Where do sets come from?

1991 ◽  
Vol 56 (1) ◽  
pp. 150-175 ◽  
Author(s):  
Harold T. Hodes
Keyword(s):  
Mathematical Object ◽  
Semantic Theory ◽  
Alternative Theory ◽  
Special Relation ◽  
Alternative Account ◽  
Usual Model ◽  
First Order ◽  
Order Language ◽  
The World ◽  
In Virtue Of

Many philosophers take set-theoretic discourse to be about objects of a special sort, namely sets; correlatively, they regard truth in such discourse as quite like truth in discourse about nonmathematical objects. There is a thin “disquotational” way of construing this construal; but that may candy-coat a philosophically substantive semantic theory: the Mathematical-Object theory of the basis for the distribution of truth and falsehood to sentences containing set-theoretic expressions. This theory asserts that truth and falsity for sentences containing set-theoretic expressions are grounded in semantic facts (about the relation between language and the world) of the sort modelled by the usual model-theoretic semantics for an uninterpreted formal first-order language. For example, it would maintain that ‘{ } ∈ {{ }}” is true in virtue of the set-theoretic fact that the empty set is a member of its singleton, and the semantic facts that ‘{ }’ designates the empty set,‘{{ }}’ designates its singleton, and ‘∈’ applies to an ordered pair of objects iff that pair's first component is a member of its second component.Now this theory may come so naturally as to seem trivial. My purpose here is to loosen its grip by “modelling” an alternative account of the alethic underpinnings of set-theoretic discourse. According to the Alternative theory, the point of having set-theoretic expressions (‘set’ and ‘∈’ will do) in a language is not to permit its speakers to talk about some special objects under a special relation; rather it is to clothe a higher-order language in lower-order garments.

Gaslighting, First- and Second-Order

Hypatia ◽  
2020 ◽  
pp. 1-21
Author(s):  
Paul-Mikhail Catapang Podosky
Keyword(s):  
Second Order ◽  
First Order ◽  
The World ◽  
In Virtue Of

Abstract In what sense do people doubt their understanding of reality when subject to gaslighting? I suggest that an answer to this question depends on the linguistic order at which a gaslighting exchange takes place. This marks a distinction between first-order and second-order gaslighting. The former occurs when there is disagreement over whether a shared concept applies to some aspect of the world, and where the use of words by a speaker is apt to cause hearers to doubt their interpretive abilities without doubting the accuracy of their concepts. The latter occurs when there is disagreement over which concept should be used in a context, and where the use of words by a speaker is apt to cause hearers to doubt their interpretive abilities in virtue of doubting the accuracy of their concepts. Many cases of second-order gaslighting are unintentional: its occurrence often depends on contingent environmental facts. I end the article by focusing on the distinctive epistemic injustices of second-order gaslighting: (1) metalinguistic deprivation, (2) conceptual obscuration, and (3) perspectival subversion. I show how each reliably has sequelae in terms of psychological and practical control.

scholarly journals הכל הבל in Ecclesiastes 1:2 and 12:8 – Descriptive metaphysics of properties as comparative-philosophical supplement

2021 ◽  
Vol 77 (1) ◽  
Author(s):  
Jaco Gericke
Keyword(s):  
Second Order ◽  
Property Theory ◽  
First Order ◽  
Conceptual Clarification ◽  
Order Language ◽  
The World ◽  
Original Contribution ◽  
The Way

In this article, a supplementary yet original contribution is made to the ongoing attempts at refining ways of comparative-philosophical conceptual clarification of Qohelet’s claim that הבל הכל in 1:2 (and 12:8). Adopting and adapting the latest analytic metaphysical concerns and categories for descriptive purposes only, a distinction is made between הבל as property of הכל and the properties of הבל in relation to הכל. Involving both correlation and contrast, the second-order language framework is hereby extended to a level of advanced nuance and specificity for restating the meaning of the book’s first-order language on its own terms, even if not in them.Contribution: By considering logical, ontological, mereological and typological aspects of property theory in dialogue with appearances of הכל and of הבל in Ecclesiastes 1:2 and 12:8 and in-between, a new way is presented in the quest to explain why things in the world of the text are the way they are, or why they are at all.

