The phenomenon of rigid designation - in particular, de jure rigidity - is typically treated metaphysically. The picture is: reference is gained in a way that puts no constraints on what an object in other worlds, or counterfactual situations must be like, in order to be the referent of that term, other than 'being this thing'. This allows 'pure metaphysical' investigation into, and discovery of 'the nature' of the referent. It is argued that this presupposes a 'privileged' ontology, of (...) a sort that is far from obvious. An alternative picture of rigidity is sketched, terms have associated criteria of identity and criteria of application for counterfactual situations. A term is rigid when these coincide. Aside from being a better account of rigidity, it also undermines the picture of rigid terms allowing us to 'metaphysically' investigate the nature of the referent: matters of identity and essence for the referent are settled by these semantic constraints (though it can be done in a way that allows are a posteriori necessities). (shrink)

Traditional psychology and psychiatry often operate with static models of identity and discrete diagnostic categories. This article proposes a unifying paradigm based on the physics of complex systems, in which the Ego is conceptualized as a Dissipative Structure — an open system that maintains its organization at the cost of a continuous flow of energy and information, resisting the natural entropic tendency of the psyche. Introducing Lempel-Ziv Complexity (LZc) as a quantitative biomarker of "entropic rigidity," the article differentiates low-entropy (...) states (e.g., melancholic depression) from high-entropy states (e.g., psychosis). The model advances a thermodynamic coordinate system (Entropy × Free Energy) to map disorders and proposes that mental health is metastability: the dynamic capacity to transition between the structure of the Self and the non-Self. (shrink)

In this fascinating work, Scott Soames offers a new conception of the relationship between linguistic meaning and assertions made by utterances. He gives meanings of proper names and natural kind predicates and explains their use in attitude ascriptions. He also demonstrates the irrelevance of rigid designation in understanding why theoretical identities containing such predicates are necessary, if true.

Rigid expressionism is the view that all natural kind terms and many other kind terms are rigid designators. Rigid expressionists embrace the ‘overgeneralization’ of rigidity, since they hold that not just natural kind terms but all unstructured kind terms are rigid designators. Unfortunately overgeneralization remains a defeating problem for rigid expressionism. It runs together natural kind terms and nominal kind terms in a way that enforces a false semantic uniformity. The Kripke/putnam view of natural kind terms minus the claim (...) of rigidity is correct, but a traditional descriptivist theory is appropriate for nominal kind terms. None of them should be thought of as either rigid or non-rigid, however. (shrink)

It is generally assumed that rigidity plays a key role in explaining the necessary a posteriori status of identity statements, both between proper names and between natural kind terms. However, while the notion of rigid designation is well defined for singular terms, there is no generally accepted definition of what it is for a general term to be rigid. In this paper I argue that the most common view, according to which rigid general terms are the ones which designate (...) the same kind in all possible worlds, fails to deliver a posteriori necessities. I also present an alternative view, on which the work of explaining a posteriori necessities is not done by rigidity, but by a related metasemantic notion, which I call actuality - dependence. (shrink)

In this paper I examine two ways of defining the rigidity of general terms. First I discuss the view that rigid general terms express essential properties. I argue that the view is ultimately unsatisfactory, although not on the basis of the standard objections raised against it. I then discuss the characterisation in terms of sameness of designation in every possible world. I defend that view from two objections but I argue that the approach, although basically right, should be interpreted (...) cautiously. (shrink)

The classification-cum-explanation Kripke assigns to rigidity requires the notion to apply to singular and general terms alike. But Kripke's own notion of rigidity is tailor-made for singular terms, and an extensive debate has not secured a general notion of rigidity apt to provide the classification-cum-explanation Kripke aims for. I propose that we look for a Kripkean alternative to generalized rigidity. I argue that on Kripkean premises, natural kind terms and proper names belong to the meta-semantic category (...) of paradigm terms. I also argue that the property of being a paradigm term effects precisely the classification-cum-explanation Kripke attributes to rigidity. I conclude that Kripkeans should acknowledge that being a paradigm term, rather than designating rigidly, plays the role Kripke delineates, and that we can stop worrying about generalizing rigidity. Kripke's notion works fine for singular terms. And there is no need for rigidity to apply beyond these. (shrink)

