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  1. #21
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by JimJones8934 View Post
    But what if the premises were incomplete but still true? Such as if we find an alternative to DNA then all the previous DNA conclusions could be invalid for space-aliens - then our previous conclusions would still be true within the context of the original premise (that all life uses DNA) but now with the new DNA-alternative the original conclusion is wrong because we now have more information.
    There's no problem with that. As we increase our knowledge about the universe, our positions change. We move from false beliefs to true beliefs, from weaker beliefs to stronger beliefs.

    Consider:

    P1: All life has DNA
    P2: DNA is the "carrier" of genetic information.
    C: Therefore, all life has a "carrier" of genetic information.

    Its premises are true, the argument is valid...this is a sound argument (deductive).



    What you are talking about is not "swapping" inductive for deductive (which is what Cac was talking about), but rather epistemology.

    So what happens if we discover alien life that doesn't have DNA? Well...that doesn't change the validity of the above argument, but it does change the truth of P1. And consequently, the conclusion is now false. It is no longer a sound argument.

    So was it ever sound? Not if alien life existed at the time we made the argument (not to be confused with our knowledge of its existence). P1 (and thus C) never corresponded to reality. Truth isn't measured by how much knowledge we have, but rather the statement corresponding to reality, or actuality.

    That's why science doesn't necessarily tell us what must be the case, but rather what has been observed to be the case.

    So what the argument above is actually saying is:

    Based on what we know so far, all life has DNA. DNA is the "carrier" of genetic information, therefore, all life has a "carrier" of information.

    And if we do find alien life without DNA, with our new knowledge, we make the change to the above argument:

    P1: All known Earth-bound life has DNA
    P2: DNA is the "carrier" of genetic information.
    C: Therefore, all known Earth-bound life has a "carrier" of genetic information.

    We just move from the general to the particular. Sometimes when we learn something we just discover a larger group...and that is what happened here. "All life" grew to be larger than expected as now it includes "alien life."

    However...

    Here's the consideration that potentially wipes the above explanation away to be irrelevant:

    CONTEXT. CONTEXT. CONTEXT.

    In this specific example...what was the context of "all life?" Was it "all known life" or was it "all possible life, even that which we have not thought of or discovered"? It would be foolish to mean the latter because we have no knowledge of that to make statements about! So it must be the former.

    That being the case, the meaning is implicit even though we used the quantifier "all". Does "all" mean "all we can reasonable speak about" or does "all" mean "all possibilities even that which we have no knowledge of?"

    So really all one has to do to refute an objection to the argument if alien life is discovered is to simply say "No...it was always sound because it is referring only to known life, not to all possibilities including those we have no knowledge of."

    -----

    Either way are fine defenses of the argument when new information is found and presented.

    But like I said...this isn't really what Cac wasn't talking about. So I may have digressed a bit. =)
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  2. #22
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Apokalupsis View Post
    There's no problem with that. As we increase our knowledge about the universe, our positions change. We move from false beliefs to true beliefs, from weaker beliefs to stronger beliefs.

    ...

    -----

    Either way are fine defenses of the argument when new information is found and presented.

    But like I said...this isn't really what Cac wasn't talking about. So I may have digressed a bit. =)
    Thanks for the digresssion! I think I understand:

    - a deductive argument (A) takes us from a set of premises (P) to a logical conclusion (C). It says nothing about the truth value, per se, of the premises: those are just taken as read as being true (although the could also be proven elsewhere). Such that A(P)=C.

    - there may be other premises (P`s) that could contradict any premises used above or even negate the conclusion but this doesn't change the truth value of the above (without those P`s) that A(P)=C. A(P)=C therefore could never be falsified then, because if we include P' into the argument A(P,P') then A(P,P') <> C, which is a different equation.

    So back to the cosmological argument (of which I only have a passing familiarity) is always going to be if one chooses to ignore scientific discoveries (say) because it doesn't really mention any. So how does one falsify CA itself if we can't change the premises. Let's say we discover that indeed there were aliens and they did indeed create the universe then CA would still be true because it doesn't take that into account. In order for CA to be falsified then it would have to include aliens, which would make it a different argument, CA'. So how do we ever falsify CA unless everyone agrees that aliens exist?

