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Philosophy discuss Deduction/Induction in the Apologetics Forum forums; Could someone please give me a really simple example of the difference between deductive and inductive reasoning? Thank you....

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    Poimen's Avatar
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    Deduction/Induction

    Could someone please give me a really simple example of the difference between deductive and inductive reasoning?

    Thank you.
    Rev. Daniel Kok
    Pastor of the Reformed Presbyterian Church of Calgary
    Calgary, Alberta CANADA

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    InChains620 is offline. Inactive User
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    I found a great site with simple examples to help you with your question:
    Here
    I hope this helps you. I found it helpful.
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    Quote Originally Posted by InChains620 View Post
    I found a great site with simple examples to help you with your question:
    Here
    I hope this helps you. I found it helpful.
    Excellent! Thank you Alex.
    Rev. Daniel Kok
    Pastor of the Reformed Presbyterian Church of Calgary
    Calgary, Alberta CANADA

    "What sort of pledge and how great is this of love towards us! Christ lives for us not for himself!"
    John Calvin, Commentary on the Hebrews (7:25)

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    Not a problem, I just joined the site. Glad I could be of some benefit, I hope it answers your questions.
    "I have sinned against the LORD......The LORD has taken away your sin. You are not going to die."
    -2 Samuel 12:13

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    I was going to post a nice detailed explanation, but the Nathaniel Bluedorn does a much better job than I would have. I also recommend their books. They are written for kids, but adults need help with logic too. You let your kids read these books without you and they are going to be teaching you a thing or two.

    I'm one of the moderators on the Christian Logic Forum. But don't let that deter you.
    R. Anthony Coletti
    Midway Presbyterian Church (PCA)
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    MW
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    The important thing to remember is that the terms relate to formal logic. In reality there is no genuine distinction between deduction and induction. Looking at the referenced article, the two examples result in probability or certainty because the author has chosen to represent his arguments in specific ways. In reality the deductive argument depends upon the certainty of its premises. Hence the deductive argument does not lead to any more certainty than an inductive argument.
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
    Victoria, Australia

    "Illum oportet crescere me autem minui."

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    In reality there is a genuine distinction between induction and deduction. Looking at the referenced article we see:
    Comparing these two types of reasoning: inductive reasoning starts with many pieces of evidence and comes up with a probable conclusion, while deductive reasoning begins with a few trustworthy statements and ends with a necessary conclusion.

    Logic Comes in Two Flavors
    The distinction is internal to the argument form. Argument forms are really real.

    A deductive argument:

    Premise 1: All cows have utters.
    Premise 2: Betsy is a cow.

    Conclusion: It is necessarily true that Betsy has utters.

    An inductive argument:

    Premise: All the crows I have ever witnessed are black.
    Conclusion: Therefore, all crows are probably black.

    This clear distinction (probable conclusion verses necessary conclusion) is the key between the two forms of argument. Whether the premises are reliable true does not effect the form of the argument. The premises could be entirely false and this will not remove the distinction. And this is speaking from the perspective of "reality".

    What Nathaniel Bluedorn has shown is how beneficial inductive reasoning is. Inductive reasoning, when it limits it's claim to probabilities is still very useful and even necessary. We use induction when analyzing the Bible all the time. And we use induction is indispensable for daily life. But this does not mean we are to confuse induction with deduction.

    It is also important to note that the "formal" in logic, while abstract is also very real. To say otherwise would lead to the strange assertion that 2 + 2 does not "really" equal 4.
    R. Anthony Coletti
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    smhbbag is offline. Puritanboard Senior
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    The important thing to remember is that the terms relate to formal logic. In reality there is no genuine distinction between deduction and induction.
    There is quite a big and important distinction.

    Looking at the referenced article, the two examples result in probability or certainty because the author has chosen to represent his arguments in specific ways. In reality the deductive argument depends upon the certainty of its premises. Hence the deductive argument does not lead to any more certainty than an inductive argument.
    Of course both types of argumentation depend on the accuracy of the premises. That is not the issue.

    The distinction comes in that, if we grant all the premises, does the conclusion follow with certainty? With deductive reasoning, it does. With inductive, it does not.

    If someone comes at me with an inductive argument, I can respond: "Well, I grant all your premises, and that you formulated your argument well....but you're still wrong and here's why."

    If they come at me with a deductive argument, no such option exists, because if the premises are true, and the formulation valid, then the conclusion is certain.

