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Topic: Logical proofs

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logical fallacies

mathematical logic

logic gate

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logical argument

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first order logic

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	If God's, then...
		Following are four attempted proofs for why God does not exist, taken from the CARM atheism discussion board.
		But since all proofs cannot be known by any one person, it is possible that there are proofs that exist that are not known.
		Because it is subjective, it is not a proof.
	www.carm.org /atheism/ifGodexists.htm (850 words)

	Logical argument - Wikipedia, the free encyclopedia
		Note that a rigorous proof does not have to be a formal proof.
		In ordinary language, people refer to the logic of an argument or use terminology that suggests that an argument is based on inference rules of formal logic.
		Grice, Logic and Conversation in The Logic of Grammar, Dickenson, 1975.
	en.wikipedia.org /wiki/Logical_argument (2092 words)

	Untitled Document (Site not responding. Last check: 2007-10-15)
		The bad part of using higher level proofs in the classroom is the misunderstanding by students.
		This shows that the need for logical explanation is not always the best route for students, but a nice and easy visualization of a problem may be what it needs to help a logical explanation take place.
		Proofs have many important functions for teachers, but it is very important for teachers to use proofs as a tool for students to acquire "'an appreciation for the invention, along with a feeling of becoming wiser'" (8).
	www.auburn.edu /~conwabm/reflections/reflection5.htm (392 words)

	Yale Scientific Magzine
		The logical framework provides a means for describing elements of logic, such as “if… then” statements, deductions, or truth assignments, and allows them to be put together in various ways and reasoned about.
		Researchers are currently very limited in their ability to share logical proofs and derivations with each other, because different sectors of the research world use different, non-compatible systems.
		Logical frameworks will be used to represent the problems and the methods used to reduce one problem to another.
	research.yale.edu /ysm/article.jsp?articleID=3&printable=1 (1548 words)

	sciforums.com - "Real" knowledge and "artificial" knowledge - I have a dilemma here
		Logical proofs aren't tentative, and I can keep them in my knowledge, but I am not going to let concepts such as that fully define my reality.
		I was thinking any logical proof could be considered subjective if all knowledge is tentative, which I agree with only to a certain extent.
		With regards to logical proofs - the proof "one = one" is fine sure, and it CAN be applied to 'objective reality', but that doesn't mean it's truly representative of it.
	www.sciforums.com /showthread.php?p=318988 (2464 words)

	Semantic Web roadmap
		This uses logical expressions which are not available at this level, but that is OK so long as the schema language is, for the moment, going to be handled by specialized schema engines only, not by a general reasoning engine.
		We need ways of writing logic into documents to allow such things as, for example, rules the deduction of one type of document from a document of another type; the checking of a document against a set of rules of self-consistency; and the resolution of a query by conversion from terms unknown into terms known.
		By contrast, logical engines have typically been able to restrict their output to that which is provably correct answer, but have suffered from the inability to rummage through the mass of intertwined data to construct valid answers.
	www.w3.org /DesignIssues/Semantic.html (3405 words)

	1__~
		Argument by example is not “irrational,” but as an independent mode of logical proof or persuasion that is not parasitic upon and does not require justification through rules.
		The relatively circumscribed contemporary inquiry into the logic of the example is also surprising in light of the widespread use of the instrument in aesthetic and legal modes of reasoning.
		Rhetoric Aristotle distinguishes “logical” proofs from those non-logical proofs derived from consideration of the character (ethos) of the speaker and the emotional state (pathos) of the audience.
	www.public.iastate.edu /~consigny/example.html (3881 words)

	Yale Scientific Magzine
		In modern logical terms, Aristotle’s syllogism has become: “Each element in the set made up of all men has the property that it is mortal.
		Logical frameworks are computer systems that enable users to work with complex logical statements.
		The Twelf logical framework is the brainchild of Schürmann and his former doctorate advisor at Carnegie Mellon University, Frank Pfenning.
	research.yale.edu /ysm/article.jsp?articleID=3 (1561 words)