scholarly journals Law’s Humility: The Possibility of Metajurisprudence

2018 ◽  
Author(s):  
Triantafyllos Gkouvas
Keyword(s):  
Legal Philosophy ◽  
Legal Authority ◽  
First Order ◽  
Slow Pace ◽  
The World ◽  
The Veil ◽  
Foundational Work ◽  
Legal Normativity ◽  
In Virtue Of ◽  
Alternative Idea

This thesis propounds a metatheoretical regimentation of legal claims that can accommodate theoretical disagreement across the board. The solution explored does not question the incommensurability between the descriptive and the normative variants of first-order disputes about the grounds of law. What it targets instead is an unpronounced agnosticism about the possibility of a more inclusive type of metajurisprudential disagreement that does not take for granted either the existence of legal facts—construed either as descriptive or as normative facts about what the law requires—as the trivial truthmakers of propositions of law or their potentially reason-giving properties. On the assumption that the fact that for every legal proposition there is something in the world that makes it true is a premise shared by all legal philosophers but those of an expressivist inclination, an unpronounced, primitive division of opinion occurs as early as one ventures to question that our commitment to the possibility of legal truth logically entails our commitment to entities of a distinctly legal kind. The alternative idea that comes out of the rejection of this entailment will be that part of what could explain the slow pace at which the positivism-antipositivism debate is moving beyond the traditional conceptual jargon of 20th century analytic jurisprudence is the fact that we may have been blind to the possibility that our quest for the ultimate grounds of law could have been taking place under the veil of a narrow understanding of the available options with regard to what could legally exist. In virtue of this reconfiguration the prospect of metajurisprudential disagreement acquires definitive shape. At this higher level of abstraction questions about the perspectival character of legal statements, the constitution of legal authority, the relation of legal truth to reality as well as about the nature of legal grounding and legal normativity become available for meaningful contestation. If there is something that could serve as a leitmotiv for this research proposal is that there is no more apt a byword for what it is to conduct foundational work in legal philosophy than that there is no royal way from semantics to ontology.

Imaginings

2017 ◽  
Vol 9 (3) ◽  
pp. 17-30
Author(s):  
Kelly James Clark
Keyword(s):  
Religious Tradition ◽  
Second Order ◽  
Fine Tuning ◽  
Intellectual Humility ◽  
First Order ◽  
Natural Processes ◽  
Empirically Supported ◽  
Group Violence ◽  
The World ◽  
The Universe

In Branden Thornhill-Miller and Peter Millican’s challenging and provocative essay, we hear a considerably longer, more scholarly and less melodic rendition of John Lennon’s catchy tune—without religion, or at least without first-order supernaturalisms (the kinds of religion we find in the world), there’d be significantly less intra-group violence. First-order supernaturalist beliefs, as defined by Thornhill-Miller and Peter Millican (hereafter M&M), are “beliefs that claim unique authority for some particular religious tradition in preference to all others” (3). According to M&M, first-order supernaturalist beliefs are exclusivist, dogmatic, empirically unsupported, and irrational. Moreover, again according to M&M, we have perfectly natural explanations of the causes that underlie such beliefs (they seem to conceive of such natural explanations as debunking explanations). They then make a case for second-order supernaturalism, “which maintains that the universe in general, and the religious sensitivities of humanity in particular, have been formed by supernatural powers working through natural processes” (3). Second-order supernaturalism is a kind of theism, more closely akin to deism than, say, Christianity or Buddhism. It is, as such, universal (according to contemporary psychology of religion), empirically supported (according to philosophy in the form of the Fine-Tuning Argument), and beneficial (and so justified pragmatically). With respect to its pragmatic value, second-order supernaturalism, according to M&M, gets the good(s) of religion (cooperation, trust, etc) without its bad(s) (conflict and violence). Second-order supernaturalism is thus rational (and possibly true) and inconducive to violence. In this paper, I will examine just one small but important part of M&M’s argument: the claim that (first-order) religion is a primary motivator of violence and that its elimination would eliminate or curtail a great deal of violence in the world. Imagine, they say, no religion, too.Janusz Salamon offers a friendly extension or clarification of M&M’s second-order theism, one that I think, with emendations, has promise. He argues that the core of first-order religions, the belief that Ultimate Reality is the Ultimate Good (agatheism), is rational (agreeing that their particular claims are not) and, if widely conceded and endorsed by adherents of first-order religions, would reduce conflict in the world.While I favor the virtue of intellectual humility endorsed in both papers, I will argue contra M&M that (a) belief in first-order religion is not a primary motivator of conflict and violence (and so eliminating first-order religion won’t reduce violence). Second, partly contra Salamon, who I think is half right (but not half wrong), I will argue that (b) the religious resources for compassion can and should come from within both the particular (often exclusivist) and the universal (agatheistic) aspects of religious beliefs. Finally, I will argue that (c) both are guilty, as I am, of the philosopher’s obsession with belief. 

