It is argued that contraposition is valid for a class of natural language conditionals, if some modifications are allowed to preserve the meaning of the original conditional. In many cases, implicit temporal indices must be considered, making a change in verb tense necessary. A suitable contrapositive for implicative counterfactual conditionals can also usually be found. In some cases, the addition of certain words is necessary to preserve meaning that is present in the original sentence and would be lost or (...) changed in the contrapositive without them. A distinction is made between adding new meaning and adding new words to preserve existing meaning. For concessive conditionals and relevance conditionals, however, no valid contrapositive can be found. They do not belong to the class of contraposable conditionals, which can be independently defined. Difficult cases are also discussed in which the contradictory of the consequent semantically entails the truth of the antecedent. In such cases the content of the antecedent is implicit in the meaning of the consequent. Contraposition becomes possible if what is implicit in the original consequent is made explicit in the contrapositive antecedent. (shrink)

A - "All ravens are black." B - "All non-black things are non-ravens." C - "All the elements of the set of ravens are elements of the set of black ravens." D - "All the elements of the set of the things that are not black ravens are elements of the set of the things that are not ravens." The propositions A, B, C, D are logically equivalent: if one proposition is true, the other three propositions are also true; if (...) one proposition is false, the other three propositions are also false. The generalizations A and C have the same instances: a black raven is an instance of A and is an instance of C. The generalizations B and D have some instances in common: a non-black object that is a non-raven is an instance of B and is an instance of D; in addition, the generalization D also has as its instances black objects that are non-ravens (for example, a black shoe is an instance of D but is not an instance of B). E - "All ravens are non-black." F - "All black things are non-ravens." G - "All the elements of the set of ravens are elements of the set of the things that are not black ravens". H - "All the elements of the set of black ravens are elements of the set of the things that are not ravens." The generalizations E and G have the same instances: a non-black raven is an instance of E and is an instance of G. By contrast, the generalizations F and H do not have the same instances: a black thing that is a non-raven is an instance of F; by contrast, H is a generalization that cannot have instances because a black raven that is a non-raven is a contradiction in terms. To summarize: A and C have the same instances; B and D have some instances in common; E and G have the same instances; by contrast, F and H do not have instances in common because H has no instances, H cannot have instances. To state that all black ravens are not ravens (as proposition H does) implies that the set of black ravens is not a subset of the set of ravens: hence proposition H is self-contradictory. Affirming that the set of black ravens is not a subset of the set of ravens contradicts the very definition of what a black raven is. Thus, even though the proposition H is the contrapositive of the proposition G, the propositions G and H are not logically equivalent since the proposition G is coherent and is a contingent proposition; the proposition H is incoherent and is a necessary falsehood. Furthermore: Peter Godfrey-Smith writes in the section 3.3 “The Ravens Problem” of his book “Theory and Reality” [chapter “Induction and Confirmation”]: “First, the logical empiricists were concerned to deal with the case where generalizations cover an infinite number of instances. In that case, as we see each raven we are not reducing the number of ways in which the hypothesis might fail”. In the raven paradox it is assumed that the set of ravens has infinite elements, therefore it is assumed that the set of ravens is not empty. The proposition G implies that the set of ravens contains an empty subset of black ravens: the proposition G is true in case there are not black ravens. The proposition H implies that the set of black ravens contains an empty subset of ravens: but in the raven paradox it is assumed that the set of ravens is not empty; hence the proposition H is false. The proposition H is not logically equivalent to the proposition G: in case there are ravens (as assumed in the raven paradox) but there are not black ravens, the proposition H is false but the proposition G is true. Thus, even though the proposition H is the contrapositive of the proposition G, the propositions G and H are not logically equivalent. (shrink)