	Additional Reading (from formal logic) -- Encyclopædia Britannica (Site not responding. Last check: 2007-10-15)
		in logic and mathematics, abstract, theoretical organization of terms and implicit relationships that is used as a tool for the analysis of the concept of deduction.
		Logic is the study of the way in which valid conclusions may be drawn from given premises.
		Discusses the Aristotelean logic, predicate calculus, geometry of Euclid, formal theories of mathematics, and Plato and Aristotle’s philosophy of mathematics.
	www.britannica.com /eb/article?tocId=65856 (938 words)

	Answers to positions held by atheists
		This is not a logical position to hold, since to know there is no God means the person would have to know all things to know there is no God.
		Logic can only disprove theistic proofs that are presented, and negating such proofs is not a refutation of all possible proofs since no one can know or present all possible proofs of God's existence.
		But since no proof of God's non-existence has been successfully defended by atheists, we can conclude that thus far, that there are no logical proofs for God's non-existence.
	www.carm.org /atheism/positions.htm (907 words)

	Alfred North Whitehead (Stanford Encyclopedia of Philosophy)
		Whitehead's philosophical influence can be felt in all three of the main areas in which he worked (i.e., logic and the foundations of mathematics, the philosophy of science, and metaphysics) as well as in other areas such as ethics, education and religion.
		Logicism, the theory that mathematics is in some important sense reducible to logic, consists of two main theses.
		The second is that all mathematical proofs can be recast as logical proofs or, in other words, that the theorems of mathematics constitute a proper subset of the theorems of logic.
	plato.stanford.edu /entries/whitehead (1813 words)

	Reason and the Baha'i Writings (Site not responding. Last check: 2007-10-15)
		This is a spiritual proof, but one which we cannot at the beginning put forth for the benefit of the materialists; first we must speak of the logical proofs, afterwards the spiritual proofs.
		He does not try to flout logic by mis-using it to proclaim two mutually contradictory statements to be true at the same time and in the same way.
		Logically speaking, we can resolve this apparent contradiction by distinguishing between God's (a) existential independence and His (b) ontological presence just as we distinguish the existence of the artist from his/her presence through a manifestation of his/her powers.
	bahai-library.com /?file=kluge_reason_bahai_writings.html (13136 words)

	Principal Problems with Principles: Limits of Logic in the Growth of Knowledge
		Scholars were used to thinking of logical deduction as a source of certain knowledge, and Newton presented his principles in the form of a series of illustrated arguments that looked a lot like geometry proofs.
		In Euclid's geometry proofs, as in later mathematical proofs, a series of simple deductive steps is used to establish that a particular relationship, a theorem, follows logically from generally accepted principles, or from principles that have already been proven.
		None of the terms in a formal logical proof, in geometry or in other mathematical discipline, can be simply identified with items and actions in our ordinary world without risking problems of various sorts.
	www.dharma-haven.org /science/limits-of-logic.htm (6833 words)

	Reason and the Baha'i Writings: the Use and Misuse of Logic and Persuasion
		If the formal logical procedure is correct, there are only 2 ways to attack this argument: (a) proving that one of the examples supporting the conclusion is factually wrong or (b) find a counter-example wherein religion acts for human regression.
		Because logic and rhetorical or persuasive devices are subject to intentional or unintentional mis-use, it is essential for a credible and effective Baha'i teacher to recognize when confronted with instances of abuse.
		It is logically obvious that if other religions with "strict internal controls" (ibid.) are experiencing "significant growth", such controls cannot be used to explain why the Baha'i Faith is not growing as fast as he thinks it should be.
	bahai-library.com /unpubl.articles/reason.writings.html (12708 words)

