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	Dallas Willard ARTICLES
		Issues of "logic and experience" became issues of "logic and language." The distance between "a formalized language" and "ordinary discourse" was emphasized (or deemphasized), and attempts were made to treat the laws of logic as (somehow) laws of language use--of what we could or could not say.
		The laws of formal logic are laws expressing the necessary truth values of propositions, insofar as those truth values are determined merely by the forms of the propositions involved.
		This theory is realist or absolutist because, according to it, the laws of logic do not in any way depend for their meaning or truth upon any mental fact, and especially upon how a particular individual, culture or species may or may not actually think about anything.
	www.dwillard.org /articles/artview.asp?artID=89 (6882 words)

	The Christian Worldview, the Atheist Worldview, and Logic. (Site not responding. Last check: 2007-11-05)
		Law of Non-Contradiction: Something cannot be its self and not itself at the same time in the same way and in the same sense.
		Though one could say that a law of physics (i.e., the angle of reflection is equal to the angle of incidence) is a statement which is conceptual, it is a statement that describes actual physical and observable behavior.
		If the atheist appeals to the scientific method to explain the laws of logic then he is using circular argumentation because the scientific method is dependent upon logic; that is, reasoned thought applied to observations.
	www.carm.org /atheism/logic.htm (1001 words)

	truth in logic
		The first is that the laws of logic are generalized, empirical truths about how things in the world behave, like the laws of science, but more abstract.
		Logics that aim to represent situations in simple, context-free sentences are called sentential (also propositional, or propositional calculus), after Gottlob Frege who founded modern mathematical logic.
		Logic was too narrow, arid and mechanical to properly represent human thought processes.
	www.poetrymagic.co.uk /literary-theory/truth-in-logic.html (921 words)

	The Nature and Necessity of Logic
		While the depreciations or denunciations of logic vary in the range of topics that are allegedly exempt from logic, or the intensity in which logic is down-played or simply denied, the above individuals have in common the concept of limiting the applicability, extent, or scope of the jurisdiction of logic/reason.
		To deny logic or say that it is false or not true or applicable to a certain topic entails the use of logic in the very assertion itself (thus, it is true or applicable).
		The fourth primary law of logic is the law of logical or rational inference.
	apologeticsinfo.org /papers/naturenecessity.html (3949 words)

	Review of "Logic" by Gordon Clark (Site not responding. Last check: 2007-11-05)
		Also fixed in Scripture are the two other principle laws of logic: the law of identity (A is A), and the law of the excluded middle (A is either B or non-B).
		In other words, it is not the laws of logic that are affected by the Fall, it is man’s ability to think logically that is so affected.
		As we have seen, the laws of logic are eternally fixed in the mind of God.
	www.fpcr.org /blue_banner_articles/ReviewClarkLogic.htm (1295 words)

	[L01] Logic - What is Logic? (Site not responding. Last check: 2007-11-05)
		The laws of biology might be true only of living creatures, and the laws of economics are only applicable to collections of agents that enagage in financial transactions.
		A second feature of the principles of logic is that they are non-contingent, in the sense that they do not depend on any particular accidental features of the world.
		The principles of logic, on the other hand, are derived using reasoning only, and their validity does not depend on any contingent features of the world.
	philosophy.hku.hk /think/logic/whatislogic.php (1256 words)

	The Bible, Logic, and the Postmodern Predicament
		Thus, logic is the study of the laws or principles of thought or reason, not just mere thought or thinking per se, but of the type of thought or thinking we term reasoning.
		These four primary laws of logic are the essence of logic and are vital to all coherent or intelligible discussions or arguments.
		The laws of logic are not a speculative prejudice imposed at a given moment of history as a transient philosophical development.
	www.apologeticsinfo.org /papers/logicpostmodern.html (4960 words)

	Westminster Confession and Logic, W. Gary Crampton (Site not responding. Last check: 2007-11-05)
		The laws of logic, of valid inference, which are applicable under the boundary do not have any application with regard to God.
		“Logic, the law of contradiction, is not affected by sin.
		As we have seen, the laws of logic are eternally fixed in the mind of God, and they cannot be affected; they are eternally valid.
	www.fpcr.org /blue_banner_articles/WCF_Logic.htm (2615 words)

	Gnostic Christianity.com. The outlawed logic/logos teachings of Jesus.
		Laws of logic are at work in our everyday lives on a scale that dwarfs the effects of even laws of mathematics.
		In the everyday world, the law of diversity would cleanse the heart and mind of prejudicial reasoning, because it teaches us that prejudice is the consequence of reasoning according to the law of identity, when it is appropriate to use the law of diversity.
		The law of complementarity would make it explicit that when classes are made up of members who are different, yet are members of the same class, it would be logically incorrect to assert that this class has either one nature or another.
	www.gnosticchristianity.com /ch7.htm (8269 words)