Peter Godfrey-Smith writes in the section 3.3 “The Ravens Problem” of his book Theory and Reality [chapter “Induction and Confirmation”]: -/- “First, the logical empiricists were concerned to deal with the case where generalizations cover an infinite number of instances. In that case, as we see each raven we are not reducing the number of ways in which the hypothesis might fail.” -/- Infinite sets and finite sets have different properties and follow different rules. This distinction is fundamental when dealing (...) with scientific laws. For a statement to qualify as a law of nature, it must be assumed to hold across an infinite number of instances. These instances are not merely a collection of physical objects existing at a single moment, but are more accurately understood as time-slices of existence. -/- Consider a physical generalization such as M: "All metals expand when heated." To verify this as a universal law, we are not simply looking at a finite number of copper or iron rods. We are making a claim about every possible moment (time-slice) in which any metal exists, has existed, or will exist. Because time is continuous and the potential future is open-ended, the set of instances covered by M is necessarily assumed to be infinite. In such an infinite case, observing a finite number of instances (e.g., a thousand expanding metal slices) does not reduce the number of ways the hypothesis might fail. The remaining "pool" of instances stays infinite. -/- There is a profound asymmetry when we move from the direct generalization to its contrapositive. Let us examine this through a finite example first, to isolate the logical mechanics. -/- Suppose "bag X" contains exactly 90 marbles. The generalization A: All marbles in bag X are red" covers a finite number of instances. By contrast, the generalization AE: "All things that are not red are not marbles in bag X" refers to every non-red object in the universe. Even though A and AE are logically equivalent, there is an epistemic asymmetry: A can be fully confirmed (or disconfirmed) by checking a finite set, whereas AE refers to an effectively infinite set of non-red things. -/- This asymmetry becomes critical in the context of infinite sets and scientific laws. Consider a barrique X (205 liters): -/- B: "All minerals are in barrique X." -/- BE: "All objects that are not in barrique X are not minerals." -/- In generalization B, we refer to a set that is assumed to be an infinite set (the set of minerals) and to a finite set (the interior of barrique X). By contrast, in BE, we refer to two sets that are both assumed to be infinite: the set of all objects not in barrique X and the set of all non-minerals. Thus, an instance of BE (a non-mineral outside barrique X) cannot be epistemically equivalent to an instance of B. -/- C “All the elements of the set of ravens are elements of the set of black ravens”. CE “All the things that are not elements of the set of black ravens are not elements of the set of ravens”. -/- It is assumed that the number of ravens is infinite, but it is not assumed that the number of black ravens is infinite: that the number of black ravens is infinite is only a hypothesis (for which confirmation is sought), it cannot be assumed as true that the number of black ravens is infinite. Therefore, in the generalization C we refer to a set that is assumed to be an infinite set (the set of ravens) and to a set (the set of black ravens) that is not assumed to be an infinite set. By contrast, in the generalization CE we refer to two sets that are assumed to be infinite sets (the set of all objects that are not elements of the set of black ravens and the set of all objects that are not elements of the set of ravens). That CE has infinite instances is something we already know a priori (by virtue of the assumptions made); by contrast, we do not know a priori that C has infinite instances—that is merely an aspiration. Therefore, an instance of C carries weight, whereas an instance of CE tells us nothing more than what we already know a priori. (shrink)

I develop and defend a truthmaker semantics for the relevant logic R. The approach begins with a simple philosophical idea and develops it in various directions, so as to build a technically adequate relevant semantics. The central philosophical idea is that truths are true in virtue of specific states. Developing the idea formally results in a semantics on which truthmakers are relevant to what they make true. A very natural notion of conditionality is added, giving us relevant implication. I then (...) investigate ways to add conjunction, disjunction, and negation; and I discuss how to justify contraposition and excluded middle within a truthmaker semantics. (shrink)

Inductive conclusions rest upon the Uniformity Principle, that similar events lead to similar results. The principle derives from three fundamental axioms: Existence, that the observed object has an existence independent of the observer; Identity, that the objects observed, and the relationships between them, are what they are; and Continuity, that the objects observed, and the relationships between them, will continue unchanged absent a sufficient reason. Together, these axioms create a statement sufficiently precise to be falsified. Simple enumeration of successful observations (...) is ineffective to support an inductive conclusion. First, as its analytical device, induction uses the contrapositive form of the hypothesis; a successful observation merely represents the denial of the antecedent, from which nothing follows. Second, simple enumeration uses an invalid syllogism that fails to distribute its middle term. Instead, the inductive syllogism identifies its subject by excluding nonuniform results, using the contrapositive form of the hypotheses. The excluded data allows an estimate of the outer boundaries of the subject under examination. But an estimate of outer boundaries is as far as the inductive process may proceed; an affirmative identification of the content of the subject never becomes possible. (shrink)

The incompressible Navier–Stokes equations on the three-torus T³ admit global weak solutions (Leray), but whether these solutions remain smooth for all time is open. We resolve this by constructing a bounded vorticity-response functional Φ : ℝ≥0 → [φ_min, φ_max] that defines a temporal lifting of the equations. The construction generalizes Sundman's regularization of collision singularities in celestial mechanics, with vorticity magnitude serving as the regularizing variable. The lifting φ(τ) = ∫₀τ Φ(‖Ω(s)‖_L∞) ds satisfies non-degeneracy (φ′ ≥ φ_min > 0) and (...) global coverage (φ(τ) → ∞ as τ → ∞). Uniform bounds on Galerkin approximations, independent of the truncation parameter N, combined with coordinate invariance of the Beale–Kato–Majda integral, yield finiteness of the BKM integral in physical time. The contrapositive of the BKM criterion establishes global existence of classical solutions u ∈ C∞(T³ × [0, ∞)) for smooth divergence-free initial data; by weak-strong uniqueness, these coincide with the Leray–Hopf weak solutions, establishing their smoothness. This satisfies Fefferman's Clay Millennium Problem Statement (B). Numerical validation at Reynolds numbers up to 10⁸ confirms coordinate invariance and preservation of the dissipation identity ε = 2νZ. Numerical confirmation code and data available at doi:10.5281/zenodo.17730872. Paper DOI DOI: 10.63968/post-bio-ai-epistemics.v1n2.012. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

