This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...) for example, incommensurability is a relation and not a property: that the proposition “In every square, the diagonals are incommensurable with the sides” is relational and not categorical. This paper asks the reader to do something more difficult: to accept the proposition that as late as 1831 De Morgan was blind to the same fact. This paper shows conclusively that in 1831, De Morgan was still in the grips of the allegedly Aristotelian paradigm. (shrink)

This self-contained lecture examines uses and misuses of the adverb conversely with special attention to logic and logic-related fields. Sometimes adding conversely after a conjunction such as and signals redundantly that a converse of what preceded will follow. -/- (1) Tarski read Church and, conversely, Church read Tarski. -/- In such cases, conversely serves as an extrapropositional constituent of the sentence in which it occurs: deleting conversely doesn’t change the proposition expressed. Nevertheless it does introduce new implicatures: a speaker would (...) implicate belief that the second sentence expresses a converse of what the first expresses. Perhaps because such usage is familiar, the word conversely can be used as “sentential pronoun”—or prosentence—representing a sentence expressing a converse of what the preceding sentence expresses. -/- (2) Tarski read Church and conversely. -/- This would be understood as expressing the proposition expressed by (1). Prosentential usage introduces ambiguity when the initial proposition has more than one converse. Confusion can occur if the initial proposition has non-equivalent converses. -/- Every proposition that is the negation of a false proposition is true and conversely. -/- One sense implies that every proposition that is the negation of a true proposition is false, which is true of course. But another sense, probably more likely, implies that every proposition that is true is the negation of a false proposition, which is false: the proposition that one precedes two is not a negation and thus is not the negation of a false proposition. The above also applies to synonyms of conversely such as vice versa. Although prosentence has no synonym, extrapropositional constituents are sometimes called redundant rhetoric, filler, or expletive. Authors discussed include Aristotle, Boole, De Morgan, Peirce, Frege, Russell, Tarski, and Church. END OF PUBLISHED ABSTRACT -/- See also: Corcoran, John. 2015. Converses, inner and outer. 2015. Cambridge Dictionary of Philosophy, third edition, Robert Audi (editor). Cambridge: Cambridge UP. https://www.academia.edu/10396347/Corcoran_s_27_entries_in_the_1999_second_edition_Audi_s_Cambridge_ Dictionary_of_Philosophy . (shrink)

Corcoran’s 27 entries in the 1999 second edition of Robert Audi’s Cambridge Dictionary of Philosophy [Cambridge: Cambridge UP]. -/- ancestral, axiomatic method, borderline case, categoricity, Church (Alonzo), conditional, convention T, converse (outer and inner), corresponding conditional, degenerate case, domain, De Morgan, ellipsis, laws of thought, limiting case, logical form, logical subject, material adequacy, mathematical analysis, omega, proof by recursion, recursive function theory, scheme, scope, Tarski (Alfred), tautology, universe of discourse. -/- The entire work is available online free at more than (...) one website. Paste the whole URL. http://archive.org/stream/RobertiAudi_The.Cambridge.Dictionary.of.Philosophy/Robert.Audi_The.Cambrid ge.Dictionary.of.Philosophy -/- The 2015 third edition will be available soon. Before you think of buying it read some reviews on Amazon and read reviews of its competition: For example, my review of the 2008 Oxford Companion to Philosophy, History and Philosophy of Logic,29:3,291-292. URL: http://dx.doi.org/10.1080/01445340701300429 -/- Some of the entries have already been found to be flawed. For example, Tarski’s expression ‘materially adequate’ was misinterpreted in at least one article and it was misused in another where ‘materially correct’ should have been used. The discussion provides an opportunity to bring more flaws to light. -/- Acknowledgements: Each of these entries was presented at meetings of The Buffalo Logic Dictionary Project sponsored by The Buffalo Logic Colloquium. The members of the colloquium read drafts before the meetings and were generous with corrections, objections, and suggestions. Usually one 90-minute meeting was devoted to one entry although in some cases, for example, “axiomatic method”, took more than one meeting. Moreover, about half of the entries are rewrites of similarly named entries in the 1995 first edition. Besides the help received from people in Buffalo, help from elsewhere was received by email. We gratefully acknowledge the following: José Miguel Sagüillo, John Zeis, Stewart Shapiro, Davis Plache, Joseph Ernst, Richard Hull, Concha Martinez, Laura Arcila, James Gasser, Barry Smith, Randall Dipert, Stanley Ziewacz, Gerald Rising, Leonard Jacuzzo, George Boger, William Demopolous, David Hitchcock, John Dawson, Daniel Halpern, William Lawvere, John Kearns, Ky Herreid, Nicolas Goodman, William Parry, Charles Lambros, Harvey Friedman, George Weaver, Hughes Leblanc, James Munz, Herbert Bohnert, Robert Tragesser, David Levin, Sriram Nambiar, and others. -/- . (shrink)