	Principia Mathematica (Stanford Encyclopedia of Philosophy)
		Written as a defense of logicism (i.e., the view that mathematics is in some significant sense reducible to logic) the book was instrumental in developing and popularizing modern mathematical logic.
		Second, it consists of the claim that all mathematical proofs can be recast as logical proofs or, in other words, that the theorems of mathematics constitute a proper subset of the theorems of logic.
		The axiom of reducibility was introduced as a means of overcoming the not completely satisfactory effects of the theory of types, the theory that Russell and Whitehead used to restrict the notion of a well-formed expression, and so to avoid paradoxes such as Russell's paradox.
	plato.stanford.edu /entries/principia-mathematica (1571 words)

	[No title]
		The prove command directs LP to initiate the proof of a conjecture, and the qed command directs LP to confirm that its proof is complete.
		LP is a proof assistant for multisorted first-order logic.
		A deduction rule is logically equivalent to the formula obtained by having the conjunction of its hypotheses imply the conjunction of its conclusions.
	nms.lcs.mit.edu /Larch/LP/all.html (10192 words)

	DAI Database: Research Paper #835 (Site not responding. Last check: 2007-10-15)
		Insight is more clearly perceived in these than in the corresponding logical proofs: they capture an intuitive notion of truthfulness that humans find easy to see and understand.
		The system that we are in the process of implementing will be given a theorem and will (initially) interactively prove it by the use of geometric manipulations on the diagram that the user chooses to be the appropriate ones.
		In this way, we hope to verify and to show that the diagrammatic proof of a gven theorem can be formalised.
	www.dai.ed.ac.uk /papers/documents/rp835.html (193 words)

	Bibliography on Logical Frameworks
		Rewriting logic as a logical and semantical framework.
		A proof of the Church-Rosser theorem and its representation in a logical framework.
		A machine-assisted proof of the fundamental theorem of arithmetic.
	www.cs.cmu.edu /afs/cs/user/fp/www/lfs-bib.html (8721 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		Such proofs are based on an analysis of motion and efficient causation.
		It assumes that causality does not exist at the microcosmic level (the "territory" we are studying) because the methods we use to study causality (the "map") at the macrocosmic level are of limited use there.
		It violates logic because to say that matter created itself is to say that it existed before it existed.
	www.geocities.com /SoHo/Den/4944/proofgod.html (3500 words)

	Some Answered Questions, Pages 194-197
		The proofs which we have adduced relative to the origin of the human species were logical proofs.
		Just as the terrestrial globe is the place where the rays of the sun are reflected--as its light, its heat and its influence are apparent and visible in all the atoms of the earth--so, in the same way, the atoms of beings, in this infinite space, proclaim and prove one of the divine perfections.
		This is a spiritual proof, but one which we cannot at the beginning put forth for the benefit of the materialists.
	www.ibiblio.org /Bahai/Texts/English/SAQ/SAQ-50.html (585 words)

	unsaved:///newpage3.htm
		The logical results of TNR-theory[19] for Biblical studies are relevant to the growing plethora of speculations about the historical authenticity especially of certain testable narrative portions of the Bible.
		According to the logical proofs of TNR-theory and the logical perfections that TNRs show in their structures, such a separation is as ridiculous as hoping to improve the faithfulness of a photograph to one of the elements it contains by cutting away all of the surrounding elements.
		Given the rigorous logical proofs of TNR-theory in predicting and describing the structure of all TNRs, it must be applicable to all narrative Rs that claim to be true.
	www.trinitysem.edu /journal/collins_ollerpap.html (13286 words)

	You frequently use analogies. Whereas according to logic, an analogy does not offer certainty, and the issues which ...
		Whereas according to logic, an analogy does not offer certainty, and the issues which require conviction to be believed in need to be based on logical proofs.
		Although according to logic analogies do not offer certainty, among the sorts of analogies there is one that it is stronger than logical proofs and gives greater certainty than deductions.
		As for the second part of the question, as you know, according to the science of eloquence, if a word or phrase is used to suggest or express a meaning other than its original one, it is called a metaphor.
	www.thewaytotruth.org /godsexistenceandunity/youfrequently.html (540 words)

