If someone unintentionally breaks the rules, do they break the rules? In the abstract, the answer is obviously “yes.” But, surprisingly, when considering specific examples of unintentional, blameless rule-breaking, approximately half of people judge that no rule was broken. This effect, known as excuse validation, has previously been observed in American adults. Outstanding questions concern what causes excuse validation, and whether it is peculiar to American moral psychology or cross-culturally robust. The present paper studies the phenomenon cross-culturally, focusing (...) on Korean and American adults, and proposes a new explanation of why people engage in excuse validation, in terms of competing forces in human norm-psychology. The principal findings are that Americans and Koreans engaged in excuse validation at similar levels, and older adults were more likely to engage in excuse validation. (shrink)

What is a valid measuring instrument? Recent philosophy has attended to logic of justification of measures, such as construct validation, but not to the question of what it means for an instrument to be a valid measure of a construct. A prominent approach grounds validity in the existence of a causal link between the attribute and its detectable manifestations. Some of its proponents claim that, therefore, validity does not depend on pragmatics and research context. In this paper, I cast (...) doubt on the possibility of a context-independent causal account of validity (what I call unconditional validity). I assess several versions, arguing that all of them fail to judge the validity of measuring instruments correctly. Because different research purposes require different properties from measuring instruments, no account of validity succeeds without referring to the specific research purpose that creates the need for measurement in the first place. (shrink)

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

Beall and Murzi :143–165, 2013) introduce an object-linguistic predicate for naïve validity, governed by intuitive principles that are inconsistent with the classical structural rules. As a consequence, they suggest that revisionary approaches to semantic paradox must be substructural. In response to Beall and Murzi, Field :1–19, 2017) has argued that naïve validity principles do not admit of a coherent reading and that, for this reason, a non-classical solution to the semantic paradoxes need not be substructural. The aim of this paper (...) is to respond to Field’s objections and to point to a coherent notion of validity which underwrites a coherent reading of Beall and Murzi’s principles: grounded validity. The notion, first introduced by Nicolai and Rossi, is a generalisation of Kripke’s notion of grounded truth, and yields an irreflexive logic. While we do not advocate the adoption of a substructural logic, we take the notion of naïve validity to be a legitimate semantic notion that points to genuine expressive limitations of fully structural revisionary approaches. (shrink)

The validity of psychological measurement is crucially connected to a peculiar form of epistemic circularity. This circularity can be a threat when there are no independent ways to assess whether a certain procedure is actually measuring the intended target of measurement. This paper focuses on how Gustav Theodor Fechner addressed the measurement circularity that emerged in his psychophysical research. First, I show that Fechner's approach to the problem of circular measurement involved a core idealizing assumption of a shared human physiology. (...) Second, I assess Fechner's approach to this issue against the backdrop of his own epistemology of measurement and the measurement context of his time. Third, I claim that, from a coherentist and historicallysituated perspective, Fechner's quantification can be regarded as a first successful step of a longer-term quantification process. To conclude, I draw from these insights some general epistemological reflections that are relevant to current quantitative psychology. (shrink)

According to a standard story, part of what we have in mind when we say that an argument is valid is that it is necessarily truth preserving: if the premises are true, the conclusion must also be true. But—the story continues—that’s not enough, since ‘Roses are red, therefore roses are coloured’ for example, while it may be necessarily truth-preserving, is not so in virtue of form. Thus we arrive at a standard contemporary characterisation of validity: an argument is valid when (...) it is NTP in virtue of form. Here I argue that we can and should drop the N; the resulting account is simpler, less problematic, and performs just as well with examples. (shrink)

This paper looks at the question of what it means for a psychological test to have construct validity. I approach this topic by way of an analysis of recent debates about the measurement of implicit social cognition. After showing that there is little theoretical agreement about implicit social cognition, and that the predictive validity of implicit tests appears to be low, I turn to a debate about their construct validity. I show that there are two questions at stake: First, what (...) level of detail and precision does a construct have to possess such that a test can in principle be valid relative to it? And second, what kind of evidence needs to be in place such that a test can be regarded as validated relative to a given construct? I argue that construct validity is not an all-or-nothing affair. It can come in degrees, because both our constructs and our knowledge of the explanatory relation between constructs and data can vary in accuracy and level of detail, and a test can fail to measure all of the features associated with a construct. I conclude by arguing in favor of greater philosophical attention to processes of construct development. (shrink)

