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The Logical Problem of the Trinity and the Strong Theory of Relative Identity

Daniel Molto
<span title="">2017</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dm7mconp5jfozktnowpwopgyhq" style="color: black;">Sophia</a> </i> &nbsp;
The Stevenson logic, for example, is a logic of relative identity in name only.  ...  What is the significance of this for the relative identity solution to the logical problem of the Trinity?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11841-017-0612-y">doi:10.1007/s11841-017-0612-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s2c2sfyiprbupicioj2mqc4yhe">fatcat:s2c2sfyiprbupicioj2mqc4yhe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180722123817/http://eprints.whiterose.ac.uk/116573/1/SOPH1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/73/b9/73b92838a0c7522e92d18c52bcd1c1ea50152b13.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11841-017-0612-y"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

The Doctrine of the Trinity and the Logic of Relative Identity

James Cain
<span title="">1989</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z24qk6dfkrea7hbziqylqpswqe" style="color: black;">Religious Studies: An International Journal for the Philosophy of Religion</a> </i> &nbsp;
a term which relativizes the identity) as being analysable in terms of absolute (or unrelativized) identity according to the following equivalence schema, (E): (E) a is the same A as b if and only if  ...  We see this as follows (it will suffice to consider just the relation of Father and Son): logicians generally treat relativized identity expressions of the form 'is the same A as' (here 'A' stands in for  ...  giving an analysis of relative identity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0034412500001761">doi:10.1017/s0034412500001761</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uidji4mxpjfnviz6eehuk3wykq">fatcat:uidji4mxpjfnviz6eehuk3wykq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809054020/http://www.andrewmbailey.com/trinity/Trinity%20and%20Relative%20identity.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d8/c3/d8c3750cb4f36cae5aa6fe17a22f1b8bbd0e5e5f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0034412500001761"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> cambridge.org </button> </a>

Page 510 of The Philosophical Review Vol. 49, Issue 5 [page]

<span title="">1940</span> <i title="Cornell University"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_philosophical-review" style="color: black;">The Philosophical Review </a> </i> &nbsp;
The question whether identity is relative or absolute is not a question about logical identity, but a question about the nature of the world, about whether it is composed of things which are independent  ...  It is wrong, therefore, to describe the opposition between the theories of internal and external relations, between relative and absolute identity, monism and pluralism, as an opposition between two logics  ... 
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Page 1353 of Mathematical Reviews Vol. , Issue 83d [page]

<span title="">1983</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Englebretsen, George 83d:03032 Do we need relative identity? Notre Dame J. Formal Logic 23 (1982), no. 1, 91-93.  ...  A relative identity statement is a statement of the form “x is the same F as y”, where F is a common noun.  ... 
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Corporate Governance Deviance

Ruth V. Aguilera, William Q. Judge, Siri A. Terjesen
<span title="">2018</span> <i title="Academy of Management"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qheyrqez25fp5hr3riqruk625y" style="color: black;">Academy of Management Review</a> </i> &nbsp;
Interestingly, identical CEO compensation practices receive different normative evaluations relative to the zone of conformity, depending on the dominant legitimate governance logic.  ...  In essence, the identity claims of the dominant governance logic are in conflict with the organization's identity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5465/amr.2014.0394">doi:10.5465/amr.2014.0394</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7jfdabprsja7natgwdbmktdw64">fatcat:7jfdabprsja7natgwdbmktdw64</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190429050218/https://digitalcommons.odu.edu/cgi/viewcontent.cgi?article=1011&amp;context=management_fac_pubs" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/85/bf/85bf5938eb2dcd376d56942dbfcbe2172f63215a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5465/amr.2014.0394"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 54 of MIND Vol. 2, Issue 5 [page]

<span title="">1877</span> <i title="Oxford Publishing Limited(England)"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mind" style="color: black;">MIND </a> </i> &nbsp;
I have, in conclusion, to make a few remarks on the “ logic of relatives”. This will probably be found to be an extension of the logic of co-existence.  ...  The terms and propositions of the logic of co-existence may be interpreted in either extension or comprehension, but those of the logic of identity in extension only.  ... 
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Page 7528 of Mathematical Reviews Vol. , Issue 98M [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
98m:03014 The axiomatics of PEL consists of (a) axioms and rules (modus ponens and universal generalization) of classical predicate logic with identity for 3, V and =, and (b) three axioms governing =:  ...  of free logics.  ... 
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Page 3091 of Mathematical Reviews Vol. , Issue 83h [page]

<span title="">1983</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The author defends the notion of identity used in classical first-order logic against the partisans of the relativity of identity, such as P. T.  ...  Longeart-Roth, Maryvonne L’identité est-elle relative? [Is identity relative] Dialogue 20 (1981), no. 4, 697-713.  ... 
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On the completeness of the classical sentential logic

