On formulas with valid cases

1956 ◽  
Vol 21 (2) ◽  
pp. 148-148
Author(s):  
W. V. Quine

Commonly, when we succeed in showing a formula of quantification theory to be consistent, we do so by producing a true interpretation. Sometimes we achieve the same effect without even exceeding the resources of quantification theory itself: we show a formula consistent by producing a valid formula from it by substitution. Example: ‘(∃x)Fx ⊃ (x)(∃y) (Gxy ▪ Fy)’ is seen consistent by noting its valid substitution case ‘(∃x)Fx ⊃ (x)(∃y)(Fx ∨ Fy ▪ Fy)’. How generally available is this latter method? I shall show that it is available if and only if the formula whose consistency is shown is satisfiable in a one-member universe.The “only if” part is immediate. For, if ψ is a substitution case of ϕ, then ϕ is satisfiable wherever ψ is; and ψ, if valid, is satisfiable in a one-member universe.Conversely, suppose a true interpretation of ϕ in a one-member universe. Each predicate letter of ϕ is thereby interpreted outright as true or false, in effect, since there is no varying the values of ‘x’, ‘y’, etc. Now form ψ from ϕ by substitution as follows: change each atomic formula ϕi(e.g. ‘Fx’, ‘Fy’, ‘Gxy’) to ⌜ϕi⊃ϕi⌝ if its predicate letter is one that was interpreted as true, or to ⌜ϕi ▪ − ⊃ϕi⌝ if its predicate letter is one that was interpreted as false. Clearly ψ under all interpretations even in large universes, will receive the truth value that ϕ received under the supposed interpretation in the one-member universe. So ψ is valid.

Imbizo ◽  
2020 ◽  
Vol 11 (2) ◽  
Author(s):  
Naomi Epongse Nkealah ◽  
Olutoba Gboyega Oluwasuji

Ideas of nationalisms as masculine projects dominate literary texts by African male writers. The texts mirror the ways in which gender differentiation sanctions nationalist discourses and in turn how nationalist discourses reinforce gender hierarchies. This article draws on theoretical insights from the work of Anne McClintock and Elleke Boehmer to analyse two plays: Zintgraff and the Battle of Mankon by Bole Butake and Gilbert Doho and Hard Choice by Sunnie Ododo. The article argues that women are represented in these two plays as having an ambiguous relationship to nationalism. On the one hand, women are seen actively changing the face of politics in their societies, but on the other hand, the means by which they do so reduces them to stereotypes of their gender.


Author(s):  
Christopher Hanlon

Emerson’s Memory Loss is about an archive of texts documenting Emerson’s intellectual state during the final phase of his life, as he underwent dementia. It is also about the way these texts provoke a rereading of the more familiar canon of Emerson’s thinking. Emerson’s memory loss, Hanlon argues, contributed to the shaping of a line of thought in America that emphasizes the social over the solipsistic, the affective over the distant, the many over the one. Emerson regarded his output during the time when his patterns of cognition transformed profoundly as a regathering of focus on the nature of memory and of thinking itself. His late texts theorize Emerson’s experience of senescence even as they disrupt his prior valorizations of the independent mind teeming with self-sufficient conviction. But still, these late writings have succumbed to a process of critical forgetting—either ignored by scholars or denied inclusion in Emerson’s oeuvre. Attending to a manuscript archive that reveals the extent to which Emerson collaborated with others—especially his daughter, Ellen Tucker Emerson—to articulate what he considered his most important work even as his ability to do so independently waned, Hanlon measures the resonance of these late texts across the stretch of Emerson’s thinking, including his writing about Margaret Fuller and his meditations on streams of thought that verge unto those of his godson, William James. Such ventures bring us toward a self defined less by its anxiety of overinfluence than by its communality, its very connectedness with myriad others.


