of the form: (the conjunction of i conditions of the form α∈K)∧(the conjunction of j conditions of the form β∉K)∧(the conjunction of k conditions of the form γ∈K_c)∧(the conjunction of l conditions of the form δ∉K_c), where i,j,k,l∈N and α,β,γ,δ are mathematical statements. In constructive mathematics and the traditional Brouwerian intuitionism, the truth of a mathematical statement means that we know a constructive proof. Therefore, the truth of a mathematical statement depends on time, where the statement is formally stated in the classical mathematics without the predicate K. In this article, mathematical statements on decidable sets X⊆N refer to time because they refer to the current mathematical knowledge on X. They cannot be formally stated in the classical mathematics without the predicate K and their logical values may change in time. For a set X⊆N whose infiniteness is false or unproven, we define which elements of X are classified as known. No known set X⊆N satisfies Conditions (1)-(4) and is widely known in number theory or naturally defined, where this term has only informal meaning. (1) A known algorithm with no input returns an integer n satisfying card(X)<ω ⇒ X⊆(-∞,n]. (2) A known algorithm for every k∈N decides whether or not k∈X. (3) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(X)=ω" is outside K. (4) There are many elements of X and it is conjectured, though so far unproven, that X is infinite. (5) X is naturally defined. The infiniteness of X is false or unproven. X has the simplest definition among known sets Y⊆N with the same set of known elements. No set X⊆N will satisfy Conditions (1)-(4) forever, if for every algorithm with no input, at some future day, a computer will be able to execute this algorithm in 1 second or less. The physical limits of computation disprove the assumption of the above statement. We prove that the set X={n∈N: the interval [-1,n] contains more than 29.5+(11!/(3n+1))∙sin(n) primes of the form k!+1} satisfies Conditions (1)-(5) except the requirement that X is naturally defined. We present a table that shows satisfiable conjunctions of the form #(Condition1)∧(Condition 2)∧#(Condition 3)∧(Condition 4)∧#(Condition 5), where # denotes the negation ¬ or the absence of any symbol. We prove that there exists a naturally defined set C⊆N which satisfies the following conditions (6)-(11). (6) A known and simple algorithm for every k∈N decides whether or not k∈C. (7) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(C)=ω" is outside K. (8) For every known algorithm A with no input, the statement "A returns the logical value of the statement card(N\C)=ω" is outside K. (9) It is conjectured, though so far unproven, that C is infinite. (10) For every known algorithm A with no input, the statement "A returns an integer n satisfying card(C)<ω ⇒ C⊆(-∞,n]" is outside K. (11) For every known algorithm A with no input, the statement "A returns an integer m satisfying card(N\C)<ω ⇒ N\C⊆(-∞,m]" is outside K. The set C={k∈N: 2^{2^k}+1 is composite} is naturally defined and satisfies conditions (6)-(11). (shrink)

The thesis of Weak Unrestricted Composition says that every pair of objects has a fusion. This thesis has been argued by Contessa and Smith to be compatible with the world being junky and hence to evade an argument against the necessity of Strong Unrestricted Composition proposed by Bohn. However, neither Weak Unrestricted Composition alone nor the different variants of it that have been proposed in the literature can provide us with a satisfying answer to the special composition question, or so (...) we will argue. We will then go on to explore an alternative family of purely mereological rules in the vicinity of Weak Unrestricted Composition, Cardinal Composition: A plurality of pairwise non-overlapping objects composes an object iff the objects in the plurality are of cardinality smaller than $$\kappa $$ κ. As we will show, all the instances for infinite $$\kappa $$ κ s determine fusion and are compatible with junk, and every instance for a $$\kappa > \aleph _0$$ κ > ℵ 0 is furthermore compatible with gunk and dense chains of parthood. (shrink)

Neutral Theory is controversial in ecology. Ecologists and philosophers have diagnosed the source of the controversy as: its false assumption that individuals in different species within the same trophic level are ecologically equivalent, its conflict with Competition Theory and the adaptation of species, its role as a null hypothesis, and as a Lakatosian research programme. In this paper, I show why we should instead understand the conflict at the level of research programs which involve more than theory. The Neutralist (...) and Competitionist research programs borrow and construct theories, models, and experiments for various aims and given their home ecological systems. I present a holistic and pragmatic view of the controversy that foregrounds the interrelation between many kinds of practices and decisions in ecological research. (shrink)

A collection of material on Husserl's Logical Investigations, and specifically on Husserl's formal theory of parts, wholes and dependence and its influence in ontology, logic and psychology. Includes translations of classic works by Adolf Reinach and Eugenie Ginsberg, as well as original contributions by Wolfgang Künne, Kevin Mulligan, Gilbert Null, Barry Smith, Peter M. Simons, Roger A. Simons and Dallas Willard. Documents work on Husserl's ontology arising out of early meetings of the Seminar for Austro-German Philosophy.