  3. #23
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by JimJones8934 View Post
    Thanks for the digresssion! I think I understand:

    - a deductive argument (A) takes us from a set of premises (P) to a logical conclusion (C). It says nothing about the truth value, per se, of the premises: those are just taken as read as being true (although the could also be proven elsewhere). Such that A(P)=C.
    Sort of. It would be more like A(P ∴ C) or something to that effect. The conclusion (C) is a part of the argument, not something outside the argument.

    But yes, from the conclusion we don't know if the premises are true. We have to evaluate the truth of the premises through other means (not the conclusion). All we are saying about the conclusion in a deductive argument is that "If P is true, then C" nothing more.

    - there may be other premises (P`s) that could contradict any premises used above or even negate the conclusion but this doesn't change the truth value of the above (without those P`s) that A(P)=C.
    I'd phrase it A(P ∴ C) or "A: P ∴ C"...just some way that shows that C is included in A.

    And yes, taken by itself, the argument is fine UNTIL P is challenged to be true. If P is shown to be not true, then the argument has problems and P needs to be amended.

    So back to the cosmological argument (of which I only have a passing familiarity) is always going to be if one chooses to ignore scientific discoveries (say) because it doesn't really mention any.
    Well, the KCA (Kalam Cosmological Argument) is an "outline" of a much bigger argument. Altogether, there are about 25 or so premises. The KCA is a simplified argument of several combined sub-arguments. In fact, almost all arguments are that way.

    Think of every premise as a conclusion of a different argument. That's why we challenge premises after all...we don't accept them to be true. Consider:

    P1 All men are mortal.
    P2 Socrates was a man.
    ∴ Socrates was mortal.

    A sound argument. However, why accept P2? It's because of another argument that argued for the existence of a man named Socrates.

    This is called inference. The conclusion in the Socrates-mortal argument is derived from premises which are assumed to be true for the sake of the argument. Assumed here doesn't mean "Well, I heard it so I assume it" or "I can't think of any other way so I just assume that's the case." Instead, it is used in the context of "Given the arguments for it, this premise is assumed to be true."

    But we don't always have to accept that assumption. In fact, in most debates, we don't. We challenge arguments typically on the reasons stated for them (and a premise is really just a reason to believe the conclusion...as well as also the conclusion of ANOTHER argument assumed to be true for the purpose of this new argument).

    So how does one falsify CA itself if we can't change the premises.
    You don't change the premises, you challenge them or object to them.

    KCA:

    1. Whatever begins to exist has a cause.

    2. The universe began to exist.

    3. Therefore, the universe has a cause.

    Read more: http://www.reasonablefaith.org/in-de...#ixzz2eWjzIv78


    Typically what is challenged here is P2 (some object to P1, but they are fewer). That is, most people who object to the KCA object on the grounds that it has a beginning. Remember that P2 is merely a conclusion of one or more other argument(s).

    So if you wanted to challenge the KCA (which relies on P1 and P2 to be true), you simply challenge one of the premises (P2 for example) and the arguments that are said to support it.

    Let's say we discover that indeed there were aliens and they did indeed create the universe then CA would still be true because it doesn't take that into account.
    In this KCA, the source of the cause isn't considered. In other cosm. arguments, the conclusion ends with God. And if it were shown that aliens instead of God created the universe, then yes, those particular (but inferior to the KCA) would be rightfully challenged and shown to be in need of a revamp (hence many, many variations of the Cosmological Argument (of which, there are at least 20 or so).

    In order for CA to be falsified then it would have to include aliens, which would make it a different argument, CA'. So how do we ever falsify CA unless everyone agrees that aliens exist?
    Let's say that aliens do exist. It isn't their mere existence that falsifies the CA, it is that they themselves are found to have created the universe.

    But then...we have that "CONTEXT. CONTEXT. CONTEXT" issue. God in that sense, could refer to any entity doing the creating of the universe. After all, the CA does not assign a particular known deity to it. It merely defines "God" as the first cause...whatever that first cause is.
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  4. #24
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    Cool Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Apokalupsis View Post
    Yes...necessarily. That is the textbook definition of a deductive argument Caconym. The deductive argument is saying that given the premises (being true) and the argument itself being valid, the conclusion is 100% to be the case.