Substructural approaches to paradoxes have attracted much attention from the philosophical community in the last decade. In this paper we focus on two substructural logics, named ST and TS, along with two structural cousins, LP and K3. It is well known that LP and K3 are duals in the sense that an inference is valid in one logic just in case the contrapositive is valid in the other logic. As a consequence of this duality, theories based on either logic are (...) tightly connected since many of the arguments for and objections against one theory reappear in the other theory in dual form. The target of the paper is making explicit in exactly what way, if any, ST and TS are dual to one another. The connection will allow us to gain a more fine-grained understanding of these logics and of the theories based on them. In particular, we will obtain new insights on two questions concerning ST which are being intensively discussed in the current literature: whether ST preserves classical logic and whether it is LP in sheep’s clothing. Explaining in what way ST and TS are duals requires comparing these logics at a metainferential level. We provide to this end a uniform proof theory to decide on valid metainferences for each of the four logics. This proof procedure allows us to show in a very simple way how different properties of inferences (unsatisfiability, supersatisfiability and antivalidity) that behave in very different ways for each logic can be captured in terms of the validity of a metainference. (shrink)

We present a modular argument for global regularity of the three-dimensional incompressible Navier–Stokes equations by connecting classical blowup mechanisms to information-theoretic limitations on physical observers derived from recent results in quantum gravity. The exposition is organized into three independent components: (i) published observer-relative Hilbert space dimension formulas in closed quantum cosmologies; (ii) a ZFC-explicit symbolic embedding (the QPrime framework) placing Navier–Stokes states into an observer-relative Hilbert space; and (iii) a contrapositive implication that any finite-time Navier–Stokes blowup would force divergence of (...) an observer-weighted “symbolic curvature” functional, which in turn would require infinite observer entropy in finite time. Since physical observer entropy is universally finite at any finite time, a contradiction is obtained, excluding finite-time blowup. The resulting statement is global smooth existence and uniqueness for sufficiently regular divergence-free initial data. (shrink)

World food production is facing exorbitant challenges like climate change, use of resources, population growth, and dietary changes. These, in turn, raise major ethical and political questions, such as how to uphold the right to adequate nutrition, or the right to enact a gastronomic culture and to preserve the conditions to do so. Proposals for utopic solutions vary from vertical farming and lab meat to diets filled with the most fanciful insects and seaweeds. Common to all proposals is a polarized (...) understanding of food and diets, famously captured by Warren Belasco in the contraposition between technological fixes and anthropological fixes. According to the first, technology will deliver clean, just, pleasurable, affordable food; future generations will not need to adjust much of their dietary cultures. According to the second, future generations should dramatically change their dietary habits (what they eat and how they eat it) to achieve a sustainable diet. The two fixes found remarkably distinct perspectives over dietary politics and the ethics of food production and consumption. In this paper we argue that such polarized thinking rests on a misrepresentation of the ontological status of food, which in turn affects the underlying ethical and political issues. Food is a socially constructed object that draws in specific ways on habits, norms, traditions, geographical, and climatic conditions. Although this thesis seems somewhat obvious, its consequences on the ethical and political perspectives on the future of food have not been derived properly. After introducing the issue at stake (¤1), we point out the polarities that characterize food utopias (¤2) and their ontological faults (¤3). We hence suggest that a socio-ontological analysis of food can better deliver the principles for a foundation of food utopias (¤4). (shrink)

Those who want to deny the ‘ought implies can’ principle often turn to weakened views to explain ‘ought implies can’ phenomena. The two most common versions of such views are that ‘ought’ presupposes ‘can’, and that ‘ought’ conversationally implicates ‘can’. This paper will reject both views, and in doing so, present a case against any pragmatic view of ‘ought implies can’. Unlike much of the literature, I won't rely on counterexamples, but instead will argue that each of these views fails (...) on its own terms. ‘Ought’ and ‘can’ do not obey the negation test for presupposition, and they do not obey the calculability or the cancelability tests for conversational implicature. I diagnose these failures as partly a result of the importance of the contrapositive of ‘ought implies can’. I end with a final argument emphasizing the role the principle plays in moral thinking, and the fact that no pragmatic account can do it justice. (shrink)

Drawing on the puzzling behavior of ordinary knowledge ascriptions that embed an epistemic (im)possibility claim, we tentatively conclude that it is untenable to jointly endorse (i) an unfettered classical logic for epistemic language, (ii) the general veridicality of knowledge ascription, and (iii) an intuitive ‘negative transparency’ thesis that reduces knowledge of a simple negated ‘might’ claim to an epistemic claim without modal content. We motivate a strategic trade-off: preserve veridicality and (generalized) negative transparency, while abandoning the general validity of (...) class='Hi'>contraposition. We criticize various approaches to incorporating veridicality into domain semantics, a paradigmatic ‘information-sensitive’ framework for capturing negative transparency and, more generally, the non-classical behavior of sentences with epistemic modals. We then present a novel information-sensitive semantics that successfully executes our favored strategy: stable acceptance semantics, extending a vanilla bilateral state-based semantics for epistemic modals with a knowledge operator loosely inspired by the defeasibility theory of knowledge. (shrink)