This article discusses various dangers that accompany the supposedly benign methods in behavioral evoltutionary biology and evolutionary psychology that fall under the framework of "methodological adaptationism." A "Logic of Research Questions" is proposed that aids in clarifying the reasoning problems that arise due to the framework under critique. The live, and widely practiced, " evolutionary factors" framework is offered as the key comparison and alternative. The article goes beyond the traditional critique of Stephen Jay Gould and Richard C. Lewontin, to (...) present problems such as the disappearance of evidence, the mishandling of the null hypothesis, and failures in scientific reasoning, exemplified by a case from human behavioral ecology. In conclusion the paper shows that "methodological adaptationism" does not deserve its benign reputation. (shrink)

It is sometimes argued that certain sentences of natural language fail to express truth conditional contents. Standard examples include e.g. Tipper is ready and Steel is strong enough. In this paper, we provide a novel analysis of truth conditional meaning using the notion of a question under discussion. This account explains why these types of sentences are not, in fact, semantically underdetermined, provides a principled analysis of the process by which natural language sentences can come to have enriched meanings in (...) context, and shows why various alternative views, e.g. so-called Radical Contextualism, Moderate Contextualism, and Semantic Minimalism, are partially right in their respective analyses of the problem, but also all ultimately wrong. Our analysis achieves this result using a standard truth conditional and compositional semantics and without making any assumptions about enriched logical forms, i.e. logical forms containing phonologically null expressions. (shrink)

I systematically defend a novel account of the grounds for identity and distinctness facts: they are all uniquely zero‐grounded. First, this Null Account is shown to avoid a range of problems facing other accounts: a relation satisfying the Null Account would be an excellent candidate for being the identity relation. Second, a plenitudinist view of relations suggests that there is such a relation. To flesh out this plenitudinist view I sketch a novel framework for expressing real definitions, use (...) this framework to give a definition of identity, and show how the central features of the identity relation can be deduced from this definition. (shrink)

At the height of the COVID-19 pandemic, stringent lockdowns and sudden adjustments were enacted, both of which had a devastating effect on the economy of the Philippines and the method of education that was in place at the time. This resulted in shifts and serious challenges for everyone, particularly pupils from marginalized homes. Hence, this study employed a correlational design to determine if there is a significant relationship between academic burnout and academic procrastination among 150 grade 12 senior high school (...) students. The researchers used two instruments: Academic Procrastination Scale (APS) and Maslach Burnout Inventory (MBI) to measure the variables. Moreover, the statistical analysis reveals that the r coefficient of 0.80 indicates a high positive correlation between the variables. The p-value of 0.00, which is less than 0.05, leads to the decision to reject the null hypothesis. Hence, a significant relationship exists between procrastination and academic burnout among grade 12 senior high school students. (shrink)

In statistics, there are two main paradigms: classical and Bayesian statistics. The purpose of this article is to investigate the extent to which classicists and Bayesians can agree. My conclusion is that, in certain situations, they cannot. The upshot is that, if we assume that the classicist is not allowed to have a higher degree of belief in a null hypothesis after he has rejected it than before, then he has to either have trivial or incoherent credences to begin (...) with or fail to update his credences by conditionalization. (shrink)

Mental health among students is one of the major concerns amidst the pandemic. Employing a correlational design, this study investigates the relationship between emotional intelligence and mental health among 152 senior high school students. Based on the statistical analysis, the r coefficient of 0.82 indicates a high positive correlation between the variables. The p-value of 0.00, which is less than 0.05, leads to the decision to reject the null hypothesis. Hence, a significant relationship exists between emotional intelligence and mental (...) health among senior high school. Implications were discussed in the study. (shrink)

It is argued that quantum theory is best understood as requiring an ontological duality of res extensa and res potentia, where the latter is understood per Heisenberg’s original proposal, and the former is roughly equivalent to Descartes’ ‘extended substance.’ However, this is not a dualism of mutually exclusive substances in the classical Cartesian sense, and therefore does not inherit the infamous ‘mind-body’ problem. Rather, res potentia and res extensa are proposed as mutually implicative ontological extants that serve to explain the (...) key conceptual challenges of quantum theory; in particular, nonlocality, entanglement, null measurements, and wave function collapse. It is shown that a natural account of these quantum perplexities emerges, along with a need to reassess our usual ontological commitments involving the nature of space and time. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...) Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