    Apok, you completely missed my point. I could make a deductive argument where I do not believe the premises are true. For instance:


    1. If Wittgenstein loved me, then I would be dead. P
    2. I am not dead. P
    3. Therefore Wittgenstein didn't love me. 1,2 MT


    Or I can make a deductive argument where I believe the premises might be true:


    1. Either we'll be able to communicate faster than the speed of light soon, or quantum mechanics is wrong. P
    2. Quantum mechanics isn't wrong. P
    3. Therefore, we'll be able to communicate faster than the speed of light soon. 1,2 DeM


    In the first case, although I made a deductive argument I do not believe the conclusion is true at all, let alone 100%. In the latter case, I'm somewhat certain of both premises, leading to me being somewhat certain of the conclusion. We might at this point wish to stop and consider fuzzy logic as a system which formalizes different certainties


    Quote Originally Posted by Apokalupsis View Post
    the premises are intended to provide such strong support for the conclusion that, if the premises are true, then it would be impossible for the conclusion to be false.

    Again, missing the point (not the IEP; you). We might not consider the premises true; we might consider them somewhat true.


    Quote Originally Posted by Apokalupsis View Post
    That is to say, these inferences are such that if the supporting evidence is accurate, the inference could not possibly go wrong.

    But we might not be absolutely sure of the supporting evidence! Do you understand my point yet?


    Quote Originally Posted by Apokalupsis View Post
    A valid argument is...

    Apok, please, this is what I mean by condescending. I have studied logic; I know what a valid argument is and what a sound argument is! But this quote mentions nothing of "deductive" arguments, which I have taken to mean valid arguments. But in any valid argument, we might consider the premises somewhat true, entailing the conclusion is somewhat true.


    Quote Originally Posted by Apokalupsis View Post
    A deductive argument is one “in which the arguer claims that it is impossible for the conclusion to be false given that the premises are true;”

    Brilliant; this doesn't contradict me whatsoever. Here, this person is taking deductive to mean valid, as did I. So, is the conclusion "guaranteed to be the case" "necessarily", as you put it? No! Because the argument may not be sound! The premises may be false! Or, the premises could be somewhat certain, leading to the conclusion being somewhat certain!


    Quote Originally Posted by Apokalupsis View Post
    You are mistaken about the function/intention of the deductive argument there Cac. Deductive arguments are arguments about certainty, not probability (that's inductive).

    No, you are mistaken! They can be "about" (to use your vague word) probability. To demonstrate:


    1. X is a random variable which takes values 1,2, or 3 only P
    2. The probability of X = 1 is 0.2 P
    3. The probability of X = 2 is 0.4 P
    4. The probability of X = 3 is 0.4 P
    5. Therefore, the expectation of X is 2.2 1,2,3,4


    This is clearly a deductive argument, seeing as it is a mathematical argument and all maths is deductive (unless you dispute this...then we really are down the rabbit hole).


    Quote Originally Posted by Apokalupsis View Post
    A deductive argument isn't qualified by being certain about the premises. I never said that. You are committing a strawman. What I said was that given the premises (them being true) and the argument being valid (thus it being sound), the conclusion necessarily follows, guarantees the truth.

    What? You said: "Deductive arguments are that which we are saying that the conclusion is guaranteed to be the case." There was no mention of "but only if the premises are certain". I did not attack a straw man.


    Quote Originally Posted by Apokalupsis View Post
    This completely misunderstand that nature of deductive and inductive arguments it seems.

    Again, what? You're going to have to point out what I have said, and how it misunderstands that dichotomy.


    Quote Originally Posted by Apokalupsis View Post
    The subject isn't the argument, the subject is what the conclusion is referring to. It's 100% true, that it there is a 30% chance that X happens (assuming the premises are true and the form of the argument valid).

    I know!!!!!!!!!!! (with added emphasis). This is what I mean about condescending. I used this example to demonstrate that we could transform inductive arguments into deductive arguments. Say:


    In an inductive argument, I conclude: "All swans are white".
    If I transformed that inductive argument to a deductive argument, I might (based on the premises) end up with: "There is a 60% probability, given all evidence I have, that all swans are white".