    So as far as:
    In reality the deductive argument depends upon the certainty of its premises.
    Nobody ever denied that.
    Jeremy
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    Quote Originally Posted by smhbbag View Post
    ...
    If someone comes at me with an inductive argument, I can respond: "Well, I grant all your premises, and that you formulated your argument well....but you're still wrong and here's why."
    ...
    I'd be careful not to say they were wrong, only that their conclusion is not necessarily true. It is possible they are right as inductive arguments are always possible right.

    But if someone give a valid deductive arguments, and you agree with his premises, then his conclusion is undeniable. It must be right if his argument is formally valid. That's the beauty of deductive logic - we can actually determine truth when we apply it to truth premises. This is why the Westminster Confession of Faith extends knowledge beyond just the actual propositions of Scripture and includes those things the follow by "good and necessary consequence".

    WCF 1:6 The whole counsel of God, concerning all things necessary for His own glory, manís salvation, faith, and life, is either expressly set down in Scripture, or by good and necessary consequence may be deduced from Scripture: unto which nothing at any time is to be added, whether by new revelations of the Spirit, or traditions of men (Gal_1:8, Gal_1:9; 2Th_2:2; 2Ti_3:15-17).

    (emphasis added)
    R. Anthony Coletti
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    MW
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    That's right, the distinction is internal to the "argument form." But everyone knows the argument form is external to the facts. Deductive argument: All cows have udders; Betsy is a cow; Betsy has udders -- depends upon the inductive argument: All cows I have ever witnessed have udders; therefore, all cows probably have udders. Likewise the inductive argument -- All the crows I have ever witnessed are black; therefore, all crows are probably black -- can be made a deductive argument with a slip of the quill: All crows are black; Jackson is a crow; therefore Jackson is black. Logic is woopy doop!
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
    Victoria, Australia

    "Illum oportet crescere me autem minui."

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    That's right, the distinction is internal to the "argument form." But everyone knows the argument form is external to the facts. Deductive argument: All cows have udders; Betsy is a cow; Betsy has udders -- depends upon the inductive argument: All cows I have ever witnessed have udders; therefore, all cows probably have udders.
    No, it does not depend on that inductive argument.

    "All cows have udders" is not a conclusion from previous induction, but simply part of a definition, which is used as a premise. You can argue whether it's a good or bad definition, but it remains just that.

    Likewise the inductive argument -- All the crows I have ever witnessed are black; therefore, all crows are probably black -- can be made a deductive argument with a slip of the quill: All crows are black; Jackson is a crow; therefore Jackson is black. Logic is woopy doop!
    What was the point in this example?

    That argument can be "made" deductive with the slip of the quill.....so what?

    When changed, even slightly, into a deductive argument, it's entire nature and substance is altered radically. Because changing it didn't take much ink, that means it's not very different?

    Yes, there's only a "slip of the quill" difference between 'can' and 'can't' - but they still mean very different things.
    Last edited by smhbbag; 04-25-2007 at 09:38 AM. Reason: a
    Jeremy
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    Quote Originally Posted by armourbearer View Post
    That's right, the distinction is internal to the "argument form." But everyone knows the argument form is external to the facts. Deductive argument: All cows have udders; Betsy is a cow; Betsy has udders -- depends upon the inductive argument: All cows I have ever witnessed have udders; therefore, all cows probably have udders.
    The premise for all cows have udders depends only on the definition of cows. It doesn't follow from observing cows. An animal without utters is not a cow by definition.

    Quote Originally Posted by armourbearer View Post
    Likewise the inductive argument -- All the crows I have ever witnessed are black; therefore, all crows are probably black -- can be made a deductive argument with a slip of the quill: All crows are black; Jackson is a crow; therefore Jackson is black.
    Your "slip of the quill" changed an inconclusive premise into a universal statement that does not follow. To say "all crow are black" means each and every crow is black. And this does not follow from a the particular "All the crows I have ever witnessed are black".

    Some (A is B)
    does not imply
    All (A is B)

    And in fact, not all crows are black.

    Quote Originally Posted by armourbearer View Post
    Logic is woopy doop!
    I hope you don't mind if I quote you on that.
    R. Anthony Coletti
    Midway Presbyterian Church (PCA)
    Jonesborough, TN
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    Quote Originally Posted by Civbert View Post

    I'm one of the moderators on the Christian Logic Forum.

    Christians and logic?

    Now there's something desperately needed.