In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

While Thomas Kuhn's theory of scientific revolutions does not specifically deal with validation, the validation of simulations can be related in various ways to Kuhn's theory: 1) Computer simulations are sometimes depicted as located between experiments and theoretical reasoning, thus potentially blurring the line between theory and empirical research. Does this require a new kind of research logic that is different from the classical paradigm which clearly distinguishes between theory and empirical observation? I argue that this is not (...) the case. 2) Another typical feature of computer simulations is their being ``motley'' (Winsberg 2003) with respect to the various premises that enter into simulations. A possible consequence is that in case of failure it can become difficult to tell which of the premises is to blame. Could this issue be understood as fostering Kuhn's mild relativism with respect to theory choice? I argue that there is no need to worry about relativism with respect to computer simulations, in particular. 3) The field of social simulations, in particular, still lacks a common understanding concerning the requirements of empirical validation of simulations. Does this mean that social simulations are still in a pre-scientific state in the sense of Kuhn? My conclusion is that despite ongoing efforts to promote quality standards in this field, lack of proper validation is still a problem of many published simulation studies and that, at least large parts of social simulations must be considered as pre-scientific. (shrink)

Nontransitive responses to the validity Curry paradox face a dilemma that was recently formulated by Barrio, Rosenblatt and Tajer. It seems that, in the nontransitive logic ST enriched with a validity predicate, either you cannot prove that all derivable metarules preserve validity, or you can prove that instances of Cut that are not admissible in the logic preserve validity. I respond on behalf of the nontransitive approach. The paper argues, first, that we should reject the detachment principle for naive validity. (...) Secondly, I show how to add a validity predicate to ST while avoiding the dilemma. (shrink)

Can judging that an agent blamelessly broke a rule lead us to claim, paradoxically, that no rule was broken at all? Surprisingly, it can. Across seven experiments, we document and explain the phenomenon of excuse validation. We found when an agent blamelessly breaks a rule, it significantly distorts people’s description of the agent’s conduct. Roughly half of people deny that a rule was broken. The results suggest that people engage in excuse validation in order to avoid indirectly blaming (...) others for blameless transgressions. Excuse validation has implications for recent debates in normative ethics, epistemology and the philosophy of language. These debates have featured thought experiments perfectly designed to trigger excuse validation, inhibiting progress in these areas. (shrink)

For semantic inferentialists, the basic semantic concept is validity. An inferentialist theory of meaning should offer an account of the meaning of "valid." If one tries to add a validity predicate to one's object language, however, one runs into problems like the v-Curry paradox. In previous work, I presented a validity predicate for a non-transitive logic that can adequately capture its own meta-inferences. Unfortunately, in that system, one cannot show of any inference that it is invalid. Here I extend the (...) system so that it can capture invalidities. (shrink)

Psychiatric research is in crisis because of repeated failures to discover new drugs for mental disorders. Lack of measurement validity could partly account for these failures. If researchers do not actually measure the effects of drugs on the disorders they aim to investigate, one should expect suboptimal treatment outcomes. I argue that this is the case, focusing on depression, and fear & anxiety disorders. In doing so, I show how psychiatric research illustrates a more general phenomenon that I call “validity (...) drift.” A validity drift occurs when, in the course of developing new measurement procedures, researchers end up studying something different from what they originally aimed to study. I analyze the different ways in which scientists attempt to validate procedures for measuring mental disorders for the purpose of testing drugs in animal models. I show how those validation efforts might fail, thereby leading to validity drifts. Overall, this analysis highlights the complex interplay between the development of new measurement procedures, their calibration, and scientific theories of the target phenomena. (shrink)

The following four theses all have some intuitive appeal: (I) There are valid norms. (II) A norm is valid only if justified by a valid norm. (III) Justification, on the class of norms, has an irreflexive proper ancestral. (IV) There is no infinite sequence of valid norms each of which is justified by its successor. However, at least one must be false, for (I)--(III) together entail the denial of (IV). There is thus a conflict between intuition and logical possibility. This (...) paper, after distinguishing various conceptions of a norm, of validity and of justification, argues for the following position. (I) is true. (II) is false for legislative justification and true for epistemic justification. (III) is true for legislative and false for epistemic justification. (IV) is true for legislative justification; for epistemic justification (IV) is true or false depending on the conception taken of a norm. Our intuition in favour of (II) must therefore be abandoned where justification is conceived legislatively. Our intuition in favour of (III) must be abandoned, and our intuition in favour of (IV) qualified, where justification is conceived epistemically. (shrink)

What are people who disagree about logic disagreeing about? The paper argues that (in a wide range of cases) they are primarily disagreeing about how to regulate their degrees of belief. An analogy is drawn between beliefs about validity and beliefs about chance: both sorts of belief serve primarily to regulate degrees of belief about other matters, but in both cases the concepts have a kind of objectivity nonetheless.

