what are inductive and deductive claims? How does "all, none or some" impact the assertions of argument?
596800
Guess you just have to use the right word at the right time!
324840
Well, the basic problem you've run into is that the conjecture isn't true.  If a = 6, b = 3, and c = 9, then a*b = 18, and 18/9 = 2, but neither 6 nor 3 is divisible by 9.\n\nTo prove that something is true you must prove it is true for all possible values of the variables, in this case a, b, and c.  However, to prove something is false, you need only supply a single counter-example.  Thus the above example disproves the conjecture that for all integers a, b, and c if a*b is divisible by c then a or b is also divisible by c.\n\nNote that a ≠ cm and b ≠ cn does not imply that ab ≠ c(cmn).  For example, if a = 6, b = 8, c = 2, m = 4, and n = 3, then cm = 2*3 = 8 ≠6 so cm ≠ a, and cn = 2 * 3 = 6 ≠ 8 so cn ≠ b.  However, (cm)(cn) = 2 * 4 * 2 * 3 = 48, and a * b = 6 * 8 = 48, so ab = (cm)(cn).  This proves that you cannot multiply not-equalities (i.e. statements with "doesn't equal).\n\nAlso, concluding that if c does not divide a or b implies that c does not divide ab is not the same as concluding that if c does divide ab it must also divide a or b.  This logical fallacy is equivalent to the statement that for all plants, not a tree implies not a rock, so being a rock implies being a tree.  The first statement is true: all plants that are not trees are also not rocks.  However, the second statement is clearly false, as no rocks are also trees.
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I can't help you justify generalizations, however, I can type about use of it in logic.  \n\nFallacies:\n\n1.)  Accident:  When one applies a generalization to an individual case that it does not properly govern. \n\n2.)  Converse Accident:   When one moves carelessly or too quickly from a single case to an indefensibly broad generalizaiton.\n\nAssumptions:\n\n1.)  An assumption is an induction.  Its like assuming the sun will rise tomorrow.  We assume its going to happen because it has for millions of years.   \n\n2.) The bad thing about assumption is that you are using probabilities to create a conclusion.
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Well, I'm not sure about a workshop. However, there is a great book called Being Logical: A guide to good thinking by D.Q. McInerny. It's only a 129 pages, but they are power packed.\n\n Here is a review:\n"Highly readable...D.Q. McInerny offers an introduction to symbolic logic in plain English, so you can finally be clear on what is deductive reasoning and what is inductive. And you'll see how deductive arguments are constructed."\n- Detroit Free Press
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The statement (which you refer to as a claim) is flawed for the reasons you gave. Your rebuttal was excellently worded, and was logical. But, there is a major flaw with your rebuttal : the people who make the claim are not logical people. The only people who can understand your rebuttal are logical. You will spend your energy preaching to the choir, because the people who make the original claim will not stay and listen to you. It was really nice to read a well-stated post.
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i believe what you mean are "existential" and "universal" claims. the word existential refers to words such as some, many, few, or any other word which implies the existence of another set which does not contain members for which the "some..." statement is referring to. a universal statement includes the other group of words including all, none, every, etc which do not imply the existence of a group without the attribute referred to by the statement containing the all, every, etc.\n\nthe problem with universal statements involves a "universal generalization" about an entire set based on the existence of a few members which meet the criterion. example. "my dog is red, joes dog is red too, therefore all dogs are red."\n\nthe problem with the existential statements involve "existential instantiation" let me give you an example. "some dogs are red, i have a dog, therefore he is red". "if it rains the sidewalk is wet. the sidewalk is wet so therefore it rained." you see the problem with this line of reasoning\n\nin short \ndont conclude "all a is b" based on "a0 is b"\ndont conclude "a0 is b" based on "some a is b"
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Inductive reasoning is the process of arriving at a conclusion based on a set of observations. \n  In itself, it is not a valid method of proof. Just because a person observes a number of situations in which a pattern exists doesn't mean that that pattern is true for all situations. \n   For example, after seeing many people outside walking their dogs, one may observe that every dog that is a poodle is being walked by an elderly person. The person observing this pattern could inductively reason that poodles are owned exclusively by elderly people. This is by no means a method of proof for such a suspicion; in fact, in the real world it is a means by which people and things are stereotyped.\n  A hypothesis based on inductive reasoning, can, however, lead to a more careful study of a situation. \n  By inductive reasoning, in the example above, a viewer has formed a hypothesis that poodles are owned exclusively by elderly people. The observer could then conduct a more formal study based on this hypothesis and conclude that his hypothesis was either right, wrong, or only partially wrong.