    I think our understanding of Theology, as a whole, would be greatly increased simply by having a grasp (collectively)of logic.
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    Quote Originally Posted by Jerusalem Blade View Post
    Here in Cyprus the crows are black and grey.
    I am reminded of Shakespeare:

    Lawn as white as driven snow,
    Cyprus black as e'er was crow,
    Gloves as sweet as damask roses,
    Masks for faces and for noses,
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    For my lads to give their dears,
    Pins and poking-sticks of steel,
    What maids lack from head to heel.
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    Welcome to Cyprus.
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    MW
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    Yes, there is a distinction so far as formal logic is concerned -- that has already been accepted; but formal logic is a rhetorical not a rational tool. It is simply an argumentative device. I inverted the two examples to show that the logical structure is not tied to the facts, but to the manner in which the person wishes to present their case. A deductive argument does not yield any more real certainty than an inductive argument because its premises depend upon induction even though its structure does not.

    The responses I received show this is the case. smhbbag says, "You can argue whether it's a good or bad definition, but it remains just that." Hence he acknowledges deductive arguments do not produce certainty because they depend upon the truthfulness of the premises. Civbert says, "To say 'all crow are black' means each and every crow is black. And this does not follow from a the particular 'All the crows I have ever witnessed are black.' Hence he shows that particulars are made a universal in the first premise of the deductive argument.
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
    Victoria, Australia

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    smhbbag is offline. Puritanboard Senior
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    A deductive argument does not yield any more real certainty than an inductive argument because its premises depend upon induction even though its structure does not.
    This has already been addressed. Deductive arguments do not ultimately rest upon induction, in most cases. Definitions are not inductive arguments.

    The argument:

    P1: All cows have udders.
    P2: Betsy is a cow
    C1: Betsy has udders.

    Does not, in any way at all, even remotely rely on induction.

    Hence he acknowledges deductive arguments do not produce certainty because they depend upon the truthfulness of the premises.
    No one here has questioned that deductive arguments only produce certain conclusions when the premises are certainly true.

    Yes, I acknowledge that, and already explicitly said so, when I said "Of course both types of argumentation depend on the accuracy of the premises." Is that unclear somehow?

    The mammoth difference is that if you have 100% certainty of the premises in an inductive argument....your conclusion may still be false.

    If you have 100% certainty of the premises in a deductive argument, your conclusion cannot be false.

    A deductive argument does not yield any more real certainty than an inductive argument
    Yes, it does. If I have certainty in my premises, my conclusion from valid deductive argumentation is 100% guaranteed to be true. If I take similar premises that I am also 100% sure of and argue inductively, my conclusion may still be wrong. That means deductive argumentation gives me more certainty.

    I may have to jump off this merry-go-round soon...
    Last edited by smhbbag; 04-25-2007 at 06:52 PM. Reason: a
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    Quote Originally Posted by armourbearer View Post
    ... Civbert says, "To say 'all crow are black' means each and every crow is black. And this does not follow from a the particular 'All the crows I have ever witnessed are black.' Hence he shows that particulars are made a universal in the first premise of the deductive argument.
    What?!? I'm speechless.
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    smhbbag is offline. Puritanboard Senior
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    Yeah, I was gonna let you try and tackle that one.
    Jeremy
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    MW
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    Quote Originally Posted by smhbbag View Post
    This has already been addressed. Deductive arguments do not ultimately rest upon induction, in most cases.
    IN MOST CASES.
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
    Victoria, Australia

    "Illum oportet crescere me autem minui."

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    Quote Originally Posted by smhbbag View Post
    No one here has questioned that deductive arguments only produce certain conclusions when the premises are certainly true.
    Then it should be as plain as day that the deductive argument does not yield certainty, contrary to the referenced article. You want to argue for formal certainty, that is, so far as the structure of the argument is concerned, and I keep saying, Sure, no problem, as long as it is understood that it does not yield real certainty.
    Yours sincerely,
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    smhbbag is offline. Puritanboard Senior
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    It does yield real certainty, if you have real certainty about the premises.