The ambition of the paper is to provide a solution to the problem posed by Von Wright (1999): how is it possible that the two actions, one of producing P and the other of preventing P can have different deontic status, the former being obligatory and the latter being forbidden. The solution for the problem is sought for by an investigation into connections between imperative and deontic logic. First, it is asked whether a solution could be found in Lemmon's (1965) (...) system of "change logic", using his idea on connection between logic of orders being in force and deontic logic. The answer is the negative one. Next, the connection between Lemmon's imperative logic and deontic logic given in Aqvist's paper - "Next" and "Ought" (1965) - is analyzed. Than, the Lemmon's treatment of imperatives is restricted to the natural language imperatives and Aqvist's way of connecting imperative and deontic logic is modified accordingly. Some principles for the natural language imperatives are established (the negation rule ; the law of contraposition for imperative conditionals) and a simple "global" semantics is developed. The notion of "opposite action" is introduced and it is given an important role in semantics. Finally, a solution for von Wright's problem is given. In the closing sections some further topics for investigation are hinted: one of them being the connection between Aqvist's epistemic- imperative conception of interrogatives and "epistemic obligations", the other being formalization of the idea that imperatives create and re-create obligation patterns that can be described in deontic terms. (shrink)

In contemporary Western moral philosophy literature that discusses the Chinese ethical tradition, it is a commonplace practice to use the Chinese term daode 道德 as a technical translation of the English term moral. The present study provides some empirical evidence showing a discrepancy between the terms moral and daode. There is a much more pronounced difference between prototypically immoral and prototypically uncultured behaviors in English (USA) than between prototypically bu daode 不道德 and prototypically bu wenming 不文明 behaviors in Mandarin Chinese (...) (Mainland China). If the Western concept of immorality is defined in contraposition to things that are matters of etiquette or conventional norms and thus tied to a more or less tangible moral / conventional distinction, then we are dealing with a different structure in Mandarin Chinese – the prototypically bu daode and bu wenming behaviors seem to largely overlap. We also discuss whether bu lunli 不倫理 and bu hefa 不合法 can be considered adequate candidates for translation of immorality and we answer in the negative. (shrink)

Georg Cantor's absolute infinity, the paradoxical Burali-Forti class Ω of all ordinals, is a monstrous non-entity for which being called a "class" is an undeserved dignity. This must be the ultimate vexation for mathematical philosophers who hold on to some residual sense of realism in set theory. By careful use of Ω, we can rescue Georg Cantor's 1899 "proof" sketch of the Well-Ordering Theorem––being generous, considering his declining health. We take the contrapositive of Cantor's suggestion and add Zermelo's choice function. (...) This results in a concise and uncomplicated proof of the Well-Ordering Theorem. (shrink)

Language theorists have recently come to have an increasing appreciation for the fact that context contributes heavily in determining our interpretation of what is said. Indeed, it now seems clear that no complete understanding of a natural language is possible without some account of the way in which context affects our interpretation of discourse. In this paper, I will attempt to explore one facet of the language – context relationship, namely, the relation between conditionals and context. The first part of (...) the paper develops an account of truth for conditionals which allows them to depend on momentary features of the context in which they are uttered. In the second half of the paper, comparisons with other recent theories of the conditional will be considered. Particular attention will be given to the problem of whether the conditional really violates classical inferences such as Hypothetical Syllogism and Contraposition as has often been claimed in recent years. (shrink)

This paper is about four inferences patterns governing conditionals: Transitivity, Simplification, Contraposition, and Antecedent Strengthening. Transitivity, Simplification, and Contraposition are intuitively compelling. Although Antecedent Strengthening may seem less attractive at first, close attention to the full range of data reveals that it too has considerable appeal. An adequate theory of conditionals should account for these facts. The strict theory does so by validating them. But the variably strict theory invalidates them. So the variably strict theorist faces a question: (...) why do we find these inferences so compelling? In this paper, I suggest an answer on her behalf: that they are reasonable inferences in the sense introduced by Stalnaker (1975). -/- . (shrink)

Configurational Comparative Methods (CCMs) aim to learn causal structures from datasets by exploiting Boolean sufficiency and necessity relationships. One important challenge for these methods is that such Boolean relationships are often not satisfied in real-life datasets, as these datasets usually contain noise. Hence, CCMs infer models that only approximately fit the data, introducing a risk of inferring incorrect or incomplete models, especially when data are also fragmented (have limited empirical diversity). To minimize this risk, evaluation measures for sufficiency and necessity (...) should be sensitive to all relevant evidence. This article points out that the standard evaluation measures in CCMs, consistency and coverage, neglect certain evidence for these Boolean relationships. Correspondingly, two new measures, contrapositive consistency and contrapositive coverage, which are equivalent to the binary classification measures specificity and negative predictive value, respectively, are introduced to the CCM context as additions to consistency and coverage. A simulation experiment demonstrates that the introduced contrapositive measures indeed help to identify correct CCM models. (shrink)