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All reasoned arguments rely on axioms, i.e. things which we take to be true, but which are not amenable to proof. The most obvious example of an axiom is the validity of reason itself - It is trivially obvious that we can't use a reasoned argument to prove that reason is valid, because we have to presume that reason is valid in order to make any kind of reasoned argument.\n\nI have another axiom, which I'm sure no sane person would dispute: That the order and complexity that we see around us in the natural universe, and particularly in the intricate structure and functions of living organisms, could not possibly just exist fully formed, with no cause, no origin, no precursor of any sort. I can't *prove* that this is the case, but it seems inconceivable to me that anyone would dispute it.\n\nSo, the logical consequence of accepting this axiom is that, for the very same reason, it's not possible that the order and complexity of the universe is sourced in an intelligent deity who designed and made the universe and *himself* exists fully formed with no cause, no origin, no precursor of any sort. I don't think any reasonable person would dispute the axiom presented here, and acceptance of the axiom leads to an indisputable proof of the non-existence of an intelligent creator.\n\nAnyone who (against all reason) asserted that the order and complexity we see in the universe *could* indeed exist fully formed with no cause and no origin, in order thereby to save the concept of an uncaused intelligent designer, would find that they had invalidated said designer by making him redundant - i.e. if the order and complexity of the universe could just exist fully formed and uncaused then it would not need (in fact, could not possibly have) a designer to cause it to exist.\n\nEither way, the concept of a creator is invalidated.\n\nLuke:  I can't see how a perception of chaos would mean the existence of a god, according to my axiom.  Even if someone rejects the notion that the universe exhibits (at least in parts) a high degree of order and complexity, it does not follow that a god is required to create it - Indeed, if the universe is nothing but chaos, then there doesn't seem to be any motivation to suggest a designer in the first place.  How can you design chaos?  Chaos is, by its very definition, the complete absence of any kind of order or complexity or design.\n\nAs to your second point, if someone is proposing that intelligence is required to design and create a universe, then the intelligence itself would be the 'form' that has to exist without any kind of origin or development or precursor.  Religious folks have enough trouble accepting the idea of mere *human* intelligence being the product of an unthinking natural process, so to argue that an intelligence capable of designing and creating an entire universe can exist without any precursor at all, not even an unthinking one, is self-contradictory in the highest degree.
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Facts are proven. They would not be facts had they not been. So if facts have been disproven, then they are no longer facts. They could have been theories. Or perhaps opinions. Facts are proven. So facts are facts until something better comes along which disproves them. ;) lol
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Deduction starts with general principles and moves to specific conclusions.  Induction starts with specific observations and moves to general principles.\n\nHere's a link that may help.\n\nhttp://www.socialresearchmethods.net/kb/dedind.htm
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Here's an example of inductive reasoning:\nWe observe gravity pulling objects together everywhere in the visible universe. We induce that gravity behaves the same in the entire universe, even in the parts we can't see.\n\nDeductive:\nI know Dana is taller than Chris, and Chris is taller than Jo. I deduce that Dana is taller than Jo.