	INTRODUCTION
		Logic is the study of the relation between premises and conclusion in Deductive Arguments.
		Moreover, the laws stand together as a trinity; to fault one, is to fault all, and to uphold one, upholds the others.
		Three reasons for the study of logic are (1) correct thinking requires it; (2) discerning minds necessarily depend on it; and (3) man is a rational being in the image of his Creator.
	www2.sjsu.edu /logic/intro.htm (983 words)

	Fourth Law of Logic
		A simple derivation of a fourth law is shown and an application rule given which itself may be regarded as a fifth law of logic.
		Laws 1, 2, and 3 are the laws of explicit monocular perception, with implicit binocular perception.
		Law four is the law of explicit binocular perception, with implicit monocular perception.
	www.cheniere.org /books/aids/appendixIII.htm (3209 words)

	Frequently Asked Questions about Logic
		Logic is within the reach of ordinary people - Dads and Moms, and their children too.
		Many Homeschooling parents are teaching logic to their children right now, and though they are finding it is a challenge, they are taking a big step in the right direction.
		Augustine explained that logic is not an invention of pagan philosophers, as some men objected, but a science which man has learned from God.
	www.christianlogic.com /articles/logic_faq.htm (1431 words)

	Philosophy \| University of Northern Colorado - The Laws of Logic
		But to address the heart of your question, while a great many systems of predicate logic do include all three of the laws you’ve mentioned among their theorems even if not as axioms, there are also systems that don’t include them all, either as axioms or as theorems.
		The man from whom I first learned logic when I was myself in school, Frederic Brenton Fitch, favored systems in which it was impossible to derive the law of excluded middle, this being his preferred way of avoiding the implications of the famous Russell paradox.
		It seems that there are three so-called "laws of logic" that are touted as being fundamental to logic itself.
	www.unco.edu /philosophy/current/forums/topic.asp?TOPIC_ID=151 (370 words)

	The Seven Truths Of Fuzzy Logic
		This wide-spread belief comes in two flavors, the first holds that fuzzy logic violates common sense and the well proven laws of logic, and the second, perhaps inspired by its name, holds that fuzzy systems produce answers that are somehow ad-hoc, fuzzy, or vague.
		The feeling persists that fuzzy logic systems somehow, through their handling of imprecise and approximate concepts, produce results that are approximations of the answer we would get if we had access to a model that worked on hard facts and crisp information.
		Much of the discomfort with fuzzy logic stems from the implicit assumption that a single ``right'' logical system exists and to the degree that another system deviates from this right and correct logic it is in error.
	www.bytecraft.com /fuzzylogictruths.html (1133 words)

	Aristotle's Logic (Stanford Encyclopedia of Philosophy)
		Modern modal logic treats necessity and possibility as interdefinable: "necessarily P" is equivalent to "not possibly not P", and "possibly P" to "not necessarily not P".
		The difference, he tells us, is in the character of their premises, not in their logical structure: whether an argument is a sullogismos is only a matter of whether its conclusion results of necessity from its premises.
		Aristotle's Modal Logic: Essence and Entailment in the Organon.
	plato.stanford.edu /entries/aristotle-logic (11058 words)

	[No title]
		But from our first alternative (God creating the laws of logic), it should follow that God is superior to the boundaries of a system that he alone created.
		Logic is neither something more divine than God, nor something expressly created by God, but rather a function of God’s nature.
		This is exactly the same conclusion for the boundaries of logic and reason: logic is not some higher power that even God is accountable to, nor is it some body of rules that God has created and thus superior to.
	www.angelfire.com /mi/logos/logicpaper.html (582 words)

	The Tree of Logic
		Logic also has many branches, all under the big heading of “logic.” The branches on the tree of logic cast a broad shadow.
		Informal logic is the practical side of the coin and consists of methods for analyzing verbal arguments to see if they really prove their point.
		Some parts are fun, such as logical fallacies, while others, such as the higher reaches of modern symbolic logic, were invented for geeks to enjoy in blissful solitude.
	www.christianlogic.com /articles/subject_of_logic.htm (1166 words)

	Logic and Meaning
		The second law of logic is the law of non-contradiction.
		The third law is the law of the excluded middle.
		It violates the law of identity and the law of identity precedes the law of the excluded middle.
	rous.redbarn.org /objectivism/Writing/JoelKatz/logic.html (3983 words)

	Quotes about Laws
		Every man, as long as he does not violate the laws of justice, is left perfectly free to pursue his own interest his own way, and to bring both his industry and capital into competition with those of any other man or order of men.
		Laws are always unstable unless they are founded on the manners of a nation; and manners are the only durable and resisting power in a people.
		It is evident, then, that the proper purpose of law is to use the power of its collective force to stop this fatal tendency to plunder instead of to work.
	www.zaadz.com /quotes/topics/laws (461 words)

	Ayer on Laws
		The restriction lies not upon the events themselves but on our method of describing them… What is describable as an event obeys the laws of logic: and what is not describable as an event is not an event at all.
		This is the crux of the reply to the conventionalist claim: we need empirical content for anything remotely resembling science, but the laws of logic have no empirical content and in part receive their necessity because of this lack of empirical content.
		Problems arise because there are laws, which we want to count as laws of nature, which have vacuous antecedents such as “a body on which no forces are acting continues at rest or in uniform motion along a straight line.” (Curd 1998 pg.
	ucsub.colorado.edu /~hafere/PHIL1400/Ayer.htm (1207 words)