Frustrating Absences

Disputatio ◽  
2019 ◽  
Vol 11 (53) ◽  
pp. 45-62
Author(s):  
André J. Abath
Keyword(s):  
Everyday Life ◽  
Alternative Account ◽  
The World

Abstract Experiences of absence are common in everyday life, but have received little philosophical attention until recently, when two positions regarding the nature of such experiences surfaced in the literature. According to the Perceptual View, experiences of absence are perceptual in nature. This is denied by the Surprise-Based View, according to which experiences of absence belong together with cases of surprise. In this paper, I show that there is a kind of experience of absence—which I call frustrating absences—that has been overlooked by the Perceptual View and by the Surprise Based-View and that cannot be adequately explained by them. I offer an alternative account to deal with frustrating absences, one according to which experiencing frustrating absences is a matter of subjects having desires for something to be present frustrated by the world. Finally, I argue that there may well be different kinds of experiences of absence.

Weakly atomic-compact relational structures

1971 ◽  
Vol 36 (1) ◽  
pp. 129-140 ◽  
Author(s):  
G. Fuhrken ◽  
W. Taylor
Keyword(s):  
Abelian Group ◽  
Model Theory ◽  
Compact Abelian Group ◽  
Finite Subset ◽  
Relational Structure ◽  
Similarity Type ◽  
First Order ◽  
Relational Structures ◽  
Order Language ◽  
Weakly Atomic

A relational structure is called weakly atomic-compact if and only if every set Σ of atomic formulas (taken from the first-order language of the similarity type of augmented by a possibly uncountable set of additional variables as “unknowns”) is satisfiable in whenever every finite subset of Σ is so satisfiable. This notion (as well as some related ones which will be mentioned in §4) was introduced by J. Mycielski as a generalization to model theory of I. Kaplansky's notion of an algebraically compact Abelian group (cf. [5], [7], [1], [8]).

scholarly journals WORLD VOLUME SOLITONS OF THE D3-BRANE IN THE BACKGROUND OF (p, q) FIVE-BRANES

2000 ◽  
Vol 15 (28) ◽  
pp. 4477-4498 ◽  
Author(s):  
P. M. LLATAS ◽  
A. V. RAMALLO ◽  
J. M. SÁNCHEZ DE SANTOS
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Brane World ◽  
Invariant Solutions ◽  
First Order ◽  
World Volume ◽  
The World ◽  
Energy Bound

We analyze the world volume solitons of a D3-brane probe in the background of parallel (p, q) five-branes. The D3-brane is embedded along the directions transverse to the five-branes of the background. By using the S duality invariance of the D3-brane, we find a first-order differential equation whose solutions saturate an energy bound. The SO(3) invariant solutions of this equation are found analytically. They represent world volume solitons which can be interpreted as formed by parallel (-q, p) strings emanating from the D3-brane world volume. It is shown that these configurations are 1/4 supersymmetric and provide a world volume realization of the Hanany–Witten effect.