E.W. Beth
<span title="">1958</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kvvpnxmxtzckhmjzlphv6nz3wa" style="color: black;">Indagationes Mathematicae (Proceedings)</a> </i> &nbsp;
The equivalence of the approaches under (A) and (B) is a relatively simple matter; it is also rather easy to prove that every formula deducible from the axioms is a logical identity.  ...  However, the problem of proving that every logical identity is deducible is not quite as simple.  ...  The equivalence of the approaches under (A) and (B) is a relatively simple matter; it is also rather easy to prove that every formula deducible from the axioms is a logical identity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1385-7258(58)50060-2">doi:10.1016/s1385-7258(58)50060-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xsplulvjjrcffhtpxy7i5x27pq">fatcat:xsplulvjjrcffhtpxy7i5x27pq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190316152744/https://core.ac.uk/download/pdf/82525571.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/52/f1/52f1d532320396a9c7bdf2df67414533c6b1bdfc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s1385-7258(58)50060-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Page 45 of The Philosophical Review Vol. 51, Issue 1 [page]

<span title="">1942</span> <i title="Cornell University"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_philosophical-review" style="color: black;">The Philosophical Review </a> </i> &nbsp;
The question whether identity is relative or absolute is not a question about logical identity, but a question about the nature of the world, about whether it is composed of things which are independent  ...  For the very principle of that theory of truth is the doctrine of identity in difference, or relational identity, which it is the purpose of Bradley’s dialectic, both in the Logic and in Appearance and  ... 
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Page 289 of Isis Vol. 22, Issue 1 [page]

<span title="">1934</span> <i title="University of Chicago, acting through its Press"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_isis" style="color: black;">Isis </a> </i> &nbsp;
In a paper of 1880 Perce argues the logical priority of his inclusion or implication over identity, on the grounds (1) that implication comes of weakening the psychologically basic connective “ ergo” by  ...  ceasing to assert the copulands, and (2) that inclusion is a genus of and therefore logically simpler than identity, which latter is that special case of inclusion in which the converse inclusion also  ... 
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Composition and Relative Counting

Massimiliano Carrara, Giorgio Lando
<span title="">2017</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzr27jqntvh4hlr767kpl6tocu" style="color: black;">Dialectica</a> </i> &nbsp;
views of identity: perhaps a form of relative identity, perhaps a milder kind of pluralism about identity.  ...  Relative identity is worse than death".  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/1746-8361.12198">doi:10.1111/1746-8361.12198</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ugup27q6fjgwboyykn6o7qbyie">fatcat:ugup27q6fjgwboyykn6o7qbyie</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180719214746/https://philpapers.org/archive/LANCAR-4.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/11/1e/111e2492996cfc8bb5f633259ab86e985f516cb8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/1746-8361.12198"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 3754 of Mathematical Reviews Vol. , Issue 80J [page]

<span title="">1980</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
After a brief survey of some of the main approaches to relative identity and its relation to absolute identity, the authors propose a formal analysis of relative identity within a slightly augmented classical  ...  80:03 018 Routley, Richard; Griffin, Nicholas Towards a logic of relative identity. Logique et Anal. (N.S.) 22 (1979), no. 85-86, 65-83.  ... 
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Admissibility in De Morgan algebras

George Metcalfe, Christoph Röthlisberger
<span title="2012-02-07">2012</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/e5brmbb4nne2bb6o5whxervgii" style="color: black;">Soft Computing - A Fusion of Foundations, Methodologies and Applications</a> </i> &nbsp;
Characterizations of admissible quasi-identities, which may be understood as quasi-identities holding in free algebras on countably infinitely many generators, are provided for classes of De Morgan algebras  ...  Acknowledgments We are grateful for the helpful comments of both the anonymous referees and Leonardo Cabrer. The authors acknowledge support from Swiss National Science Foundation Grant 20002_129507.  ...  quasi-identities of Q essentially involves finding a set of quasi-identities that are admissible in Q and that axiomatize a structurally complete quasivariety relative to Q: More precisely Lemma 3 Let  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00500-012-0839-z">doi:10.1007/s00500-012-0839-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6cxzt3bninbjphaid5i7yklxxi">fatcat:6cxzt3bninbjphaid5i7yklxxi</a> </span>
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A Logic for Dually Hemimorphic Semi-Heyting Algebras and its Axiomatic Extensions [article]

Juan M. Cornejo, Hanamantagouda P. Sankappanavar
<span title="2022-02-08">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Surprisingly, many of these logics turn out to be connexive logics, a few of which are presented in this paper.  ...  Firstly, we present a Hilbert-style axiomatization of a new logic called Dually hemimorphic semi-Heyting logic (DHMSH, for short), as an expansion of semi-intuitionistic logic SI (also called SH) introduced  ...  Its dual will give the partial poset of the axiomatic extensions of the logic DQDSH. Note that the links in the poset do not, in general, represent the covers.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1908.02403v2">arXiv:1908.02403v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nl7uizxal5h4hcspv2oispov54">fatcat:nl7uizxal5h4hcspv2oispov54</a> </span>
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