    Quote Originally Posted by Apokalupsis View Post
    How is disagreeing with your understanding of deductive arguments "condescending"? Either you don't know how to read people or you have far too thin a skin to debate Cac. I'm making a statement about the nature of the deductive argument, nothing more. If you agree, then say "agreed" if you disagree then put up a defense. And how can you say you have been "saying that" given what you posted above? There's a huge inconsistency there.

    Apok, the only inconsistency is in your misunderstanding what I'm saying, not the other way around. I agree with: "The truth of deductive argument conclusions is contained in the premises of the argument itself. The conclusion never goes beyond what the truth of the premises implicitly requires. This is what makes deductive arguments so strong, so persuasive."


    Where did I say this before? Here:


    "Successful <--> A sound argument


    A sound argument <--> (A valid argument) & (Premises are true in reality)"


    And finally, A valid argument <--> A deductive argument.


    Happy?


    Quote Originally Posted by Apokalupsis View Post
    You are trying to "transform" something that cannot be nor should be.

    Aarrgh. An example:


    Inductive:


    1. She sent me a love letter. P
    2. Therefore she loves me.


    Deductive:


    1. She sent me a love letter. P
    2. The probability that she would send me a love letter if she loved me is 0.7 P
    3. The probability that she loves me (before I knew she sent me this letter) is 0.1 P
    4. The probability that she would send me this letter (regardless of whether she loves me or not) is 0.4 P
    5. Therefore, the probability that she loves me given that she sent me a love letter is 0.175 1-4


    (Haha, a good reason not to read too much into valentine's day!)


    Quote Originally Posted by Apokalupsis View Post
    What is wrong with that is the the argument already does that. Changing "highly probable" into a numerical representation doesn't make the argument deductive. So I don't understand your point here.

    Well, yes it does, because probability theory allows us to make valid arguments, in which the conclusions contain remarks associated with probability and so do the premises. And valid arguments are deductive arguments.


    Quote Originally Posted by Apokalupsis View Post
    Remember, the issue was changing an inductive into a deductive argument with the express purpose of "Make the argument so that if these statements are correct, then it's very probable that John committed the murder."

    Your example was very tricky. However, I can solve a simpler version of:


    Let W = A witness said he saw John murder Sophie.
    Let M = John did, in fact, murder Sophie.


    1. W P
    2. P(W|M) = 0.2 P
    3. P(M) = 0.05 P
    4. P(W|ŽM) = 0.01 P
    5. P(ŽM) = 0.95 From 3 - highlighting for clarity
    6. P(M|W) = (20/39) approx 51.3% 1-5


    Obviously this isn't a formal inductive argument; it's a sketch of one. To do it fully you'd need to go right down to the axioms of mathematics. Surprisingly, I don't have that time.


    Quote Originally Posted by Apokalupsis View Post
    There's nothing to change. You claimed we should or at least we can, go from inductive --> deductive and for the purpose stated above. That purpose already exists (it's fulfilled).

    Hang on a second here. I never said we should always change our inductive arguments into deductive ones. I simply said we could.


    Quote Originally Posted by Apokalupsis View Post
    that does not change the conclusion nor does it "transform" the inductive argument into a deductive argument.

    Given my example above, you might want to rethink this.


    Quote Originally Posted by Apokalupsis View Post
    Inductive arguments deal with probabilities, deductive arguments deal with certainty.

    Again, you might want to rethink.


    Quote Originally Posted by Apokalupsis View Post
    World-renowned physicist Stephen Hawking says that the condition of the universe at the instant of the Big Bang was more highly ordered than it is today. In view of Hawking’s stature in the scientific community, we should conclude that this description of the universe is correct.


    So here's the challenge (or exercise):


    1) Take one of the inductive arguments above and "transform" it into a deductive argument.
    2) The conclusion of the transformed argument must contain the truth of the premise and not go beyond them.
    3) Then explain how the conclusion in this new deductive argument is saying: "if these premises are true, then C is highly probable or likely to be true" and how that differs from the inductive argument form it is in now.

    Let A = The condition of the universe at the instant of the Big Bang was more highly ordered than it is today.
    Let B = World-renowned physicist Stephen Hawking says that the condition of the universe at the instant of the Big Bang was more highly ordered than it is today.