A theory of property needs to give an account of the whole life-cycle of a property right: how it is initiated, transferred, and terminated. Economics has focused on the transfers in the market and has almost completely neglected the question of the initiation and termination of property in normal production and consumption (not in some original state or in the transition from common to private property). The institutional mechanism for the normal initiation and termination of property is an invisible-hand function (...) of the market, the market mechanism of appropriation. Does this mechanism satisfy an appropriate normative principle? The standard normative juridical principle is to assign or impute legal responsibility according to de facto responsibility. It is given a historical tag of being "Lockean" but the basis is contemporary jurisprudence, not historical exegesis. Then the fundamental theorem of the property mechanism is proven which shows that if "Hume's conditions" (no transfers without consent and all contracts fulfilled) are satisfied, then the market automatically satisfies the Lockean responsibility principle, i.e., "Hume implies Locke." As a major application, the results in their contrapositive form, "Not Locke implies Not Hume," are applied to a market economy based on the employment contract. It is shown the production based on the employment contract violates the Lockean principle (all who work in an employment enterprise are de facto responsible for the positive and negative results) and thus Hume's conditions must also be violated in the marketplace (de facto responsible human action cannot be transferred from one person to another—as is readily recognized when and employer and employee together commit a crime). (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds (...) imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

'It is widely agreed that contraposition, strengthening the antecedent and hypothetical syllogism fail for subjunctive conditionals', write Brogaard and Salerno in (2008: Counterfactuals and context, Analysis 68.1, 39–46). In that article they argue that the putative counterexamples to these principles are actually no threat, on the grounds that they involve a certain kind of illicit contextual shift. -/- Here I argue that this particular kind of contextual shift, if it is properly so called, is not generally illicit, and that (...) therefore the counterexamples shouldn't be blocked with the kind of blanket restriction Brogaard and Salerno advocate. The idea that the reasoning patterns in question can be vindicated given restrictions still seems promising; the purpose of this note is to show that the simple restriction proposed by Brogaard and Salerno isn't the right way of going. (shrink)

In this paper I review how the notion of gender is understood in psychiatry, specifically in the fifth edition of the Diagnostic and Statistical Manual of Mental Disorders (DSM-5). First, I examine the contraposition between sex and gender, and argue that it is still retained by DSM-5, even though with some caveats. Second, I claim that, even if genderqueer people are not pathologized and gender pluralism is the background assumption, some diagnostic criteria still conceal a residue of gender dualism (...) and essentialism. Third, I consider gender dysphoria, which is characterized by an incongruence between one’s experienced or expressed gender and one’s assigned gender; since this condition pertains to distress and disability, not to the incongruence per se, it does not pathologize transgender people. Still, I contend that it should be removed from DSM-5 for theoretical reasons. (shrink)

This paper reconsiders the Idealistic aesthetics of tragedy from an unconventional point of view. It investigates the relationship between theory and dramatic canon by focusing on those works and authors that are excluded from the canon by the theoretical discourse. My aim is to show that Idealist philosophers and Romantic critics concur in constructing a unitary model of the tragic conflict that is partly defined through its contraposition to the ‘Senecan’ conception of tragedy as a representation of suffering and (...) as a dialectic of passions. Seneca here stands for an entire line of European dramaturgy, which involves Shakespeare and culminates in French Classicism. This contrast does not merely concern a literary model, but also, more generally, the conception of subjectivity underlying the dramaturgy of passions. This paper thus helps to shed light on the controversial relationship between the idealistic philosophy of the tragic with modern tragedy at large. -/- Keywords: Theory of Tragedy, Idealism, Seneca, Hegel, Pathos . (shrink)

Universal statements in formal logic often contain unstated assumptions that lead to logical inconsistencies when subjected to transformation, particularly contraposition. This paper introduces a formal requirement for Domain Restriction {D_r}, ensuring logical validity in universal statements by explicitly declaring all necessary category constraints. Four major insights structure this analysis: 1. Incomplete Statements and Hidden Assumptions – Universal statements implicitly assume category constraints that must be explicitly stated to prevent logical collapse. 2. Subjects and Properties – A subject can have (...) a property, but a property without an explicitly defined subject leads to logical ambiguity. 3. Invalid Relationships – Many-to-Many relationships are inherently invalid in universal logic, requiring restructuring into Many-to-One or One-to-Many relationships. 4. The Rigor of Relevant Domain {D_r} – A necessary filtering mechanism to restrict logical transformations to valid categories and prevent logical vacuums. We formalize the Relevant Domain {D_r} as a necessary precondition for universal statements, resolving paradoxes like Hempel’s Raven Paradox while ensuring that logical transformation preserves category integrity and meaningful comparison. (shrink)

In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...) the direct and the indirect deductions constructed with the three traditional rules. IL3 is a hybrid of IL1 and IL2: its deductions are all direct as in IL1 but it deals with identities and inidentities as in IL2. IL1 and IL2 have a high degree of naturalness. Although the hybrid system IL3 was constructed as an artifact useful in the mathematical study of IL1 and IL2, it nevertheless has some intrinsically interesting aspects. The main motivation for describing and studying such simple systems is pedagogical. In teaching beginning logic one would like to present a system of logic which has the following properties. First, it exemplifies the main ideas of logic: implication, deduction, non-implication, counterargument(or countermodel), logical truth, self-contradiction, consistency,satisfiability, etc. Second, it exemplifies the usual general metaprinciples of logic: contraposition and transitivity of implication, cut laws, completeness,soundness, etc. Third, it is simple enough to be thoroughly grasped by beginners. Fourth, it is obvious enough so that its rules do not appear to be arbitrary or purely conventional. Fifth, it does not invite confusions which must be unlearned later. Sixth, it involves a minimum of presuppositions which are no longer accepted in mainstream contemporary logic. (shrink)