We prove that quantum mechanics is the unique theory compatible with normalization- induced curvature on complex Hilbert space. Two rigidity theorems establish: (1) Lin- earity: continuous, reversible, scale-invariant flows necessarily have linear generators, and (2) Born rule: the assignment P (ϕ|ψ) = |⟨ϕ, ψ⟩|2 is the unique probability mea- sure compatible with cone geometry, unitary invariance, and orthogonal additivity. These are not interpretations but uniqueness results—no other mathematical struc- tures are possible given the geometric assumptions. We derive the Schr¨odinger (...) equa- tion, interference, Berry phase, and uncertainty relations as consequences of the master equation CurvC(X, Y ) = [X, Y ] − ⟨∇N,[X,Y ]⟩ ⟨∇N,x⟩ x applied to the quantum cone. The re- construction inverts standard quantum foundations: rather than postulating Hilbert space structure, we show it emerges from reversible dynamics on normalized states. (shrink)

Rigid designators for concrete objects and for properties -- On the coherence of the distinction -- On whether the distinction assigns to rigidity the right role -- A uniform treatment of property designators as singular terms -- Rigid appliers -- Rigidity - associated arguments in support of theoretical identity statements: on their significance and the cost of its philosophical resources -- The skeptical argument impugning psychophysical identity statements: on its significance and the cost of its philosophical resources -- (...) The skeptical argument further examined: on resources, allegedly overlooked, for confirming psychological identities. (shrink)

We give a unified overview of the study of the effects of additional set theoretic axioms on quotient structures. Our focus is on rigidity, measured in terms of existence (or rather non-existence) of suitably non-trivial automorphisms of the quotients in question. A textbook example for the study of this topic is the Boolean algebra $\mathcal {P}({\mathbb N})/\operatorname {\mathrm {Fin}}$, whose behavior is the template around which this survey revolves: Forcing axioms imply that all of its automorphisms are trivial, in (...) the sense that they are induced by almost permutations of ${\mathbb N}$, while under the Continuum Hypothesis this rigidity fails and $\mathcal {P}({\mathbb N})/\operatorname {\mathrm {Fin}}$ admits uncountably many non-trivial automorphisms. We consider far-reaching generalisations of this phenomenon and present a wide variety of situations where analogous patterns persist, focusing mainly (but not exclusively) on the categories of Boolean algebras, Čech–Stone remainders, and $\mathrm {C}^{*}$ -algebras. We survey the state of the art and the future prospects of this field, discussing the major open problems and outlining the main ideas of the proofs whenever possible. (shrink)

I have been told that for some twenty minutes after reading this paper Kripke believed I had shown that proper names could be non-rigid designators. (Then, apparently, he found a crucial error in the set-up.) I take great pride in this (alleged) fact.

In this paper, I will show that typical formal semantic reconstructions of the rigidity of proper names neglect the important aspect that the rigidity of names is determined by our ordinary use of a name relative to the actual world. This fact was clearly pointed out by Kripke, but overlooked by the subsequent discussion concerning this topic. Based on this diagnosis, I will distinguish three different actualized notions of rigidity. Firstly, I will introduce two different new varieties (...) of known versions of rigidity; namely, actualized persistent and actualized obstinate rigidity. Secondly, I will make use of the tools provided by free logic and introduce a new and overlooked version of rigidity, which I will call actually restricted rigidity. Against this background, I will argue that we have different options to formally model the rigidity of proper names in natural languages. Which option we choose, mainly depends on our philosophical background assumptions. For someone who believes in non-existent objects and the possibility of naming such objects, it is the best choice to hold that proper names are actually obstinately rigid designators. For someone who rejects non-existent objects and the possibility of naming such objects, actually restricted rigidity is a better choice than actualized persistent rigidity. (shrink)

The paper takes a detailed look at a surprising new aspect of the dynamics of rigid bodies. Far from the usual consideration of rigid body theory as a merely technical chapter of classical physics, I demonstrate here that there are solutions to the conservation equations of mechanics that imply the spontaneous, unpredictable splitting of a rigid body in free rotation, something that has direct implications for the problem of causality. The paper also shows that the instability revealed in indeterminist splitting (...) processes does not depend solely on the bodies’ inertial properties but also on the number of dimensions of the physical space they inhabit. The paper concludes with a conjecture on the behavior of rigid bodies in four-dimensional space. (shrink)