The replication crisis has caused researchers to distinguish between exact replications, which duplicate all aspects of a study that could potentially affect the results, and direct replications, which duplicate only those aspects of the study that are thought to be theoretically essential to reproduce the original effect. The replication crisis has also prompted researchers to think more carefully about the possibility of making Type I errors when rejecting null hypotheses. In this context, the present article considers the utility of (...) two types of Type I error probability: the Neyman–Pearson long run Type I error rate and the Fisherian sample-specific Type I error probability. It is argued that the Neyman–Pearson Type I error rate is inapplicable in social science because it refers to a long run of exact replications, and social science deals with irreversible units that make exact replications impossible. Instead, the Fisherian sample-specific Type I error probability is recommended as a more meaningful way to conceptualize false positive results in social science because it can be applied to each sample-specific decision about rejecting the same substantive null hypothesis in a series of direct replications. It is concluded that the replication crisis may be partly due to researchers’ unrealistic expectations about replicability based on their consideration of the Neyman–Pearson Type I error rate across a long run of exact replications. (shrink)

This study investigates the significant relationship between procrastination and academic burnout among first-year college students. Employing correlational design and standardized tests, the statistical analysis reveals that the r coefficient of 0.33 indicates a low positive correlation between the variables. The p-value of 0.00, which is less than 0.05, leads to the decision to reject the null hypothesis. Hence, a significant relationship exists between procrastination and academic burnout among college students.

This study investigates the relationship between self-efficacy and resilience among 150 first-year college students. This study used a correlational research design. Thus, General Self-Efficacy Scale and Resilience Scale were utilized to measure the variables. Furthermore, the statistical analysis reveals that the r coefficient of 0.48 indicates a low positive correlation between the variables. The p-value of 0.00, which is less than 0.05, leads to the decision to reject the null hypothesis. Hence, a significant relationship exists between self-efficacy and resilience (...) among first-year college students. Implications were discussed in the study. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

Where $\underline{a}$ is a Turing degree and ξ is an ordinal $ , the result of performing ξ jumps on $\underline{a},\underline{a}^{(\xi)}$ , is defined set-theoretically, using Jensen's fine-structure results. This operation appears to be the natural extension through $(\aleph_1)^{L^\underline{a}}$ of the ordinary jump operations. We describe this operation in more degree-theoretic terms, examine how much of it could be defined in degree-theoretic terms and compare it to the single jump operation.

Scientists often adjust their significance threshold during null hypothesis significance testing in order to take into account multiple testing and multiple comparisons. This alpha adjustment has become particularly relevant in the context of the replication crisis in science. The present article considers the conditions in which this alpha adjustment is appropriate and the conditions in which it is inappropriate. A distinction is drawn between three types of multiple testing: disjunction testing, conjunction testing, and individual testing. It is argued that (...) alpha adjustment is only appropriate in the case of disjunction testing, in which at least one test result must be significant in order to reject the associated joint null hypothesis. Alpha adjustment is inappropriate in the case of conjunction testing, in which all relevant results must be significant in order to reject the joint null hypothesis. Alpha adjustment is also inappropriate in the case of individual testing, in which each individual result must be significant in order to reject each associated individual null hypothesis. The conditions under which each of these three types of multiple testing is warranted are examined. It is concluded that researchers should not automatically assume that alpha adjustment is necessary during multiple testing. Illustrations are provided in relation to joint studywise hypotheses and joint multiway ANOVAwise hypotheses. (shrink)

Several researchers have recently argued that p values lose their meaning in exploratory analyses due to an unknown inflation of the alpha level (e.g., Nosek & Lakens, 2014; Wagenmakers, 2016). For this argument to be tenable, the familywise error rate must be defined in relation to the number of hypotheses that are tested in the same study or article. Under this conceptualization, the familywise error rate is usually unknowable in exploratory analyses because it is usually unclear how many hypotheses have (...) been tested on a spontaneous basis and then omitted from the final research report. In the present article, I argue that it is inappropriate to conceptualize the familywise error rate in relation to the number of hypotheses that are tested. Instead, it is more appropriate to conceptualize familywise error in relation to the number of different tests that are conducted on the same null hypothesis in the same study. Under this conceptualization, alpha level adjustments in exploratory analyses are (a) less necessary and (b) objectively verifiable. As a result, p values do not lose their meaning in exploratory analyses. (shrink)