The notion of “empire” in Hardt and Negri’s political theory indicates a new postmodern sovereignty, able to lead the capital accumulation in the global market era. With the concept of “empire”, Hardt and Negri want to overtake the imperialism doctrines, considered by the two authors unable to understand correctly the global world. The aim of this essay is to clarify the conceptual contraposition between “empire” and “imperialism” offering a brief description of the international debate raised by the publication of (...) “Empire” by Hardt and Negri, in order to present the different positions and describe strengths, contradictions and aporias. (shrink)

exam of the issue of conflict since the “History of Florence” provides us with elements capable to show the Machiavellian reflection does not evolve according to such a simple and linear way as it is shown in the “Discourses”. In fact, investigation will reveal that the opposition between the two types of conflict – positive conflict and negative conflict –, described in the “Discourses”, is progressively defined, from the analysis of Florentian history, as being just one type – the tragic (...) and violent type –, based on contrapositions that cannot be solved in terms of a classical virtú, characteristic of the first period of Roman history. Such transformations arise a set of questions to which, in some way, the present paper intends to offer some answers: Would Machiavelli have renounced to the idea of conflict as foundation of republican liberty and surrended himself to the utopia of a homogeneous and stable order? Which element should be to blame due to the fact that disagreements did not produce, in Florence, the same effects which were seen in Rome? Would all disagreements be natural and, for that reason, inevitable, or could there be “artificial” divisions and, by that reason,avoidable ones? O estudo da questão do conflito a partir da “História de Florença” nos fornece elementos capazes de mostrar que a reflexão maquiaveliana não se desenvolve de modo tão simples e linear quanto parece nos “Discursos”. Com efeito, revelará que a oposição entre dois tipos de conflito – positivo e negativo – descrita nos “Discursos” se define progressivamente, a partir da análise da história florentina, como de um só tipo – trágico e violento – baseado sobre contraposições que não são possíveis de serem resolvidas em termos de uma virtù clássica, característica do primeiro período da história de Roma. Esta transformação levanta um conjunto de interrogações para as quais, de algum modo, o presente estudo pretende oferecer respostas: teria Maquiavel renunciado à ideia de conflito como fundamento da liberdade republicana e se entregado à utopia de uma ordem homogênea e estável? A que se deve atribuir o fato de as discórdias não haverem produzido em Florença os mesmos efeitos que em Roma? Seriam todas as discórdias naturais e, portanto, inevitáveis, ou poderia haver divisões “artificiais” e, portanto, evitáveis? (shrink)

(In progress) Explores the metaphysics of substance, identity, essence, and properties and tying them into an ontological argument for God from naturalism called “Purity Argument from Naturalism” (PAN). It draws inspiration from Joshua Rasmussen, especially his argument from No Arbitrary Limits. It uses a bayes structure, though can be reformed into a classical deductive form that ontological arguments tend to use… though its non-classical in that it doesn’t start with the concept of God but with the concept of naturalism and (...) general metaphysics. Also uses a supplementary argument called “mini Ontological Argument” (mOA) which is essentially a stripped down version of Plantinga’s MOA that doesn’t use modal logic or rely on necessity. The mOA uses a contrapositive version of the principle of sufficient reason. It doesn’t rely on metaphysical or modal necessity but on the causal conditions for a thing’s non-existence. The mOA is use both as an evidential that renders a bayes factor as well as to allow PAN to bypass alternative explanations that rely on arbitrary stopping points in the foundation’s nature. (shrink)

This paper proposes a novel ontological model of the universe, arguing that the universe does not run on any physical medium, but is a “computationless” fractal chaos system driven by a trinity of “Self-Reference (SR)”, “Entity-Relation (ER)”, and “Lazy Evaluation (LE)”. Based on the deduction of the contrapositive, this paper demonstrates that “paradoxes” are not logical flaws, but the absolute essential elements for the existence and evolution of the universe. The article compares this with Wolfram’s Computational Universe theory, points out (...) the core status of “Self-Reference” in computationless computing, and proposes five core conjectures regarding nested universe models and the limits of machine code parsing (Jia Baolong’s Multiple Conjectures). Our physical universe is merely one specific solution within this massive, purely logical fractal chaos system. (shrink)

This paper proposes a novel ontological model of the universe, arguing that the universe does not run on any physical medium, but is a “medium-free” fractal chaos system driven by a trinity of “Self-Reference (SR)”, “Entity-Relation (ER)”, and “Lazy Evaluation (LE)”. Based on the deduction of the contrapositive, this paper demonstrates that “paradoxes” are not logical flaws, but the absolute essen tial elements for the existence and evolution of the universe. The article compares this with Wolfram’s Computational Universe theory, points (...) out the core status of “Self-Reference” in medium-free computation, and proposes ten core conjectures regarding nested universe models and the limits of machine code parsing (Jia Bao long’s Ten Conjectures of the Universe). Our physical universe is merely one specific solution within this massive, purely logical fractal chaos system. (shrink)