Kripke distinguishes necessity and priority as two different categories: priority is a notion of epistemology, while necessity is a notion of metaphysics. Based on this fundamental argument, Kripke objects to Descriptivism, which takes certain properties as the criteria of identity across all possible worlds, and he argues for the legitimacy of a posteriori necessary truths. Kripke also criticizes Russell’s methods for dealing with empty descriptions, and he puts forward a modal world to explain the rigidity of proper names. However, (...) the concept of rigid designation faces some challenges, including Kripke admitting to weak essentialism when he rejects transworld identification, and the fact that the truth value of a sentence containing a rigid designator may change. (shrink)

What does it mean for a general term to be rigid? It is argued by some that if we take general terms to designate their extensions, then almost no empirical general term will turn out to be rigid; and if we take them to designate some abstract entity, such as a kind, then it turns out that almost all general terms will be rigid. Various authors who pursue this line of reasoning have attempted to capture Kripke’s intent by defining a (...) rigid general term as one that applies to the objects in its extension essentially. I argue that this account is significantly mistaken for various reasons: it conflates a metaphysical notion (essentialism) with a semantic one (rigidity); it fails to countenance the fact that any term can be introduced into a language by stipulating that it be a rigid designator; it limits the extension of rigid terms so much that terms such as ‘meter’, ‘rectangle’, ‘truth’, etc. do not turn out to be rigid, when they obviously are; and it wrongly concentrates on the predicative use of a general term in applying a certain test offered by Kripke to determine whether a term is rigid. (shrink)

Kripke defines a rigid designator as one that designates the same object in every possible world in which that object exists. He argues that proper names are rigid. So also, he claims, are various natural kind terms. But we wonder how they could be. These terms are general and it is not obvious that they designate at all. It has been proposed that these kind terms rigidly designate abstract objects. This proposal has been criticized because all terms then seem to (...) come out rigid, thus trivializing rigidity. The paper starts with further criticisms of this proposal aimed particularly at a recent version given by LaPorte. The paper goes on to develop and defend an alternative proposal presented briefly in Devitt and Sterelny (1999): instead of taking those natural kind terms to rigidly designate an object we take them to rigidly apply to the members of their extensions. Schwartz has rightly insisted that a notion of rigidity must do some theoretical work if it is to be interesting. The paper argues that rigid application for kind terms does the same primary work as rigid designation for singular terms, the work of refuting description theories of some terms; and it does the same secondary work, of explaining certain modal phenomena (with one exception). (shrink)

Though it is often claimed that some general terms are rigid designators, it has turned out to be difficult to give a satisfying definition that avoids making all general terms rigid, and even if a non-rigid reading is available, makes that non-rigid reading matter. Several authors have attempted to develop examples that meet the trivialization challenge, with Martí and Martínez-Fernández providing what is, perhaps, the most convincing strategy. I show that the type of example Martí and Martínez-Fernández offer nevertheless fails (...) to meet the trivialization challenge and, accordingly, that we should still have serious doubts about whether continuing the search for a non-trivial definition of general term rigidity would be fruitful. (shrink)

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

Rigid designators designate whatever they do in all possible worlds. Mathematical definite descriptions are usually considered paradigmatic examples of such expressions. The main aim of the present paper is to challenge this view. It is argued that mathematical definite descriptions cannot be rigid in the same sense as ordinary empirical definite descriptions because—assuming that mathematical facts are not determined by goings on in possible worlds—mathematical descriptions designate whatever they do independently of possible worlds. Nevertheless, there is a widespread practice of (...) treating mathematical definite descriptions as rigid. Apart from this, there might be theoretical reasons for admitting that they are rigid in some sense. The second part of the paper suggests a way out. Borrowing from ideas proposed by Kit Fine, it develops and defends an extended notion of rigidity, which can be applied to mathematical definite descriptions. Importantly, this notion is fully compatible with the claim that mathematical facts are independent of possible worlds. (shrink)