Computer simulations of the formation and evolution of large-scale structure in the universe are integral to the enterprise of modern cosmology. Establishing the reliability of these simulations has been extremely challenging, primarily because of epistemic opacity. In this setting, robustness analysis defined by requiring converging outputs from a diverse ensemble of simulations is insufficient to determine simulation validity. We propose an alternative path of structured code validation that applies eliminative reasoning to isolate and reduce possible sources of error, a (...) potential path that is already being explored by some cosmologists. (shrink)

In this paper we describe a few interrelated issues for validating theories that posit levels of consciousness. First, validating levels of consciousness requires consensus about the ordering of conscious states, which cannot be easily achieved. This problem is particularly severe if we believe conscious states can be irreducibly smeared over time. Second, the relationship between conscious states is probably sometimes intransitive, which means levels of consciousness will not be amenable to a single continuous measure. Finally, even if a multidimensional approach (...) to levels of consciousness is adopted, we argue that there are further problems for its validation. (shrink)

Thomas Hofweber takes the semantic paradoxes to motivate a radical reconceptualization of logical validity, rejecting the idea that an inference rule is valid just in case every instance thereof is necessarily truth-preserving. Rather than this “strict validity”, we should identify validity with “generic validity”, where a rule is generically valid just in case its instances are truth preserving, and where this last sentence is a generic, like “Bears are dangerous”. While sympathetic to Hofweber’s view that strict validity should be replaced (...) by something allowing for exceptions, I argue that this should instead be truth-conduciveness, a matter of a large majority of instances being truth-preserving. The fact that inference rules have uncountably many instances, I argue, can be handled by defining truth-conduciveness as relative to finite sets of instances. Moreover, I argue that Hofweber’s position, while seemingly radical, may be less so under closer scrutiny. For the mere claim that classical rules and unrestricted truth rules are generically valid (or truth-conducive) is not in itself controversial. Also, if there is an answer to the question of which of these are also strictly valid, then the claim that generic validity is the central notion in logic is at most an interest-relative matter, since there is then also a fact of the matter as to which inference rules are (not) strictly valid. If no solution operating with strict validity to the paradoxes can be had, however, then the claim that validity should be identified with a weaker notion is better motivated. I argue that it is reasonable, in view of past failures, to conjecture that no ordinary solution will score high enough relative to standard (uncontroversial) desiderata to merit justified belief. Hence, it is unknowable which solution is correct. I further argue that this is best explained by its being metaphysically indeterminate which solution is correct. If this conjecture is true, then we ought instead to think of validity as allowing exceptions, and then take the “true logic” to be one that takes both the classical rules and the truth rules to be valid, i.e., truth-conducive. This logic scores very high on the desiderata on logics, and is therefore preferable to any logic operating with strict validity. (shrink)

We report on an exploratory study of the way eight mid-level undergraduate mathematics majors read and reflected on four student-generated arguments purported to be proofs of a single theorem. The results suggest that mid-level undergraduates tend to focus on surface features of such arguments and that their ability to determine whether arguments are proofs is very limited -- perhaps more so than either they or their instructors recognize. We begin by discussing arguments (purported proofs) regarded as texts and validations of (...) those arguments, i.e., reflections of individuals checking whether such arguments really are proofs of theorems. We relate the way the mathematics research community views proofs and their validations to ideas from reading comprehension and literary theory. We then give a detailed analysis of the four student-generated arguments and finally analyze the eight students' validations of them. (shrink)

Firstly I characterize Simple Partial Logic (SPL) as the generalization and extension of a certain two-valued logic. Based on the characterization I present two definitions of validity in SPL. Finally I show that given my characterization these two definitions are more appropriate than other definitions that have been prevalent, since both have some desirable semantic properties that the others lack.

Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious (...) problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty. (shrink)

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...) in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

Introduction The Defining Issues Test (DIT) aimed to measure one’s moral judgment development in terms of moral reasoning. The Neo-Kohlbergian approach, which is an elaboration of Kohlbergian theory, focuses on the continuous development of postconventional moral reasoning, which constitutes the theoretical basis of the DIT. However, very few studies have directly tested the internal structure of the DIT, which would indicate its construct validity. Objectives Using the DIT-2, a later revision of the DIT, we examined whether a bi-factor model or (...) 3-factor CFA model showed a better model fit. The Neo-Kohlbergian theory of moral judgment development, which constitutes the theoretical basis for the DIT-2, proposes that moral judgment development occurs continuously and that it can be better explained with a soft-stage model. Given these assertions, we assumed that the bi-factor model, which considers the Schema-General Moral Judgment (SGMJ), might be more consistent with Neo-Kohlbergian theory. Methods We analyzed a large dataset collected from undergraduate students. We performed confirmatory factor analysis (CFA) via weighted least squares. A 3-factor CFA based on the DIT-2 manual and a bi-factor model were compared for model fit. The three factors in the 3-factor CFA were labeled as moral development schemas in Neo-Kohlbergian theory (i.e., personal interests, maintaining norms, and postconventional schemas). The bi-factor model included the SGMJ in addition to the three factors. Results In general, the bi-factor model showed a better model fit compared with the 3-factor CFA model although both models reported acceptable model fit indices. Conclusion We found that the DIT-2 scale is a valid measure of the internal structure of moral reasoning development using both CFA and bi-factor models. In addition, we conclude that the soft-stage model, posited by the Neo-Kohlbergian approach to moral judgment development, can be better supported with the bi-factor model that was tested in the present study. (shrink)

Tarski's Undefinability of Truth Theorem comes in two versions: that no consistent theory which interprets Robinson's Arithmetic (Q) can prove all instances of the T-Scheme and hence define truth; and that no such theory, if sound, can even express truth. In this note, I prove corresponding limitative results for validity. While Peano Arithmetic already has the resources to define a predicate expressing logical validity, as Jeff Ketland has recently pointed out (2012, Validity as a primitive. Analysis 72: 421-30), no theory (...) which interprets Q closed under the standard structural rules can define nor express validity, on pain of triviality. The results put pressure on the widespread view that there is an asymmetry between truth and validity, viz. that while the former cannot be defined within the language, the latter can. I argue that Vann McGee's and Hartry Field's arguments for the asymmetry view are problematic. (shrink)

Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they recommend a radical (...) solution to both paradoxes, involving a substructural logic, in particular, one without structural contraction. In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together, there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the second incompleteness theorem. (shrink)

This paper examines the role existence plays in measurement validity. I argue that existing popular theories of measurement and of validity follow a correspondence framework, which starts by assuming that an entity exists in the real world with certain properties that allow it to be measurable. Drawing on literature from the sociology of measurement, I show that the correspondence framework faces several theoretical and practical challenges. I suggested the validity-first framework of measurement, which starts with a practice-based validation process (...) as the basis for a measurement theory, and only posits objective existence when it is scientifically useful to do so. (shrink)

What accounts for how we know that certain rules of reasoning, such as reasoning by Modus Ponens, are valid? If our knowledge of validity must be based on some reasoning, then we seem to be committed to the legitimacy of rule-circular arguments for validity. This paper raises a new difficulty for the rule-circular account of our knowledge of validity. The source of the problem is that, contrary to traditional wisdom, a universal generalization cannot be inferred just on the basis of (...) reasoning about an arbitrary object. I argue in favor of a more sophisticated constraint on reasoning by universal generalization, one which undermines a rule-circular account of our knowledge of validity. (shrink)

There is an old worry, which dates back to Mill but has analogs even in Sextus, that the very definition of ‘validity’ implies that all valid arguments are circular. This paper investigates how contemporary formal tools can ellucidate that old worry. Its main finding is the existence of a genuine puzzle: a difficult-to-avoid correspondence between the definitions of ‘valid argument’ and ‘premise circular argument’.