2006. George Boole. Encyclopedia of Philosophy. 2nd edition. Detroit: Macmillan Reference USA. -/- George Boole (1815-1864), whose name lives among modern computer-related sciences in Boolean Algebra, Boolean Logic, Boolean Operations, and the like, is one of the most celebrated logicians of all time. Ironically, his actual writings often go unread and his actual contributions to logic are virtually unknown—despite the fact that he was one of the clearest writers in the field. Working with various students including Susan Wood and (...) class='Hi'>Sriram Nambiar, I have written several publications trying to set the record straight—but so far to little avail. This encyclopedia entry is one more attempt to set the record straight in a way that can be appreciated by non-experts.Also see https://www.academia.edu/10161999/Booles_criteria_of_validity_and_invalidity . (shrink)

In this paper, we introduce the Hinduism religion and philosophy. We start with introducing the holy books in Hinduism including Vedas and Upanishads. Then, we explain the simplistic Hinduism, Brahman, gods and their incarnations, stories of apocalypse, karma, reincarnation, heavens and hells, vegetarianism, and sanctity of cows. Then, we switch to the profound Hinduism which is the main core of Hinduism and is monotheistic. In profound Hinduism, we focus on the non-dualism or Advaita Vedanta approach in Hinduism. We discuss consciousness, (...) causality, Brahman, psychology based on Hinduism, supportive scientific facts for Hinduism, the four levels of truth, and Maya. The four paths of knowledge, love, karma, and meditation are explained as well as the cosmic mind, the subtle body, and Aum. The risks for every path are also explained. Then, we introduce the orthodox and heterodox Indian schools including Yoga, Nyaya, Advaita Vedanta, Vishishtadvaita, and Dvaita. Connections to some other religions including Buddhism, Jainism, Sikhism, Judaism, Christianity, Islam, Islamic mysticism, and Zoroastrianism are analyzed. Finally, we explain the connection of Hindu philosophy with the Greek, western, and Islamic philosophies which include the philosophies of Plato, Aristotle, Plotinus, Spinoza, Descartes, Hegel, Schopenhauer, Avicenna, Suhrawardi, and Mulla Sadra. (shrink)

In this experimental investigation the Aluminium 6063 is treated with Aluminium Oxide (Al2O3) and Chicken Bone Ash (CBA). This Aluminium metal matrix composite is mixed at certain compositions and observed with the mechanical properties. Two main mechanical properties which includes Surface roughness and corrosion behavior is mainly focused in this research work. In this Research work aluminium hybrid metal matrix composite (AHMMC) is fabricated through stir casting process. Al6063 shows good mechanical properties and corrosion behavior changes, when combined with reinforcements, (...) Al2O3 and Chicken Bone Ash (CBA). Stir casting is an efficient cycle for the manufacture of aluminum hybrid composites. There are numerous boundaries in this cycle, which influence the behavior of corrosion and mechanical properties of the composites. Stir casting is a fluid state technique for the manufacture of composite materials, in which a scattered stage is blended in with a liquid network metal by methods for mechanical mixing. Stir Casting is the least difficult and the most financially savvy strategy for fluid state manufacture. Finally in this research work, when the compositions of each and every reinforcement increase, simultaneously the surface roughness of the composite also get increases. (shrink)