This chapter introduces the general topic of the book and lays out its basic plan. First the rigid — nonrigid distinction is clarified in its full generality, with no special regard to the specific case of property designators: the basic modal and epistemological interest of the distinction, most notably in identity statements, is clarified. Then an account of the rigid — nonrigid distinction for property designators specifically is offered. Interesting work performed by rigidity in property designators is discussed, especially (...) as it pertains to theoretical identity statements including psychophysical identity statements. Complications and objections to applying rigidity to property designators are introduced. Chapters to come will address these complications and objections, allowing for further articulation and support of the distinction. The chapter ends with a chapter-by-chapter agenda for the rest of the book. (shrink)

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term ‘rigid body’ in relativistic straight line motion. We show that the definition of ‘rigid body’ in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe The motion of a rigid body undergoing constant acceleration to a given velocity.The acceleration of a rigid (...) body due to an applied impulse.Collisions between rigid bodies. (shrink)

Few philosophers today doubt the importance of some notion of rigid designation, as suggested by Kripke and Putnam for names and natural kind terms. At the very least, most of us want our theories to be compatible with the most plausible elements of that account. Anaphoric theories of reference have gained some attention lately, but little attention has been given to how they square with rigid designation. Although the differences between anaphoric theories and many interpretations of the New Theory of (...) reference are substantial, I argue that rigid designation and anaphoric theories can be reconciled with one another and in fact complement one another in important ways. (shrink)

Confessional rigidity between Roman Catholics and Protestants is not adequately explained by doctrinal disagreement alone. This study argues that the persistence and intensity of confessional antagonism arise from a deeper convergence of psychological needs, anthropological patterns, sociological pressures, and theological commitments that shape how individuals and communities hold their beliefs. Fear, insecurity, and unresolved trauma, both individual and collective, often transform doctrinal claims into mechanisms of identity protection rather than instruments of discernment. Through the TAPS framework, together with original (...) analytical constructs such as R.I.G.I.D., S.A.F.E., and the developmental sequence of Fear to Fixation to Ferocity, the analysis demonstrates how ritual, symbol, communal memory, attachment disruptions, and group threat responses interact to produce defensive and inflexible confessional postures. Catholic and Protestant traditions each contain healthy orientations that can become distorted under conditions of perceived threat, particularly when trauma constricts cognitive and emotional flexibility. The study concludes that spiritual maturity, characterized by grounded identity, humility, interpretive charity, and ecumenical openness, provides a constructive path toward healing and enables believers to move from defensive identity fortressing toward a more integrated, compassionate, and dialogical form of Christian engagement. (shrink)

Saul Kripke introduced the notion of rigid designation for singular terms to disprove the description theory of meaning for names, and to argue that true identity statements with rigid designators are necessarily true, although a posteriori. He proceeded to apply the notion to general terms for natural kinds, stuffs and phenomena, and claimed that true theoretical identifications with rigid general terms are also necessary a posteriori truths. Michael Devitt pointed out that, regardless of whether general terms are taken to designate (...) their extensions or abstract entities, rigid designation cannot single out the terms Kripke considered rigid. Devitt suggested that, in the case of general terms, rigid designation should be replaced with a notion of rigid application, where rigid appliers stand for essential properties. He showed that rigid application allows for creating ‘lost rigidity arguments’ against description theories of meaning for natural kind terms, but that it cannot ensure the necessity of true theoretical identifications with rigid appliers. In this paper, I will argue that necessitism, that is, the claim that anything which exists in any possible world exists in every possible world, is both necessary and sufficient to bridge the gap between rigid application and metaphysical necessity. (shrink)

In Naming and Necessity Kripke argues 'intuitively' that names are rigid. Unlike Kripke, Ben-Yami first introduces and justifies the Principle of the Independence of Reference (PIR), according to which the reference of a name is independent of what is said in the rest of the sentence containing it. Ben-Yami then derives rigidity, or something close to it, from the PIR. Additional aspects of the use of names and other expressions in modal contexts, explained by the PIR but not by (...) the rigidity claim, are then discussed. Ben-Yami next examines a difficulty in accepted definitions of rigidity, stemming from the fact that the same name can be used to name different particulars. This difficulty might force us to adopt a revised form of the rigidity claim. (shrink)

The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behaviour under rotations, etc., are all shown to be related to the unsuitable choice of functions representing the states with opposite projections of angular momentum. By a correct choice of functions and definition of inner product those difficulties do not (...) occur. And yet the orbital angular momentum in the ordinary configuration space can have integer eigenvalues only, for the reason which have roots in the nature of quantum mechanics in such space. The situation is different in the velocity space of the rigid particle, whose action contains a term with the extrinsic curvature. (shrink)

Aspects of kripke's recent work in philosophy are considered in connection with the formal approach he set forth over a decade ago regarding semantics for modal logic. An ambiguity is pointed out concerning kripke's intuitive test for rigid designators and it is argued that, Relative to an appropriate framework for considering actual and possible physical objects, Certain proper names fail to be rigid designators.