scholarly journals ON PRODUCTS OF ELEMENTARILY INDIVISIBLE STRUCTURES

2016 ◽  
Vol 81 (3) ◽  
pp. 951-971
Author(s):  
NADAV MEIR
Keyword(s):  
New Products ◽  
Elementary Substructure ◽  
First Order ◽  
Order Language ◽  
Image Position

AbstractWe say a structure ${\cal M}$ in a first-order language ${\cal L}$ is indivisible if for every coloring of its universe in two colors, there is a monochromatic substructure ${\cal M}\prime \subseteq {\cal M}$ such that ${\cal M}\prime \cong {\cal M}$. Additionally, we say that ${\cal M}$ is symmetrically indivisible if ${\cal M}\prime$ can be chosen to be symmetrically embedded in ${\cal M}$ (that is, every automorphism of ${\cal M}\prime$ can be extended to an automorphism of ${\cal M}$). Similarly, we say that ${\cal M}$ is elementarily indivisible if ${\cal M}\prime$ can be chosen to be an elementary substructure. We define new products of structures in a relational language. We use these products to give recipes for construction of elementarily indivisible structures which are not transitive and elementarily indivisible structures which are not symmetrically indivisible, answering two questions presented by A. Hasson, M. Kojman, and A. Onshuus.

scholarly journals Word order in Latin locative constructions: a corpus study in Caesar’s De bello gallico

2011 ◽  
Vol 64 (2) ◽  
Author(s):  
Stavros Skopeteas
Keyword(s):  
Word Order ◽  
Information Structure ◽  
Motion Verbs ◽  
Structural Domains ◽  
Corpus Study ◽  
First Order ◽  
Order Language ◽  
Free Word

AbstractClassical Latin is a free word order language, i.e., the order of the constituents is determined by information structure rather than by syntactic rules. This article presents a corpus study on the word order of locative constructions and shows that the choice between a Theme-first and a Locative-first order is influenced by the discourse status of the referents. Furthermore, the corpus findings reveal a striking impact of the syntactic construction: complements of motion verbs do not have the same ordering preferences with complements of static verbs and adjuncts. This finding supports the view that the influence of discourse status on word order is indirect, i.e., it is mediated by information structural domains.

scholarly journals GENERATIVE CREATING OF SACRAL SPACE: MYTHOLOGY, COSMOLOGY AND PLACES FOR CULT RITUALS

2021 ◽  
Vol 4 ◽  
pp. 626-652
Author(s):  
Silvija Ozola
Keyword(s):  
Research Problem ◽  
Moral Values ◽  
Special Relation ◽  
Creative Thought ◽  
Religious Ritual ◽  
Strong Energy ◽  
Sign System ◽  
The World ◽  
Research Goal ◽  
The Universe

Signs are an integral part of the existence of humanity. The Latvians have one of the most complicated symbolic sign system in the world—the Lielvārde belt which includes symbols of strong energy and encodes ancient information that characterizes the special relation to nature and the Universe. God is the basis of moral values and the origin of all events. The understanding of Latvian deities is based on creative thought, and each sign of the deity image is a structural whole with a certain informative value. The Balts’ tribes for cult rituals chose energetically powerful places. Generative creating of sacral space and religious ritual is connected by concepts the Place, the Way and the Symbol. Research object: Latvian wisdom and spiritual traditions, sacral space for the worship of God. Research goal: analysis of the influence of the Latvian wisdom on traditions of the establishment of early places of worship. Research problem: common and different features of the sacral space of the Latvians and other nations have been little studied. Research novelty: detailed studies of generative creating of early places of worship based on Latvian mythology and cult ritual traditions of other nations. Research methods: analysis of archive documents and cartographic materials, study of published literature and inspection of sacral places in nature.

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