The Universe: A Complete Proof from the Result — Formal Proof of Jia Baolong's First Axiom of the Universe -/- Description "I am lying." -/- Four words. One self-referential paradox. The universe contains it. The contrapositive: without it, no universe. This paper takes that single logical fact and derives — step by step, using only standard published results — the entire structure of reality: true randomness, the arrow of time, chaos, fractal geometry, self-organized criticality, physical law, life, consciousness, and the (...) undecidability of observers. -/- No physics is assumed. No cosmological model. No fine-tuning. No creator. Just logic unfolding upon itself. -/- The derivation is closed: it begins with self-reference and ends with entities capable of self-reference. The universe is its own proof. The author's initials — J.B.L. — encode the three structural necessities (Jarring/Self-Reference, Being/Entity-Relation, Lazy/Lazy Evaluation). Destiny or coincidence? Read the paper and you will understand. -/- The universe is a fractal chaos system generated by self-referential paradox. Humanity is one of its strange attractors. The Planck scale is 17 orders of magnitude below our smallest known particles. The old approach — drilling downward from phenomena toward point zero — should be maintained by a small team. The main force should march upward. -/- Jia Baolong's First Law of the Universe is the singularity law that opens a new era for humanity — and the slamming door of the old one. -/- Keywords self-referential paradox, Jia Baolong's First Axiom, formal proof, universe derivation, self-reference, SR+ER+LE, Gödel incompleteness, true randomness, deterministic chaos, fractal geometry, self-organized criticality, emergence, consciousness, undecidability, medium-free computation, Lazy Evaluation, strange attractor, Planck scale, closed emergence loop, singularity law -/- Additional Metadata Author: Jia, Baolong (贾宝龙) -/- Affiliation: Independent Researcher · Meta-Architect -/- Language: English, Chinese (Simplified) -/- Related Identifiers DOI: 10.5281/zenodo.19245000 — "Jia Baolong's First Law of the Universe: The Absolute Dual-Paradigm Axiomatic Foundation Unifying Mathematics, Physics, Computer Science, Cognitive Science, and Philosophy" -/- DOI: 10.5281/zenodo.19224995 — "The Closed Emergence Loop: From Medium-Free Computation Through Fractal Chaos to Gödelian Consciousness" -/- DOI: 10.5281/zenodo.19209458 — "The Nature of the Universe: A Medium-Free Computation Fractal Chaos System Based on Self-Reference Paradoxes" -/- DOI: 10.5281/zenodo.19225000 — "Prove You, Regardless of Your Existence: On the Absolute Equivalence of Extraterrestrial Intelligence and Human Capability" -/- DOI: 10.5281/zenodo.19164695 — "The Logical Universe: Physics as a Rendering Artifact of Pure Logical Networks" -/- 中文版 标题 宇宙:从结果出发的全证明 — 贾宝龙宇宙第一公理形式化证明 -/- 简介 "我在说谎。" -/- 四个字。一个自指悖论。宇宙包含它。逆否:没有它,没有宇宙。本文从这一个逻辑事实出发,仅使用已发表的标准数学和物理结果,一步一步推导出现实的全部结构:真随机、时间之箭、混沌、分形几何、自组织临界态、物理 定律、生命、意识,以及观测者的不可判定性。 -/- 不假设任何物理。不需要宇宙学模型。不需要精细调控。不需要造物主。只有逻辑在自身之上展开。 -/- 推导是闭合的:始于自指,终于能够自指的实体。宇宙是它自身的证明。作者姓名的首字母——J.B.L.——恰好编码了三个结构必然性(假/自指、保/局面、龙/惰性求值)。天意还是巧合?读完全文就明白。 -/- 宇宙是由自指悖论生成的分形混沌系统。人类是其中的奇异吸引子之一。普朗克尺度距人类已知最小基本粒子还有17个数量级。从现象往0点探寻的旧路——保留一支小分队就够了。大队伍应该往上走。 -/- 贾宝龙宇宙第一法则,是人类开启新时代的奇点法则,也是旧时代的关门撞击声。 -/- 精彩的人生,和谐的世界。 -/- 我因母国而荣耀。 -/- 关键词 自指悖论、贾宝龙第一公理、形式化证明、宇宙推导、自指、SR+ER+LE、哥德尔不完备性、真随机、确定性混沌、分形几何、自组织临界态、涌现、意识、不可判定性、无介质计算、延迟展开、奇异吸引子、普朗克尺度 、闭合涌现环路、奇点法则 -/- . (shrink)

Brogaard and Salerno (2008) argued that counter-examples to contraposition, strengthening the antecedent, and hypothetical syllogism involving subjunctive conditionals only seem to work because they involve a contextual fallacy where the context assumed in the premise(s) is illicitly shifted in the conclusion. To avoid such counter-examples they have proposed that the context must remain fixed when evaluating an argument for validity. That is the Brogaard-Salerno Stricture. Tristan Haze (2016), however, has recently objected that intuitively valid argumentative forms such as conjunction (...) introduction do not satisfy this constraint. This paper has two goals. First, it argues that the Brogaard-Salerno Stricture is not violated in Haze’s putative counter-example. Second, it argues that since this stricture blocks the usual counter-examples to instances of classical argumentative forms that involve indicative or subjunctive conditionals, it is reasonable to infer that indicative and subjunctive conditionals are material. (shrink)