Joseph Almog says concerning “a certain locus where Quine doesn’t exist…qua evaluation locus, we take to it [singular] propositions involving Quine [as a constituent] which we have generated in our generation locus.” This seems to be either murder, or worse, self-contradiction. It presumes that certain designators designate their designata even at loci where the designata do not exist, i.e., the designators have “Kaplan rigidity.” Against this view, this paper argues that negative existentials such as “Quine does not exist” are (...) true only at ordered couples of loci (times or possible worlds) < l, l’ > such that the constituents of the truthmaker are the designatum itself from l and whatever corresponds to “does not exist” from l’. (shrink)

The OntoClean methodology was based on a set of formal meta-properties whose semantics were specified in S5 modal logic. One of these metaproperties, Rigidity, has come under more focused scrutiny by the ontology community, and several problems with the formalization have been discussed along with several solutions. In this paper, we attempt to reconcile these results in a larger framework that exposes different kinds of rigidity, as well as two new metaproperties, actuality and permanence, which deal more specifically (...) with the behavior of properties with respect to time and existence. (shrink)

The question whether the notion of rigidity can be extended in a fruitful way beyond singular terms has received a standard answer in the literature, according to which non‐singular terms designate kinds, properties or other abstract singular objects, and generalized rigidity is the same thing as singular term rigidity, but for terms designating such objects. I offer some new criticisms of this view and go on to defend an alternative view, on which non‐singular terms designate extensions in (...) general, and generalized rigidity is identity of extension across possible worlds. I develop some fundamental positive considerations that make this view virtually inevitable as a view of generalized rigidity, emphasizing its exclusive ability to offer a purely logical justification of the necessity of several kinds of statements that go beyond true identity statements between rigid singular terms. (shrink)

While extant replies to Jonathan Schaffer’s putative counterexamples to the transitivity of grounding have made significant strides against the charge of transitivity failure, the replies pay insufficient attention to the common structure of the counterexamples, overlooking a deeper structural feature that contributes to their prima facie plausibility. Putative counterexamples to the transitivity of grounding, I argue, trade on the distinction between what I call ‘rigid’ and ‘non-rigid’ grounding, and confusion over how rigid and non-rigid grounding react when combined pumps the (...) intuition that the counterexamples’ chained conclusions are false. The rigid/non-rigid grounding distinction also reveals plausible weakening inference rules that have been overlooked in treatments of the logic of grounding. (shrink)

examine Nathan Salmon’s solution to the problem of trivialization, as it arises for conceptions of general term rigidity that construe it as identity of designation across possible worlds. I argue that he does not succeed in showing that some alleged general terms, such as “the colour of the sky” are non-rigid, but also that a small class of different examples that he presents, which can be construed as second order descriptions, are indeed non-rigid general terms, although for reasons different (...) from those he thought. (shrink)

The notion of rigidity looms large in philosophy of language, but is beset by difficulties. This paper proposes a simple theory of rigidity, according to which an expression has a world-relative semantic property rigidly when it has that property at, or with respect to, all worlds. Just as names, and certain descriptions like The square root of 4, rigidly designate their referents, so too are necessary truths rigidly true, and so too does cat rigidly have only animals in (...) its extension. After spelling out the theory, I argue that it enables us to avoid the headaches that attend the misbegotten desire to have a simple rigid/non-rigid distinction that applies to expressions, giving us a simple solution to the problem of generalizing the notion of rigidity beyond singular terms. (shrink)

According to S. Kripke, an expression is rigid provided it refers to the same object in all possible worlds in which the object exists. On the other hand, H. Putnam claims that an expression is rigid provided it refers to the same object in all possible worlds in which it refers to anything at all. The paper shows that the two notions of rigidity are not equivalent because Putnam's rigidity is much broader than Kripke's; unlike Putnam's rigidity, (...) Kripke's is interwoven with essentialism; and identity statements between rigid designators in Putnam's sense need not be necessarily true. (shrink)