    IN MOST CASES.
    Is that supposed to invalidate anything I said, or is it just for rhetorical effect?
    Last edited by smhbbag; 04-25-2007 at 07:10 PM. Reason: a
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    MW
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    Quote Originally Posted by smhbbag View Post
    It does, if you have real certainty about the premises.
    First, then the reality does not depend on the argument. Second, where is the real certainty of a generalisation when men only know particulars?
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
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    Quote Originally Posted by smhbbag View Post
    It does, if you have real certainty about the premises.
    Like the propositions of Scripture.
    R. Anthony Coletti
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    smhbbag is offline. Puritanboard Senior
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    First, then the reality does not depend on the argument. Second, where is the real certainty of a generalisation when men only know particulars?
    I'm sorry, but I honestly don't know what you're asking.
    Jeremy
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    Quote Originally Posted by smhbbag View Post
    I'm sorry, but I honestly don't know what you're asking.
    Then I'm not sure why you responded negatively to my critique of the article that deductive arguments yield certainty. In order to establish certainty the argument must be couched in universals. If there is a sphere in which the premise is not true it does not yield certainty. Now man's knowledge is limited to a particular sphere. Hence he should really only be saying, "... I have seen." Yet he passes his knowledge off as something universally true in and of itself when he says, "All ... are ..."
    Yours sincerely,
    Rev. Matthew Winzer
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    Quote Originally Posted by armourbearer View Post
    ...Now man's knowledge is limited to a particular sphere. Hence he should really only be saying, "... I have seen." Yet he passes his knowledge off as something universally true in and of itself when he says, "All ... are ..."
    This is the most telling flaw in your understanding - you claim that man's knowledge it limited to particulars. If that is the case, then Scripture is meaningless because it's propositions are universals. But I suspect your understanding of the differences between universals and particulars must be defective because you would not deny universals like "all men are sinners" and "Jesus was crucified". Rather you will deny these are universals. This is a very fundamental error in your understanding of logic. I'm sorry to criticize you so directly - but I can't think of any other way to point out the error than to be direct.
    R. Anthony Coletti
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    Quote Originally Posted by Civbert View Post
    This is the most telling flaw in your understanding - you claim that man's knowledge it limited to particulars. If that is the case, then Scripture is meaningless because it's propositions are universals. But I suspect your understanding of the differences between universals and particulars must be defective because you would not deny universals like "all men are sinners" and "Jesus was crucified". Rather you will deny these are universals. This is a very fundamental error in your understanding of logic. I'm sorry to criticize you so directly - but I can't think of any other way to point out the error than to be direct.
    The defect is in the person who makes a claim of universal knowledge and does not quote the authority for it. The proposition should include, the Bible teaches, or, God says. Then it will be clear Who the person is relying on for his knowledge of universals, and his claim can be tested accordingly. As it stands, Civbert has not shown that man himself knows the universal, only that the man is relying on the testimony of a higher authority in his claim of a universal fact.
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
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    "Illum oportet crescere me autem minui."

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    Quote Originally Posted by armourbearer View Post
    The defect is in the person who makes a claim of universal knowledge and does not quote the authority for it. The proposition should include, the Bible teaches, or, God says. Then it will be clear Who the person is relying on for his knowledge of universals, and his claim can be tested accordingly. As it stands, Civbert has not shown that man himself knows the universal, only that the man is relying on the testimony of a higher authority in his claim of a universal fact.
    I'm a Scripturalist. The God's Word is the athority because God spoke it.

    If man only knows particulars - he can not know what God's says in Scripture since Scripture makes universal statements.
    R. Anthony Coletti
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    Quote Originally Posted by Civbert View Post
    If man only knows particulars - he can not know what God's says in Scripture since Scripture makes universal statements.
    No, he cannot know based on a rationalist justification of belief. He can know based on a relation justification of belief. I.e., I trust God, therefore I believe what the Holy Spirit speaks to me in the Word.
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
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    "Illum oportet crescere me autem minui."

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    Quote Originally Posted by armourbearer View Post
    No, he cannot know based on a rationalist justification of belief.
    Which I never made.

    Quote Originally Posted by armourbearer View Post
    He can know based on a relation justification of belief. I.e., I trust God, therefore I believe what the Holy Spirit speaks to me in the Word.
    And I never said otherwise.
    R. Anthony Coletti
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    So do you agree knowledge is fundamentally relational, not propositional?
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
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    "Illum oportet crescere me autem minui."

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    Quote Originally Posted by armourbearer View Post
    So do you agree knowledge is fundamentally relational, not propositional?
    I don't know what you mean by these terms. But but by my understanding of the terms it is not either or, but both.
    R. Anthony Coletti
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    Quote Originally Posted by Civbert View Post
    I don't know what you mean by these terms. But but by my understanding of the terms it is not either or, but both.
    You accepted the either/or above when you said "Which I never made" and "And I never said otherwise." Are you now saying that knowledge is based on a rationalist justification of belief?
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
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    "Illum oportet crescere me autem minui."