Instructional material is an integral part of teaching and learning process. Validating instructional materials is imperative to ensure quality before widespread utilization. This study validated the developed Gamified Instructional Material (GIM) in genetics for grade 12 STEM students. It employed the descriptive-developmental research design involving 41 STEM students and 11 Biology education experts chosen through purposive sampling. Findings revealed that students and experts strongly agreed that the GIM satisfied the criteria for a sound and valid instructional material. Further, the significant (...) change in the pretest and posttest scores of students indicated an improvement of their knowledge in genetics. It is recommended that the GIM be used as supplementary instructional material in teaching genetics. (shrink)

This study used a structural equation modelling approach to assess the association between employee work- life policies, psychological empowerment, and academic staff job commitment in universities in Cross River State, Nigeria. Three null hypotheses were formulated to guide the study following a descriptive survey research design. Multistage sampling procedure was adopted in the selection of 315 academic staff from two universities in the study area. “Work-Life Policies, Psychological Empowerment and Job Commitment Questionnaire (WPPEJCQ)” was used as the instrument for data (...) collection. The construct validity of the instrument was ascertained through an Exploratory Factor Analysis (EFA) using the Principal Component Analysis (PCA). The Kaiser-Meyer-Ohlin of .894 and the Bartlett coefficient of 7795.820 were obtained. Several fit indices of Confirmatory Factor Analysis were used to accept the model such as RMSEA=.031, TLI=.969, CFI=.971 and many others. The null hypotheses were all tested using Path analysis. Findings revealed, among others, that there is a significant effect of work-life policies on the affective (β=.774,t=21.636,p<.05), continuance (β=.450,t=8.932,p<.05), and normative (β=490,t=9.967,p<.05) dimensions of academic staff commitment; furthermore, psychological empowerment has a significant effect on the affective (β=.795,t=23.199,p<.05), continuance (β=.501,t=10.261,p<.05) and normative (β = .520, t = 10.795, p< .05) dimensions of staff commitment; and there is a significant composite effect of work-life policies and psychological empowerment on the affective, continuance, and normative commitment levels of academic staff in universities. Based on these findings, conclusions and recommendations were made. (shrink)

Havstad (2022) argues that the argument from inductive risk for the claim that non-epistemic values have a legitimate role to play in the internal stages of science is deductively valid. She also defends its premises and thus soundness. This is, as far as we are aware, the best reconstruction of the argument from inductive risk in the existing literature. However, there is a small flaw in this reconstruction of the argument from inductive risk which appears to render the argument invalid. (...) This flaw is superficial, and a small amendment to it rescues the claim of validity. (shrink)

The terms ‘verification’ and ‘validation’ are widely used in science, both in the natural and the social sciences. They are extensively used in simulation, often associated with the need to evaluate models in different stages of the simulation development process. Frequently, terminological ambiguities arise when researchers conflate, along the simulation development process, the technical meanings of both terms with other meanings found in the philosophy of science and the social sciences. This article considers the problem of verification and (...) class='Hi'>validation in social science simulation along five perspectives: The reasons to address terminological issues in simulation; the meaning of the terms in the philosophical sense of the problem of “truth”; the observation that some debates about these terms in simulation are inadvertently more terminological than epistemological; the meaning of the terms in the technical context of the simulation development process; and finally, a comprehensive outline of the relation between terminology used in simulation, different types of models used in the development process and different epistemological perspectives. (shrink)

This article argues for the formal validity of and the truth of the premises and conclusion of a version of Aquinas' "Third Way" that says: If each of the parts of nature is contingent, the whole of nature is contingent. Each of the parts of nature is contingent. Therefore, the whole of nature is contingent--where "contingent" means having a cause and not existing self-sufficiently.

The Defining Issues Test (DIT) has been widely used in psychological experiments to assess one’s developmental level of moral reasoning in terms of postconventional reasoning. However, there have been concerns regarding whether the tool is biased across people with different genders and political and religious views. To address the limitations, in the present study, I tested the validity of the brief version of the test, that is, the behavioral DIT, in terms of the measurement invariance and differential item functioning (DIF). (...) I could not find any significant non-invariance at the test level or any item demonstrating practically significant DIF at the item level. The findings indicate that neither the test nor any of its items showed a significant bias toward any particular group. As a result, the collected validity evidence supports the use of test scores across different groups, enabling researchers who intend to examine participants’ moral reasoning development across heterogeneous groups to draw conclusions based on the scores. (shrink)