Is there a theoretically interesting notion that is a natural extension of the concept of rigidity to general terms? Such a notion ought to satisfy two Kripkean conditions. First, it must apply to typical general terms for natural kinds, stuffs, and phenomena, and fail to apply to most other general terms. Second, true 'identification sentences' (such as 'Cats are animals') containing general terms that the notion applies to must be necessary. I explore a natural extension of the notion of (...) rigidity to general terms, the notion of an essentialist predicate. I argue that, under natural assumptions, this notion satisfies the two Kripkean conditions. (shrink)

Eliminativists say that the idea of extending rigidity beyond singular terms must be abandoned, especially because they claim that Kripkean “identifications” involving natural kind terms can be shown to be necessary if true by the standard theory of reference fixing, using at most singular term rigidity. First I note that this claim is false for Cats are animals and analogous identifications involving ordinary natural kind terms of different types. Then I recall that the view of rigidity as (...) necessary application provides a modal-logical derivation of the necessity of those identifications, and is thus supported by this set of facts. I also consider, on behalf of the eliminativist, a rigidity-free derivation of that necessity, using the apparatus of higher-order metaphysics. I note that this derivation does not better motivate eliminativism, in part because its conceptual apparatus is not clearly more fundamental or less controversial than the apparatus of rigidity as necessary application. (shrink)

Epistemic modal predicate logic raises conceptual problems not faced in the case of alethic modal predicate logic : Frege’s “Hesperus-Phosphorus” problem—how to make sense of ascribing to agents ignorance of necessarily true identity statements—and the related “Hintikka-Kripke” problem—how to set up a logical system combining epistemic and alethic modalities, as well as others problems, such as Quine’s “Double Vision” problem and problems of self-knowledge. In this paper, we lay out a philosophical approach to epistemic predicate logic, implemented formally in Melvin (...) Fitting’s First-Order Intensional Logic, that we argue solves these and other conceptual problems. Topics covered include: Quine on the “collapse” of modal distinctions; the rigidity of names; belief reports and unarticulated constituents; epistemic roles; counterfactual attitudes; representational vs. interpretational semantics; ignorance of co-reference vs. ignorance of identity; two-dimensional epistemic models; quantification into epistemic contexts; and an approach to multi-agent epistemic logic based on centered worlds and hybrid logic. (shrink)

This paper challenges Saul Kripke’s theory of rigid designation using a real-world counterexample—a seasonal ice formation named 'Rigid Designator.' While composed of H2O, the structure does not function or persist like water, thus undermining Kripke’s claim that 'Water is H2O' is a metaphysically necessary truth. This empirical Encryptment, combined with critiques from philosophers such as Mark Johnston, highlights the recursive, context-sensitive nature of identity. The paper also critiques Kripke’s misapplication of 'baptism' in his theory of naming, suggesting that 'christening' more (...) accurately captures the recursive and ontological depth of naming. The phenomenon of Encryptment reveals that identity and naming operate through symbolic recursion and informational fields—not causal chains or modal rigidity. My Chemical Engineering degree prohibits me from adopting Kripke's rather 'ignorant' and casual viewpoint. (shrink)

We analyze a countable support product of a free Suslin tree which turns it into a highly rigid Kurepa tree with no Aronszajn subtree. In the process, we introduce a new rigidity property for trees, which says roughly speaking that any non-trivial strictly increasing function from a section of the tree into itself maps into a cofinal branch.

Against the backdrop of economic internationalization and market globalization, the world has witnessed faster competitive contents with a more dynamic market environment, a more rapid technological innovation, and more diverse customer needs. Thus, for every enterprise especially led by entrepreneurs, the focus is to maintain the sustainability of competitive advantages and dynamically transform core capacity to avoid rigidity. This paper introduces the process of the deepened rigidity in WS Co. Company, which occurs due to the wrong cognition of (...) Dr. S and his teams who managed or failed to respond to the rigidity encountered by the company during different periods. The rigidity of its capacity is believed to be caused by the cognitive errors of the entrepreneur and his team facing every period of potential rigidity, which makes them fail to deal with it, thus leading to complete rigidity. This paper intends to explain how rigidity takes shape from the cognitive aspect of senior managers, which may serve as illuminations for the similar enterprises led by entrepreneurs. (shrink)