A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...) using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)

Because of the COVID-19 pandemic, procrastination has become commonplace due to changes in teaching and learning, which trigger students' academic burnout. As a result, it has increased the intensity of procrastination among students who are enrolled in online learning programs. As a result, students have difficulty as a result of the rapid change from in-person learning to online learning. The study investigates the relationship between academic burnout and procrastination among 150 grade 12 senior high school students. Hence, this study employed (...) a correlational design. Based on the inferential analysis, the r coefficient of 0.71 indicates a high positive correlation between the variables. The p-value of 0.00, which is less than 0.05, leads to the decision to reject the null hypothesis. Hence, a significant relationship exists between academic burnout and academic procrastination among grade 12 senior high school students. (shrink)

We argue that genuine modal realism can be extended, rather than modified, so as to allow for the possibility of nothing concrete, a possibility we term ‘metaphysical nihilism’. The issue should be important to the genuine modal realist because, not only is metaphysical nihilism itself intuitively plausible, but also it is supported by an argument with pre-theoretically credible premises, namely, the subtraction argument. Given the soundness of the subtraction argument, we show that there are two ways that the genuine modal (...) realist can accommodate metaphysical nihilism: (i) by allowing for worlds containing only spatiotemporal points and (ii) by allowing for a world containing nothing but the null individual. On methodological grounds, we argue that the genuine modal realist should reject the former way but embrace the latter way. (shrink)

This paper defends a realist account of the composition of Newtonian forces, dubbed ‘residualism’. According to residualism, the resultant force acting on a body is identical to the component forces acting on it that do not prevent each other from bringing about its acceleration. Several reasons to favor residualism over alternative accounts of the composition of forces are advanced. (i) Residualism reconciles realism about component forces with realism about resultant forces while avoiding any threat of causal overdetermination. (ii) Residualism provides (...) a systematic semantics for the term ‘force’ within Newtonian mechanics. (iii) Residualism allows us to precisely apportion the causal responsibility of each component force in the ensuing acceleration. (iv) Residualism handles special cases such as null forces, single forces, and antagonistic forces in a natural way. (v) Residualism provides a neat picture of the causal powers of forces: each force essentially has two causal powers⎯the power to bring about accelerations (sometimes together with other co-directionnal forces) and the power to prevent other forces from doing so⎯exactly one of which is manifested at a time. (vi) Residualism avoids commitment to unobservable effects of forces: forces cause either stresses (tensile or compressive) or accelerations. (shrink)

This thesis inquires what it means to interpret non-relativistic quantum mechanics (QM), and the philosophical limits of this interpretation. In pursuit of a scientific-realist stance, a metametaphysical method is expanded and applied to evaluate rival interpretations of QM, based on the conceptual distinction between ontology and metaphysics, for objective theory choice in metaphysical discussions relating to QM. Three cases are examined, in which this metametaphysical method succeeds in indicating what are the wrong alternatives to interpret QM in metaphysical terms. The (...) first two cases failed in doing so due to different kinds of underdetermination. In the third case, unlike underdetermination, where there are many choices to be made, a “null-determination” is proposed where there may be no metaphysical choices in the available metaphysical literature. Considering what has been discussed, an agnostic philosophic position is adopted concerning the possibility of interpreting QM from a scientific-realistic point of view. (shrink)

This study evaluates the relationship between mental health and academic motivation among third-year college TES grantees. Thus, correlational design was employed to determine if there is a significant relationship between mental health and academic motivation among 150 third-year TES grantees. Statistical findings reveal that the r coefficient of 0.52 indicates a moderate positive correlation between the variables. The p-value of 0.00, which is less than 0.05, leads to rejecting the null hypothesis. Hence, a significant relationship exists between mental health (...) and academic motivation of third-year college TES grantees. Implications were discussed in the study. (shrink)

The COVID-19 outbreak had a profound impact on many facets of society, particularly on the educational system. Therefore, all educational content must be delivered to students online, and it is the student’s responsibility to adjust to this new norm. Hence, this study sought to investigate if there is a significant relationship between self-efficacy and resilience among senior high school students. This study utilized correlational research, with the 150 grade 12 senior high school students enrolled in 2022-2023 as respondents. Thus, the (...) researchers employed General Self-Efficacy and Resilience Scale. Finally, the statistical analysis reveals that the r coefficient of 0.53 indicates a moderate positive correlation between the variables. The p-value of 0.00, less than 0.05, leads to rejecting the null hypothesis. Hence, a significant relationship exists between self-efficacy and resilience among senior high school students. (shrink)