Prisoners, those who probably engaged in criminal activities, might possess different perceptions and notions of moral foundations than non-prisoners. Thus, assessing such foundations among the population without testing the validity of the measure may produce biased outcomes. To address the potential methodological issue, we examined the validity of the measurement model for moral foundations among prisoners and community members, i.e., non-prisoners. We conducted the measurement invariance test and measurement alignment to test whether the model was consistently valid across the groups. (...) We also employed the differential item functioning test to examine whether item responses were not biased between the different populations. Results demonstrated significant measurement non-invariance and differential item functioning. However, measurement alignment could address the non-invariance issue. Between-group comparisons of moral foundations were consistent with findings from prior research after performing the alignment. (shrink)

It is one thing for a given proposition to follow or to not follow from a given set of propositions and it is quite another thing for it to be shown either that the given proposition follows or that it does not follow.* Using a formal deduction to show that a conclusion follows and using a countermodel to show that a conclusion does not follow are both traditional practices recognized by Aristotle and used down through the history of logic. These (...) practices presuppose, respectively, a criterion of validity and a criterion of invalidity each of which has been extended and refined by modern logicians: deductions are studied in formal syntax (proof theory) and coun¬termodels are studied in formal semantics (model theory). The purpose of this paper is to compare these two criteria to the corresponding criteria employed in Boole’s first logical work, The Mathematical Analysis of Logic (1847). In particular, this paper presents a detailed study of the relevant metalogical passages and an analysis of Boole’s symbolic derivations. It is well known, of course, that Boole’s logical analysis of compound terms (involving ‘not’, ‘and’, ‘or’, ‘except’, etc.) contributed to the enlargement of the class of propositions and arguments formally treatable in logic. The present study shows, in addition, that Boole made significant contributions to the study of deduc¬tive reasoning. He identified the role of logical axioms (as opposed to inference rules) in formal deductions, he conceived of the idea of an axiomatic deductive sys¬tem (which yields logical truths by itself and which yields consequences when ap¬plied to arbitrary premises). Nevertheless, surprisingly, Boole’s attempt to imple¬ment his idea of an axiomatic deductive system involved striking omissions: Boole does not use his own formal deductions to establish validity. Boole does give symbolic derivations, several of which are vitiated by “Boole’s Solutions Fallacy”: the fallacy of supposing that a solution to an equation is necessarily a logical consequence of the equation. This fallacy seems to have led Boole to confuse equational calculi (i.e., methods for gen-erating solutions) with deduction procedures (i.e., methods for generating consequences). The methodological confusion is closely related to the fact, shown in detail below, that Boole had adopted an unsound criterion of validity. It is also shown that Boole totally ignored the countermodel criterion of invalid¬ity. Careful examination of the text does not reveal with certainty a test for invalidity which was adopted by Boole. However, we have isolated a test that he seems to use in this way and we show that this test is ineffectual in the sense that it does not serve to identify invalid arguments. We go beyond the simple goal stated above. Besides comparing Boole’s earliest criteria of validity and invalidity with those traditionally (and still generally) employed, this paper also investigates the framework and details of THE MATHEMATICAL ANALYSIS OF LOGIC. (shrink)

The notion of validity for modal languages could be defined in two slightly different ways. The first is the original definition given by S. Kripke, for which a formula φ of a modal language L is valid if and only if it is true in every actual world of every interpretation of L. The second is the definition that has become standard in most textbook presentations of modal logic, for which a formula φ of L is valid if and only (...) if it is true in every world in every interpretation of L. For simple modal languages, “Kripkean validity” and “Textbook validity” are extensionally equivalent. According to E. Zalta, however, Textbook validity is an “incorrect” definition of validity, because: (i) it is not in full compliance with Tarski’s notion of truth; (ii) in expressively richer languages, enriched by the actuality operator, some obviously true formulas count as valid only if the Kripkean notion is used. The purpose of this paper is to show that (i) and (ii) are not good reasons to favor Kripkean valid- ity over Textbook validity. On the one hand, I will claim that the difference between the two should rather be seen as the result of two different conceptions on how a modal logic should be built from a non-modal basis; on the other, I will show the advantages, for the question at issue, of seeing the actuality operator as belonging to the family of two-dimensional operators. (shrink)