Saul Kripke’s “modal argument” against the description theory of proper names turns on a distinction between reference-fixing and meaning-giving. In this essay Shieh argues first that without further explanation of meaning-giving, it is unclear how this argument shows that the meanings of names cannot be given by descriptions. Second, Shieh shows that an explanation of meaning-giving sufficient to sustain the modal argument requires a notion of modal properties of meaning. This notion, in turn, yields a notion of rigidity of (...) names that can be explained in terms of Gareth Evans’s notion of deep necessity. Shieh concludes that Kripke’s modal argument is not based simply on untutored linguistic intuitions or facts of ordinary language use but presupposes substantial metaphysical commitments. (shrink)

This chapter discusses a version of the descriptive account of content which is compatible with rigidity thesis (RT) and critiques of RT. The rigidity of proper names demonstrates that utterances of sentences containing proper names, and utterances of sentences differing from those sentences only in containing non‐rigid descriptions in place of the proper names, differ in content. The fact that natural‐language proper names are rigid designators is an empirical discovery about natural language. The chapter intends to be a (...) survey of both the background and contemporary discussion of this discovery. However, the survey takes place in the context of an evaluation of the extent to which the discovery that English proper names are rigid itself threatens the descriptive picture of the content of names. The goal is to show that the exact philosophical significance of the discovery that natural‐language proper names are rigid designators is still, and should still be, a matter of controversy. (shrink)

Design problems in structural engineering are often modeled as differential equations. These problems are posed as initial or boundary value problems with several possible variations in structural designs. In this paper, we have derived a mathematical model that represents different structures of beam-columns by varying axial load with or without internal forces including bending rigidity. We have also developed a novel solver, the LeNN-NM algorithm, which consists of weighted Legendre polynomials, and a single path following optimizer, the Nelder–Mead algorithm. (...) To evaluate the performance of our solver, we have considered three design problems representing beam-columns. The values of performance indicators, MAD, TIC, NSE, and ENSE, are calculated for a hundred simulations. The outcome of our statistical analysis points to the superiority of the LeNN-NM algorithm. Graphical illustrations are presented to further elaborate on our claims. (shrink)

Zemach's arguments have gone to show that terms might be rigid designators in ordinary language even though they are not natural kind terms. It has been argued that his argument is inconclusive. However it has been claimed that Putnam's argument is much too strong for it would preclude interesting scientific hypotheses about identity between what appear to be different substances, solely on the grounds of modal necessity.It has been shown that rigid designators can be disjunctive but that this possibility is (...) not a foregone conclusion, as Zemach would have us believe. We have to allow for differences between how wesingled out the extension of a natural kind termin the past and how we intend to single out such extensionin the future. Language is not inherently conservative. There is much room for reformist manoevres. *** DIRECT SUPPORT *** A0985038 00002. (shrink)

Between James Parkinson's 'shaking palsy' and the first report of the post-encephalitic manifestation — initially not recognizable as a complication of that incipient 'Spanish flu' epidemic — it took over a hundred years to arrive at a clear appreciation and differentiation of its most disabling feature: rigidity. This paper traces the development, step by hesitant or bold step, of the pertinent ideas and terms regarding muscle tone before and after Parkinson, their basis in neuropathological advances as they were made (...) for related syndromes of basal ganglia disorders, toward the eventual clinical correlation. Chief credits, after Sauvages, must go to Charcot for emphasizing the increase in muscle tone, and to Kinnier Wilson for establishing the extrapyramidal connection. (shrink)

This paper addresses recent literature on rigid designation and natural kind terms that draws on the inferentialist approaches of Sellars and Brandom, among others. Much of the orthodox literature on rigidity may be seen as appealing, more or less explicitly, to a semantic form of “the given” in Sellars’s terms. However, the important insights of that literature may be reconstructed and articulated in terms more congenial to the Pittsburgh school of normative functionalism.

Michael McKinsey raises several important and far-reaching issues in his critical examination of Beyond Rigidity. I am happy to have a chance to respond, and thereby, I hope, to advance the debate.