Author(s):  
Hugh H. Benson
Keyword(s):  
The One ◽  

This chapter presents a reading of Plato’s Euthyphro, Apology, and Crito. These dialogues, in which Plato depicts the weeks leading up to Socrates’s last day, are replete with various philosophical explorations. Among those explorations is the question of how to live our lives. On the one hand, Socrates is clear and straightforward. We should live the examined life—making logoi and examining ourselves and others in order to determine whether we are as wise as we think we are, and we should live the virtuous life. This is how Socrates lives his life. On the other hand, the examined life undercuts, or at least should undercut, the confidence with which he seeks to live the virtuous life. It may help bring some stability to the general principles by which he lives his life, but it can do so only defeasibly and without certainty.


2020 ◽  
Vol 13 (2) ◽  
pp. 331-360
Author(s):  
Antonio Fábregas ◽  
Rafael Marín

AbstractThe goal of this article is to discuss the nature of so-called perfective adjectives in Spanish (desnudo ‘naked,’ suelto ‘loose’). We do so through a discussion of the problem that participles are blocked by perfective adjectives in some contexts (Dejó la habitación {limpia / ∗limpiada} ‘He left the room {clean / ∗cleaned}). We will argue that perfective adjectives contain in their internal structure a StateP that can contextually be interpreted as a result state; this head has morphological, syntactic and semantic effects, and makes the structure spelled out by the perfective adjective identical to the one associated with a small participle, with the result that a principle of lexical economy blocks the participial morphology in situations where only the small participle is allowed.


1998 ◽  
Vol 16 (4) ◽  
pp. 387-400 ◽  
Author(s):  
Felicity J Callard

Geographers are now taking the problematic of corporeality seriously. ‘The body’ is becoming a preoccupation in the geographical literature, and is a central figure around which to base political demands, social analyses, and theoretical investigations. In this paper I describe some of the trajectories through which the body has been installed in academia and claim that this installation has necessitated the uptake of certain theoretical legacies and the disavowal or forgetting of others. In particular, I trace two related developments. First, I point to the sometimes haphazard agglomeration of disparate theoretical interventions that lie under the name of postmodernism and observe how this has led to the foregrounding of bodily tropes of fragmentation, fluidity, and ‘the cyborg‘. Second, I examine the treatment of the body as a conduit which enables political agency to be thought of in terms of transgression and resistance. I stage my argument by looking at how on the one hand Marxist and on the other queer theory have commonly conceived of the body, and propose that the legacies of materialist modes of analysis have much to offer current work focusing on how bodies are shaped by their encapsulation within the sphere of the social. I conclude by examining the presentation of corporeality that appears in the first volume of Marx's Capital. I do so to suggest that geographers working on questions of subjectivity could profit from thinking further about the relation between so-called ‘new’ and ‘fluid’ configurations of bodies, technologies, and subjectivities in the late 20th-century world, and the corporeal configurations of industrial capitalism lying behind and before them.


1925 ◽  
Vol 9 (2) ◽  
pp. 269-284 ◽  
Author(s):  
Otto Glaser

1. For the heart rate in Pterotrachea coronata, intermediate temperatures disclose a thermal increment of 11,200 ±. This value is identical with the one reported by Crozier and Stier for the lamelli-branch, Anodonta. In the pteropod, Tiedemannia neapolitana the same temperatures typically reveal in the heart rate a µ value of 16,200 ± This agrees quantitatively with 16,300 found by Crozier and Stier for the heart of the slug, Limax maximus. 2. At high temperatures the average value of µ for Pterotrachea is 7,300: for Tiedemannia, 7,400. The corresponding averages at the lower limits are 22,000 and 23,000. 3. The great variability found near the edges of the temperature field are explicable in two ways. During intermissions characteristic of high temperatures and occurring also at low, we can assume a restorative process; while at both the upper and lower limits we may, in addition, find that reactions assume control which under ordinary circumstances never do so. Special evidence indicates that the highest temperatures employed, 27°C., and the lowest, 4°C., caused no irreversible changes in mechanism. 4. The theoretical analysis of the experimental facts makes use of Meyerhof's conception of carbohydrate metabolism and projects the cyclical nature of rhythm into the substrate of control. Assuming as a source of energy an original supply of material O, the value of 22,000 ± is assigned provisionally to a mobilization hydrolysis while 11,200 ± and 16,000 ± are attached to oxidative reactions influenced respectively by OH' and possibly Fe, or some other catalyst. The lowest value, 7,300 ± is assumed to indicate a synthetic process (lactic acid → glycogen?), possibly limited by CO2 excretion. In the present state of our knowledge, this distribution and interpretation seems to account reasonably for the experimental facts, but until we know more about the neurogenic controls, is entitled to rank only as an hypothesis.