	Ramon Lull's Ars Magna (Site not responding. Last check: 2007-10-15)
		first person in the history of formal logic to use a mechanical device to generate (so-called) logical proofs was the Spanish theologian Ramon Lull (see also logic diagrams and logic machines).
		This magnum opus described a number of eccentric logical techniques, but the one of which Lull was most proud (and which received the most attention) was based on concentric disks of card, wood, or metal mounted on a central axis.
		Well by some strange quirk of fate, Lull's work fired the imagination of several characters with whom we are already familiar, such as Gottfried von Leibniz who invented the mechanical calculator called the Step Reckoner.
	www.maxmon.com /1274ad.htm (464 words)

	Synopses of Topics - Direct Proofs
		One of the turning points in the development of mathematics was the introduction by the Greeks of the concept of a logical proof.
		One of the sources of this power is the purity of the logical process by which mathematics is built.
		A direct proof consists of an initial statement connected to a statement to be proven by a finite number of intermediate statements, P
	math.usask.ca /emr/dirp.html (615 words)

	Theism, Atheism, and Logic
		In modern times most of the answers come in the form of logical “proofs” or “disproof” of the existence of God; however, these logical arguments often reduce to an assumption or some other logical flaw.
		Perhaps the ultimate proof of the existence of God is the existence of miracles.
		Before analyzing the logical flaws of these arguments a review of his history of logic might be in order.
	www.geocities.com /williamiv.geo/Stories/Logicv3.htm (5863 words)

	Citations: Tactic theorem proving with refinement-tree proofs and metavariables - Felty, Howe (ResearchIndex)
		In, proof trees are represented in a logical theory where justifications of proof steps can be representations of tactics.
		Another approach is to design a new logic programming language for the specific purpose of meta programming in the ground representation, with a specialized semantics for dealing with unification....
		we want to reuse successful proof plans, but we believe that, by learning the patterns of occurrences for each tactic by understanding its use in each step of a set of proofs, we can produce more flexible tools (the methods) which can be combined in efficient proof search strategies.
	citeseer.ist.psu.edu /context/59617/225515 (1268 words)

	Belief and the 'proofs' of god
		The logical outcome of believing the New Testament claims regarding Jesus and his birth is simply this - Mary is indeed the Mother of God, and ipso facto herself divine.
		And the traditional 'proofs' of the Christian god (please note carefully I did not say 'GOD'), a favourite subject in older theological treatises, turn upon the logical necessity of such a Being existing, or so we are assured, under four main heads - on teleological, ontological, cosmological, and moral.
		For the logical proofs represent the highest endeavour of what is termed natural theology to explain the universe.
	www.felicity.com.au /paper-proofs.htm (7075 words)

	Boise Bahá'í Faith: Session 8: Proofs
		Christianity was spread before the conversion of Constantine the Great and the assistance of the Caesars and so was not dependent upon their assistance, likewise, were it not for the Word of God, the armies would have been enlisted by the ranks of the "infidels", hence would have opposed the Manifestations.
		It is not a proof to those who did not witness the event for over the passing of time it becomes a belief which can be disputed.
		There are two aspects to this: the revelation of prophecies concerning the next Manifestation is itself a proof of being a Manifestation, for those individuals who are not do not think to reaffirm the continuity of the Divine Plan.
	bci.org /boise/session8.htm (3153 words)

	Abstract of E.A.Hirsch's talk (Site not responding. Last check: 2007-10-15)
		Nevertheless, it is a very important problem, because it is closely related to the celebrated P vs NP question (one of the seven questions for which Clay Mathematics Institute offers a $1,000,000 prize).
		Naturally, no such fact is proved for any of the known proof systems, though for some of them negative results (exponential lower bounds) are known.
		During the past decade, not only "pure logical" proof systems attracted researchers, but also (and mainly) other systems, e.g., "algebraic" systems (which work with polynomials instead of logical formulas).
	logic.pdmi.ras.ru /GeneralSeminar/abstr/042.html (166 words)

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