Background: Moral Growth Mindset (MGM) is a belief about whether one can become a morally better person through efforts. Prior research showed that MGM is positively associated with promotion of moral motivation among adolescents and young adults. We developed and tested the English version of the MGM measure in this study with data collected from college student participants. Methods: In Study 1, we tested the reliability and validity of the MGM measure with two-wave data (N = 212, Age mean = (...) 24.18 years, SD = 7.82 years). In Study 2, we retested the construct validity of the MGM measure once again and its association with other moral and positive psychological indicators to test its convergent and discriminant validity (N = 275, Age mean = 22.02 years, SD = 6.34 years). Results: We found that the MGM measure was reliable and valid from Study 1. In Study 2, the results indicated that the MGM was well correlated with other moral and positive psychological indicators as expected. Conclusions: We developed and validated the English version of the MGM measure in the present study. The results from studies 1 and 2 supported the reliability and validity of the MGM measure. Given this, we found that the English version of the MGM measure can measure one’s MGM as we intended. (shrink)

An inference is valid if it guarantees the transferability of knowledge from the premisses to the conclusion. If knowledge is here understood as demonstrative knowledge, and demonstration is explained as a chain of valid inferences, we are caught in an explanatory circle. In recent lectures, Per Martin-Löf has sought to avoid the circle by specifying the notion of knowledge appealed to in the explanation of the validity of inference as knowledge of a kind weaker than demonstrative knowledge. The resulting explanation (...) is the main topic of this article. (shrink)

Some philosophers argue that a theory of logical validity should not interpret its own language, because a Russellian argument shows that self-applicability is inconsistent with the ability to capture all the interpretations of its own language. First, I set up a formal system to examine the Russellian argument. I then defend the need for self-applicability. I argue that self-applicability seems to be implied by generality, and that the Russellian argument rests on a test for meaning that is biased against self-applicability. (...) I propose an alternative test which is unproblematic for self-applicability. I conclude that self-applicability can be vindicated and the Russellian argument can be resisted. (shrink)

In this paper, I claim that two ways of defining validity for modal languages (“real-world” and “general” validity), corresponding to distinction between a correct and an incorrect way of defining modal valid- ity, correspond instead to two substantive ways of conceiving modal truth. At the same time, I claim that the major logical manifestation of the real- world/general validity distinction in modal propositional languages with the actuality operator should not be taken seriously, but simply as a by-product of the way (...) in which the semantics of such an operator is usually given. (shrink)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

Friendship is an important bond in the personal and social growth of an individual and plays a prominent role during youth. Most scales to measure it are aimed at children and adolescents but none measure character friendship, a type of selfless friendship with ethical traits an d Aristotelian roots. Therefore, the aim of the research is to design and validate the youth Character Friendship Scale (CFS) in a sample of 1587 young Spanish people. The final version of the CFS is (...) composed of 35 items distributed over three dimensions: "Selfless love and intimacy" (21), "Trust" (7) and "Respect and forgiveness" (7) with ordinal reliability coefficients of 0.94, 0.79 and 0.7 respectively and good model fits (CFI = 0.986; TLI = 0.986; RMSEA = 0.043; SRMR = 0.054; GFI = 0.997). It is concluded that the CFS is a scale with good psychometric properties for measuring character friendship in young adults. The results obtained from its application will lead to a better understanding of the importance of character friendship for the socioemotional development or happiness of young adults and will enable the development of intervention programmes that enhance aspects of friendship such as trust, respect, forgiveness or mutual knowledge, which can facilitate collaborative relationships and contribute to social cohesion. (shrink)

Hardcore actualism (HA) grounds all modal truths in the concrete constituents of the actual world (see, e.g., Borghini and Williams (2008), Jacobs (2010), Vetter (2015)). I bolster HA, and elucidate the very nature of possibility (and necessity) according to HA, by considering if it can validate S5 modal logic. Interestingly, different considerations pull in different directions on this issue. To resolve the tension, we are forced to think hard about the nature of the hardcore actualist's modal reality and how radically (...) this departs from possible worlds orthodoxy. Once we achieve this departure, the prospects of a hardcore actualist validation of S5 look considerably brighter. This paper thus strengthens hardcore actualism by arguing that it can indeed validate S5–arguably the most popular logic of metaphysical modality–and, in the process, it elucidates the very nature of modality according to this revisionary, but very attractive, modal metaphysics. (shrink)