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    Quote Originally Posted by armourbearer View Post
    You accepted the either/or above when you said "Which I never made" and "And I never said otherwise." Are you now saying that knowledge is based on a rationalist justification of belief?
    No, I'm not saying that. I didn't say it the first time, and I'm not saying it this time either.

    But you still have not explained what you mean by relational and propositional.

    And since the second part of you statement did not contain an "only" clause, it did imply an either|or situation.
    He can know based on a relation justification of belief.
    R. Anthony Coletti
    Midway Presbyterian Church (PCA)
    Jonesborough, TN
    [i]et venite et arguite me dicit Dominus[/i]

  36. #36
    MW
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    Please tell me, Civbert, if you cannot know universals how you can justify beliefs based on rational considerations? If you are dependent upon the testimony of Another, how are you not affirming that the justification for your beliefs are entirely dependent upon your relationship to (trust in) the One who gives that testimony?
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
    Victoria, Australia

    "Illum oportet crescere me autem minui."

  37. #37
    Civbert's Avatar
    Civbert is offline. Puritanboard Junior
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    Quote Originally Posted by armourbearer View Post
    Please tell me, Civbert, if you cannot know universals how you can justify beliefs based on rational considerations?
    But one can know universals. I never said otherwise.

    Quote Originally Posted by armourbearer View Post
    If you are dependent upon the testimony of Another, how are you not affirming that the justification for your beliefs are entirely dependent upon your relationship to (trust in) the One who gives that testimony?
    It does. It depends on the testimony of God through His Word. I base knowledge on my faith in the truths of Scripture as testified by the Holy Spirit which enables me to both understand and believe God's Word.
    R. Anthony Coletti
    Midway Presbyterian Church (PCA)
    Jonesborough, TN
    [i]et venite et arguite me dicit Dominus[/i]

  38. #38
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    Armourbearer's point, if I understand him correctly, is that premises in deductions are essentially the conclusions of inductive reasoning. Therefore, conclusions of deductions, though 100% certain if the premises are true, cannot, themselves be 100% certain.

    Civrbert's point is, if I understand him correctly, is that we can be 100% certain of certain premises based on the authority of Scripture.

    Couldn't peace be made by simply saying:

    All knowledge, whether arrived at inductively or deductively, regardless of its degree of certainty, is communicated and received via propositions...and that these propositions are communicated and received via relationship between recipient and object. If the object (giver of the proposition) is God, then the recipient is justified in believing that deductions on such premises/propositions, are100% certain.

    If so, it seems we are squarely in Van Tillian territory (ie, that God can and does communicate, that we can receive it and understand such communication, that the Bible is the locus of such communication, etc)...or perhaps we are squarely back at the first line of Calvin's Institutes:
    "Our wisdom, in so far as it ought to be deemed true and solid Wisdom, consists almost entirely of two parts: the knowledge of God and of ourselves. But as these are connected together by many ties, it is not easy to determine which of the two precedes and gives birth to the other."

    Apologies if I am making for more confusion....
    Joel Batts
    Christ Presbyterian Church (PCA) - Memphis, TN

    I believe that many would find that the heart sings unbidden while they are working their way through a tough bit of theology with a pipe in their teeth and a pencil in their hand. - CS Lewis

  39. #39
    MW
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    Quote Originally Posted by Civbert View Post
    But one can know universals. I never said otherwise.
    Only One can know universals, and that is the God Who is everywhere present to know them. If you know anything it is only because God tells you. You do not know the universal, but the God Who knows the universal -- there is a fundamental difference. If you only know things because God tells you it is quite obvious that your knowledge is based solely upon trust in His testimony. So let's not hear any more nonsense about a piece of dust knowing universals.
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
    Victoria, Australia

    "Illum oportet crescere me autem minui."

  40. #40
    MW
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    Quote Originally Posted by sotzo View Post
    If so, it seems we are squarely in Van Tillian territory (ie, that God can and does communicate, that we can receive it and understand such communication, that the Bible is the locus of such communication, etc)...or perhaps we are squarely back at the first line of Calvin's Institutes:
    "Our wisdom, in so far as it ought to be deemed true and solid Wisdom, consists almost entirely of two parts: the knowledge of God and of ourselves. But as these are connected together by many ties, it is not easy to determine which of the two precedes and gives birth to the other."
    If we can forget about the VanTillian addition, the insight of Calvin is priceless. Thankyou.
    Yours sincerely,
    Rev. Matthew Winzer
    Australian Free Church,
    Victoria, Australia

    "Illum oportet crescere me autem minui."

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