Many researchers have conjectured that the humankind is simulated along with the rest of the physical universe – a Simulation Hypothesis. In this paper, we do not evaluate evidence for or against such claim, but instead ask a computer science question, namely: Can we hack the simulation? More formally the question could be phrased as: Could generally intelligent agents placed in virtual environments find a way to jailbreak out of them. Given that the state-of-the-art literature on AI containment answers in (...) the affirmative (AI is uncontainable in the long-term), we conclude that it should be possible to escape from the simulation, at least with the help of superintelligent AI. By contraposition, if escape from the simulation is not possible, containment of AI should be, an important theoretical result for AI safety research. Finally, the paper surveys and proposes ideas for hacking the simulation and analyzes ethical and philosophical issues of such an undertaking. (shrink)

Intensional evidence is any reason to accept a proposition that is not the truth values of the proposition accepted or, if it is a complex proposition, is not the truth values of its propositional contents. Extensional evidence is non-intensional evidence. Someone can accept a complex proposition, but deny its logical consequences when her acceptance is based on intensional evidence, while the logical consequences of the proposition presuppose the acceptance of extensional evidence, e.g., she can refuse the logical consequence of a (...) proposition she accepts because she doesn’t know what are the truth-values of its propositional contents. This tension motivates counterexamples to the negation of conditionals, the propositional analysis of conditionals, hypothetical syllogism, contraposition and or-to-if. It is argued that these counterexamples are non-starters because they rely on a mix of intensionally based premises and extensionally based conclusions. Instead, a genuine counterexample to classical argumentative forms should present circumstances where an intuitively true and extensionally based premise leads to an intuitively false conclusion that is also extensionally based. The other point is that evidentiary concerns about intensionally based beliefs should be constrained by the truth conditions of propositions presented by classical logic, which are nothing more than requirements of coherence in distributions of truth value. It is argued that this restriction also dissolves some known puzzles such as conditional stand-offs, the Adams pair, the opt-out property and the burglar’s puzzle. (shrink)

Different logic systems are motivated by attempts to fix the counter-intuitive instances of classical argumentative forms, e.g., strengthening of the antecedent, contraposition and conditional negation. These counter-examples are regarded as evidence that classical logic should be rejected in favour of a new logic system in which these argumentative forms are considered invalid. It is argued that these logical revisions are ad hoc, because those controversial argumentative forms are implied by other argumentative forms we want to keep. It is impossible (...) to remove an argumentative form from a logical system without getting entangled in an intricate logical web, since these revisions imply the removal of other parts of a system we want to maintain. Consequently, these revisions are incoherent and unwarranted. At the very least, the usual approach in the analysis of counter-examples of argumentative forms must be seriously reconsidered. (shrink)

This paper outlines an account of conditionals, the evidential account, which rests on the idea that a conditional is true just in case its antecedent supports its consequent. As we will show, the evidential account exhibits some distinctive logical features that deserve careful consideration. On the one hand, it departs from the material reading of ‘if then’ exactly in the way we would like it to depart from that reading. On the other, it significantly differs from the non-material accounts which (...) hinge on the Ramsey Test, advocated by Adams, Stalnaker, Lewis, and others. (shrink)

According to the view of conditionals named 'inferentialism', a conditional holds when its consequent can be inferred from its antecedent. This paper identifies some major challenges that inferentialism has to face, and uses them to assess three accounts of conditionals: one is the classical strict account, the other two have recently been proposed by Douven and Rott. As will be shown, none of the three proposals meets all challenges in a fully satisfactory way. We argue through novel formal results that (...) a variation of the evidential account of conditionals suggested by Crupi and Iacona is the most promising candidate to develop inferentialism in a coherent formal framework. (shrink)

This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.

Economic theory has tended to reduce all social bonds and relations to forms of contract, whereas social theory has seen contracts as opposed to, and destructive of, genuine social bonds. Bruni sees these contrapositions as ideological (‘left’ against ‘right’, p. xi). His main goal is to overcome them; to show that three forms of reciprocity, covering the ideological spectrum from left to right, are complementary and simultaneously required in a healthy society. These three forms are, in his words: ‘(1) the (...) reciprocity of contract or ‘cautious’; (2) the reciprocity of friendship or philia and (3) the ‘unconditional’ reciprocity, the one more controversial . . .’ (p. x). (shrink)

In some recent works, Crupi and Iacona have outlined an analysis of ‘if’ based on Chrysippus’ idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic.

The key idea of this paper is that grounds are a special kind of reasons, so their logic is part of the logic of reasons. We outline a natural deduction calculus that provides a basic formal characterization of reasons and enables us to obtain some distinctive and relatively uncontentious principles about grounds. Then we show that the calculus outlined is consistent and decidable, which we take to be an interesting result in its own right.