2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Anita Naemi Holm

This article presents a theoretical view on culturally embedded thinking and action in encounters between patient and health professional. A key point of the analysis indicates that a highly efficient health sector may entail an implicit duality: on the one hand, the health professional can and often must relate pragmatically to the patient in order to solve problems and do so quickly, while on the other, the professional may be personally challenged when embedded cultural thinking leads to conflicts or dilemmas. This means that a purely pragmatic perspective will be challenged when such conflicts arise. The article looks at interrelated concepts such as ‘culture’, ‘prejudice’ and ‘meaning’ in order to shed light on the presuppositions that are brought into the cultural encounter between patient and health professional. This kind of analysis will hopefully contribute to a raised awareness of what is actually – apart from pragmatic problem solving – going on in such encounters. The conceptual framework used in this article primarily draws on the German philosopher Hans-Georg Gadamer, which is contrasted with the pragmatic perspective from the American philosopher Richard Rorty.


2018 ◽  
Author(s):  
Michael J. Morgan ◽  
Joshua A. Solomon

AbstractIt is usually assumed that sensory adaptation is a universal property of human vision. However, in two experiments designed to measure adaptation without bias, we have discovered a minority of participants who were unusual in the extent of their adaptation to motion. One experiment was designed so that targets would be invisible without adaptation; the other, so that adaptation would interfere with target detection. In the first, participants adapted to a spatial array of moving Gabor patches. On each trial the adapting array was followed by a test array in which but all of the test patches except one were identical to their spatially corresponding adaptors; the target moved in the opposite direction to its adaptor. Participants were required to identify the location of the changed target with a mouse click. The ability to do so increased with the number of adapting trials. Neither search speed nor accuracy was affected by an attentionally-demanding conjunction task at the fixation point during adaptation, suggesting low-level (pre-attentive) sites in the visual pathway for the adaptation. However, a minority of participants found the task virtually impossible. In the second experiment the same participants were required to identify the one element in the test array that was slowly moving: reaction times in this case were elevated following adaptation. The putatively weak adapters from the first experiment found this task easier than the strong adapters.


2021 ◽  
Vol 24 (1) ◽  
pp. 37-46
Author(s):  
João Carlos Coimbra ◽  
Tiago Menezes Freire

A robust biostratigraphic zonation based on microfossils supports the stratigraphic framework and correlation of the interior basins of the Lower Cretaceous of NE Brazil. This zonation has also allowed correlations with coeval sections in the Brazilian marginal basins and in the Gabon and Congo basins (central-west Africa). These records, consisting mainly of non-marine sediments, were a great challenge with regard to the correlation with the International Chronostratigraphic Chart. Therefore, local stages were used, the most recent being the Alagoas local Brazilian Stage, with which the Post-rift Sequence I of the Araripe Basin is related. Regarding lithostratigraphy, this sequence includes the Rio da Batateira (Barbalha for some authors) and Santana formations, the last one with the famous Crato, Ipubi, and Romualdo members, from the base to the top. Although currently there is a consensus on the age of the Alagoas local Brazilian Stage in the Araripe Basin, recently a new age for at least part of the Post-rift Sequence I was proposed. This new proposal, based on isotopic analysis of Re-Os, arose as a panacea to correlate the Rio da Batateira Formation and the Crato and Ipubi members with the international stages. Surprisingly, their authors, although on the one hand, they seem to underestimate biostratigraphic results, on the other they seek to support their proposal from microfossils studied by previous authors, but they do so in an inappropriate way, leading readers to misinterpret their results. Therefore, this paper presents a critical review on the age of the Alagoas local Brazilian Stage in the Araripe Basin and nearby basins, refuting a Barremian age for part of the Post-rift Sequence I. Keywords: Alagoas local Brazilian Stage, biostratigraphy, ostracods, palynomorphs, radiometric ages.


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