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:}  No one can know anything for a fact beyond any doubt..\n\nEven our very senses fool us. There are dreams and mirages. We’ve all thought we heard saw or smelled something that was inaccurate.\n\nThoreau in Walden Pond, Presented the idea that we could know that we exist because if we did not we could not question whether we did or not.\n\nHaving established that nothing, beyond perhaps our own existence, can be established with absolute certainty, we must proceed to behave as if those things for which there is significant evidence, in fact exist and work as the evidence would suggest they do.\n\nWhile this procedure at times will lead to error, for the most part it is necessary to pursue this line of reasoning, called inductive logic, if we are to conduct normal life functions.\n\nIs there a god?  I use the same process. So for my purposes Yes, as far as my data goes in allowing  me to analyze the information, the preponderance of evidence suggest that God is a certain fact.  \n\nThen using the scientific method it simply remains to see if the predictions I make based on this hypothesis come to be\n\nAnd they have.\n\nI'm 100% sure \n\n\n\nOne additional fact \nMy salvation depends less on my faith than on his faithfulness!
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this is my humble understanding,Ok, what I understand from the Relevancy; collateral matters. there must be an evidence such a relativity to the fact in issue as to persuade belief in its being or absence. Evidence on collateral matters shall not be permissible, except for when it tends to be any reasonable degree to establish the probability or improbability of the fact in issue.
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I had a professor who was always very adamant that you could not prove the hypothesis. Something about you don't actually test the hypothesis, you test the question....or somehting. He was very odd. I think there's a difference between a hypothesis and fact.
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Unsound arguments can be based on incorrect assumptions or on "facts" that prove to be incorrect.  An invalid argument is one that is internally flawed.  An argument can be either or both.  It is possible to build a valid argument that is utterly incorrect or to build an unsound argument that is internally valid.  Goal is for it to be both sound and valid.
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it is impossible to prove a negative.  One cannot prove the non-existance of god just as they could not prove the non-existance of WMD's in Iraq.  The lack of evidence against something in both cases is not evidence of it's existance.
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To begin with we need to look at the question and the language used to ask for answers. First is "logic". A simple definition is provided by Wikipedia which states:\n\n"Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. However the subject is grounded, the task of the logician is the same: to advance an account of valid and fallacious inference to allow one to distinguish good from bad arguments.\n\nTraditionally, logic is studied as a branch of philosophy. Since the mid-nineteenth century logic has been commonly studied in mathematics, and, even more recently, in computer science. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialist analyses of reasoning such as probably correct reasoning and arguments involving causality."\n\nSecond, we must look at the word "truth". It is important to note that the word is not capitalized so we can avoid metaphysical theory or definitions based on cultist beliefs, such as christianity or other god-dependent or deity dependent definitions. The Internet Encyclopedia of Philosophy is quoted as proposing that truth is:\n\nA preliminary issue, although somewhat subsidiary, is to decide what sorts of things can be true. Is truth a property of sentences (which are linguistic entities in some language or other), or is truth a property of propositions (nonlinguistic, abstract and timeless entities)? The principal issue is: What is truth? It is the problem of being clear about what you are saying when you say some claim or other is true. The most important theories of truth are the Correspondence Theory, the Semantic Theory, the Deflationary Theory, the Coherence Theory, and the Pragmatic Theory. Whichever theory of truth is advanced to settle the principal issue, there are a number of additional issues to be addressed: \n     1. Can claims about the future be true now? \n     2. Can there be some algorithm for finding truth –        some recipe or procedure for deciding, for any claim in the system of, say, arithmetic, whether the claim is true? \n     3. Can the predicate "is true" be completely defined in other terms so that it can be eliminated, without loss of meaning, from any context in which it occurs? \n     4. To what extent do theories of truth avoid paradox? \n     5. Is the goal of scientific research to achieve truth? \n\nLogic is one form of epistemological approach to ascertaining knowledge. It is the "how we know what we know and the limitations of that knowledge". Logic is a tool for explanation of the ideas, observations, and experiences. It could also be said that logic is sometimes used poorly to acertain truth. Most clearly in areas of theology. Logical fallacies and faulty logic come most readily to mind. But that is another question for another time.