The first learning game to be developed to help students to develop and hone skills in constructing proofs in both the propositional and first-order predicate calculi. It comprises an autotelic (self-motivating) learning approach to assist students in developing skills and strategies of proof in the propositional and predicate calculus. The text of VALIDITY consists of a general introduction that describes earlier studies made of autotelic learning games, paying particular attention to work done at the Law School of Yale University, called (...) the ALL Project (Accelerated Learning of Logic). Following the introduction, the game of VALIDITY is described, first with reference to the propositional calculus, and then in connection with the first-order predicate calculus with identity. Sections in the text are devoted to discussions of the various rules of derivation employed in both calculi. Three appendices follow the main text; these provide a catalogue of sequents and theorems that have been proved for the propositional calculus and for the predicate calculus, and include suggestions for the classroom use of VALIDITY in university-level courses in mathematical logic. (shrink)

Abstract. First-year mathematics education students often face challenges with College and Advanced Algebra assessments. This study aimed to develop and validate a 100-item multiple-choice midterm test for College and Advanced Algebra, ensuring the test's validity and reliability. The test was designed following a structured process that included creating a Table of Specifications (TOS) based on the approved syllabus. To ensure content accuracy and relevance, the test was reviewed by three subject matter experts and evaluated for clarity by 15 students. Pilot (...) testing was conducted with 82 fourth-year Bachelor of Secondary Education Mathematics (BSEd Mathematics) students. The pilot test results underwent detailed item analysis, focusing on metrics such as the difficulty index, discrimination index, and overall reliability using the Kuder-Richardson Formula 20 (KR-20). Of the 100 items, 22 were retained, 48 were revised, and 30 were discarded. The test achieved a reliability coefficient of 0.876, indicating strong internal consistency. The findings suggest that the validated test questionnaire is a dependable tool for accurately assessing students’ knowledge in College and Advanced Algebra, providing valuable feedback for educators and students. (shrink)

The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics _S__T_ and _T__S_. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that in (...) these systems derivability can be characterized in terms of a notion we call absolute global validity. However, arriving at these results doesn’t lead us to disregard local validity. First, because we discuss the conditions under which local, and also global validity, can be expected to coincide with derivability. Secondly, because we show how taking into account certain families of valuations can be useful to describe derivability for different calculi used to present _S__T_ and _T__S_. (shrink)

This paper develops an account of normative validity and illustrates it through poverty measures. Many ideas addressed below are legatees of Anna Alexandrova’s reflections on what she called “value-aptness” in measuring well-being. To my knowledge, she introduced the term “normative validity” (Alexandrova, 2017: 151). Still, my goal is to address normative validity in a broader context than she did, highlighting its significance not only for well-being but also for other concepts, particularly poverty. I will further discuss how normative validity can (...) provide deeper insights into an important debate in poverty measurement: that between normative-driven approaches like Amartya Sen’s and data-driven ones like Peter Townsend’s. (shrink)

Formalizations in first-order logic are standardly used to represent logical forms of sentences and to show the validity of ordinary-language arguments. Since every sentence admits of a variety of formalizations, a challenge arises: why should one valid formalization suffice to show validity even if there are other, invalid, formalizations? This paper suggests an explanation with reference to criteria of adequacy which ensure that formalizations are related in a hierarchy of more or less specific formalizations. This proposal is then compared with (...) stronger criteria and assumptions, especially the idea that sentences essentially have just one logical form. (shrink)

Concurring to information from the Centresfor Illness Control and Anticipation, instruction and religion are both capable indicators of lasting or dissolving unions. The chance of a marriage finishing in separate was lower for individuals with more knowledge, with over half of relational unions of those who did not complete high school having finished in separate compared with roughly 30 percent of relational unions of college graduates. With this overview, the divorce rate dataset from UCI dataset repository is used for predicting (...) the divorce class target with the following contributions. Firstly, the Divorce rate dataset is subjected with the data cleaning and exploratory data analysis. Secondly, the data set is settled with different classifiers to look at the classification before and after feature scaling. Thirdly, the dataset is processed with various cross validation of training and testing dataset i.e 80:20, 30:70, 40:60, 50:50 to improve the accuracy of all the classifiers. Fourth, the dataset is processed with 15, 20 and 30 components of principal component analysis and then applied with all classifier algorithm to analyze the accuracy of divorce rate prediction. Fifth, the performance analysis is done with precision, recall, accuracy, fscore and running time to infer the classification before and after feature scaling. Experimental results show that the Random Forest classifier is found to have the accuracy of 98% for all PCA reduced dataset with 15, 20 and 30 components. The result showsthat Random Forest classifier is found to have the accuracy of 98% for 40:60, 50:50 of training and testing dataset. (shrink)