	Why Study Logic?
		The study of logical fallacies (common mistakes in reasoning) is important to critically reason through the arguments of others.
		The laws of logic, in one way or another, are fundamental to every academic discipline.
		Unfortunately, the study of logic is dispensed with in the modern curriculum.
	www.triviumpursuit.com /articles/why_study_logic.php (321 words)

	Logic
		We rarely have to travel far in philosophical territory to hear talk of the “laws of logic”, often accompanied by a suggestion that rejecting them is tantamount to insanity.
		The law of non-contradiction is discarded by dialethic logic (from di and alethic, meaning “two truths”), or dialetheism.
		The value of logic in philosophy (or philosophical logic, to be more accurate) is thus quite plain: we can use it to take arguments apart and study their structure in more detail than a cursory glance would otherwise allow.
	www.galilean-library.org /int4.html (2739 words)

	The Math Forum - Math Library - Logic/Foundations (Site not responding. Last check: 2007-11-05)
		Arché: Centre for the Philosophy of Logic, Language, Mathematics and Mind - Crispin Wright, Director; University of St. Andrews, U.K. Arché is a new research centre within the School of Philosophical and Anthropological Studies, St Andrews.
		Aristotle and the Paradoxes of Logic - Gilbert Voeten
		The Association for Symbolic Logic (ASL) is an international organization supporting the presentation, publication, and critical discussion of scholarly work in the field of logic.
	mathforum.org /library/topics/logic (2213 words)

	AskPhilosophers.org
		It's tempting to say that one can't justify anything without using the laws of logic, but that is arguably too strong.
		I think my belief that there is a computer in front of me is justified by my perception of it, and I doubt that the laws of logic have to be invoked there.
		Moreover, it is not obvious that the laws of deductive logic have always to be invoked even when justification is somehow "inferential".
	www.amherst.edu /askphilosophers/question/442 (507 words)

	Aristotle and the Paradoxes of Logic
		A paradox however is only due to a striking violation of at least one of Aristotle's laws of logic.
		The barber is not aware that his claim violates both the laws of noncontradiction and identity.
		And that is a violation of the law of the excluded middle.
	www.homestead.com /nilog/files/aristotle_and_the_paradoxes_of_l.htm (1985 words)

	Why The Laws of Thought Are, After All, the Laws of (Evolutionary) Logic by William D. Casebeer [The Evolution of ...
		Why The Laws of Thought Are, After All, the Laws of (Evolutionary) Logic by William D. Casebeer [The Evolution of Reason: Logic as a Branch of Biology by William S. Cooper]
		William Cooper’s The Evolution of Reason: Logic as a Branch of Biology is a fascinating contribution to evolutionary epistemology, and as such, it focuses primarily on the last two fields, with the emphasis on reasoning classically construedas computation across representations, where the computational structure takes canonically rational form.
		Critics may not be persuaded, but we should not let their demands for a priori discussion of the conceptual distinctions between facts and norms put a stop to what may prove to be an extremely fruitful line of inquiry (it’s where I’m placing my bets).
	human-nature.com /nibbs/03/cooper.html (989 words)

	About "Aristotle and the Paradoxes of Logic" (Site not responding. Last check: 2007-11-05)
		In section 1 a more adequate form is given to Aristotle's laws and several hitherto neglected operators in Boolean logic are introduced.
		Section 2 shows how easily logical paradoxes can be eliminated if one takes Aristotle's laws of logic into account.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/view/10691.html (111 words)

	Concept Script: Frege
		Frege's attempt to set up the natural numbers in logic is based on what he calls his definition of a sequence -- this is his main application of his logic to mathematics.
		In particular Schröder thought Boole's logical system was far superior -- Boole used the arithmetic notation for plus and times, and had marvelled at how much the laws of logic were like the laws of arithmetic.
		His final theorem in Fundamental Laws II is a proof of the commutative law for addition for so called positive classes (which are defined to be classes having several of the properties of the positive reals).
	www.math.uwaterloo.ca /~snburris/htdocs/scav/frege/frege.html (1883 words)

	Grounds of Validity of the Laws of Logic
		It will be said that my deduction of logical principles, being itself an argument, depends for its whole virtue upon the truth of the very principles in question; so that whatever my proof may be, it must take for granted the very things to be proved.
		These propositions are both true, and the law of contradiction is not violated which asserts only that nothing has contradictory predicates: only, it follows from these propositions that the man will not deliberately overturn his inkstand.
		This would serve as a complete establishment of private logicality, were it not that the assumption, that man or the community (which may be wider than man) shall ever arrive at a state of information greater than some definite finite information, is entirely unsupported by reasons.
	www.peirce.org /writings/p41.html (10428 words)

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