Online education has become an essential component of education. Thus, several factors, such as the student’s learning strategy and motivation, generally contribute to their academic success. This study investigates the relationship between learning strategies, motivation, and online learning environment among 150 first-year college students. Employing correlational design, the statistical findings of the study reveal that the r coefficient of 0.59 indicates a moderate positive correlation between the variables. The p-value of 0.00, which is less than 0.05, leads to the decision (...) to reject the null hypothesis. Hence, a significant relationship exists between learning strategies, motivation, and the online learning environment. (shrink)

This study assessed quality assurance practices and students’ performance evaluation in universities of South-South Nigeria using an SEM approach. Three null hypotheses guided the study. Based on factorial research design, and using a stratified random sampling technique, a sample of 878 academic staff were drawn from a sampling frame of 15 universities in South-South Nigeria. Quality Assurance Practices Students’ Performance Evaluation Scale (QAPSPES) with split-half reliability estimates ranging from .86–.92, was used as the instruments for data collection. Multiple regression (...) and Confirmatory Factor Analyses (CFA) were used for the analysis of data, model building, and testing of the hypotheses at .05 alpha level. Findings showed a significant composite and relative influence (F=48.19, P<.05) of school management, staff, and students’ quality assurance practices on students’ performance evaluation. The results also indicated that there were positive and significant covariances between the four variables of this study, with the CFI, RMSEA, TLI, and SRMR values indicating a good model fit. It was recommended, based on the findings of this study that, each school should organize quality assurance orientation campaigns for new students and set up quality assurance committees at the school, faculty and departmental levels for optimal performance in schools. (shrink)

Due to the COVID-19 Pandemic, several changes have been forcibly made and observed in various fields and areas of society, one of which include the field of education; the foundation of the formation of intellect and knowledge. After two years of studying indoors and private educational institutions holding virtual classes, the time has finally come for students to be re- adjusted once more to the blended mode of learning; a combination of virtual and in-person classes. Thus, this study aimed to (...) investigate the development of students’ study habits and how these habits could potentially affect the students’ academic achievement or performance. The study utilized a descriptivecorrelational design to examine the impact of study habits to the academic performance of 137 senior high school students. The study made use of the Palsane and Sharma’s Study Habits Inventory, or also known as PSSHI, and using this instrument, the study has been able to procure sufficient results that will answer the present study’s problems. Using linear regression analysis, the present study found that there was a significance between the study habits and academic performance of the senior high school students, thus the study’s null hypothesis was eventually rejected. (shrink)

The abrupt shift in learning mode demands students to adjust from the comfort of their homes, as well as the challenges of face-to-face learning. As a result, as the pandemic fades, institutions in the Philippines have begun to reopen their doors to students. Hence, this study employed a correlational design to investigate the relationship between procrastination and academic burnout among 150 first-year college students in a state university. Based on the statistical analysis, the r coefficient of 0.67 indicates a moderate (...) positive correlation between the variables. The p-value of 0.00, which is less than 0.05, leads to the decision to reject the null hypothesis. Hence, a significant relationship exists between procrastination and academic burnout among first-year college students. Implications and recommendations were discussed in the study. (shrink)

This study investigated innovation management and effectiveness of educational research in tertiary institutions in Cross River State. One research question and one null hypothesis were formulated to direct the study. The study adopted factorial research design. Census technique was adopted by the researcher in selecting the entire population of 80 participants from four (4) tertiary institutions in Cross River State. “Innovation Management Questionnaire (IMQ)” and “Effectiveness of Educational Research Rating Scale (EERRS) were used as instruments for data collection. The (...) reliability of the instruments was established through test-retest method and reliability estimates of .89 and .86 were obtained. The null hypothesis was tested at .05 level of significance using multiple regression analysis with the aid of SPSS version 21. Findings from the study established a composite contribution of 70.5% of data management innovations, research ethics management, provision of research grants to effectiveness of educational research (Adj. R2= .705). The findings of this study also established that; data management innovations, research ethics management, and provision of research grants jointly has a significant influence on effectiveness of educational research (F = 64.055, p <.05). Data management innovations was the highest predictor (β = .501, t = 7.778), followed by research ethics management ethics management (β = .311, t = 3.956), and provision of research grants (β = .291, t = 3.707) in that order. Based on the findings, it was recommended, amongst others, that educational research data (including coded data) should be effectively managed by tertiary institutions using both manual and computerized data management devices with corresponding appropriate retrieval systems. (shrink)

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.