    1. B P
    2. P(B|A) = 0.6 P
    3. P(A) = 0.5 P
    4. P(B|ŽA) = 0.01 P
    5. P(ŽA) = 0.5 From 3
    6. P(A|B) = 60/61 approx 98.4% 1-5


    Your exercise: 1 TICK, 2 TICK, time for 3!


    The conclusion shows that P(The condition of the universe at the instant of the Big Bang was more highly ordered than it is today | World-renowned physicist Stephen Hawking says that the condition of the universe at the instant of the Big Bang was more highly ordered than it is today) is highly probable. But we know that he said that. So we know that "The condition of the universe at the instant of the Big Bang was more highly ordered than it is today" is highly probable.


    How does this differ from the inductive form? The conclusion doesn't. The way to get there does. Most importantly, I included a whole load more premises which were "hidden" in the inductive form.

    TICK.

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  6. #25
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Caconym View Post
    Apok, please, this is what I mean by condescending. I have studied logic; I know what a valid argument is and what a sound argument is!

    I know!!!!!!!!!!! (with added emphasis). This is what I mean about condescending.
    Caconym, this may be your perception of condescending, but Apok is not patronizing you. You're both simply discussing aspects of logic and he's pointing out something that you may already know and visa versa, not a big deal and often done in debate.


    adjective: condescending

    1. having or showing a feeling of patronizing superiority.

    Logicians can be humble.
    Last edited by eye4magic; September 10th, 2013 at 04:18 PM.
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  7. #26
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Caconym View Post
    Apok, you completely missed my point. I could make a deductive argument where I do not believe the premises are true.
    Of course you can. That was never under contention.

    For instance:


    1. If Wittgenstein loved me, then I would be dead. P
    2. I am not dead. P
    3. Therefore Wittgenstein didn't love me. 1,2 MT
    Right. This is a valid argument (modus tollens). And what is under contention is the truth of the premises (P1).

    But if the premises are true, then it is absolutely, categorically, beyond a shadow of a doubt, that the conclusion is true. That's the very nature of deductive arguments Caco. The conclusion NECESSARILY follows the premises and it, in a sound argument, will always be 100% true.

    In an inductive argument, this is not the case. The inductive argument deals with degrees of probability being the case.


    Or I can make a deductive argument where I believe the premises might be true:


    1. Either we'll be able to communicate faster than the speed of light soon, or quantum mechanics is wrong. P
    2. Quantum mechanics isn't wrong. P
    3. Therefore, we'll be able to communicate faster than the speed of light soon. 1,2 DeM
    Right. 100% of the time in this argument, if the premises are true, then the conclusion likewise, will be true. It isn't "Given the premises being true, the conclusion is likely to be true" but rather "...will be true."

    In the first case, although I made a deductive argument I do not believe the conclusion is true at all, let alone 100%.
    You misunderstand. You are going beyond what the premises contains. The truth of the conclusion is contained in the premises, always, in a deductive argument. It never goes beyond what is observed in the deductive argument. It does however (or we can) in an inductive argument.

    So what's the truth of the conclusion that is contained in the premises?

    1. If Wittgenstein loved me, then I would be dead. P
    2. I am not dead. P
    3. Therefore Wittgenstein didn't love me. 1,2 MT

    Contained truth of premises: The result of Witt loving me (I'm dead) and me not being dead.

    ---------------------

    1. Either we'll be able to communicate faster than the speed of light soon, or quantum mechanics is wrong. P
    2. Quantum mechanics isn't wrong. P
    3. Therefore, we'll be able to communicate faster than the speed of light soon. 1,2 DeM

    Contained truth of premises: We can either comm faster than sol soon, or qm is wrong; qm isn't wrong.


    100% of the time, if it is the case that P1 and P2 are true, then the conclusion will follow (and be true). No exceptions. That isn't an issue of probability, but one of certainty.

    Again, missing the point (not the IEP; you). We might not consider the premises true; we might consider them somewhat true.
    This has absolutely no bearing on the conclusion being true if the premises are true like they are said to be. The function of the deductive argument is to work within the observations in the premises as well as providing certainty of the outcome. There is no room for probability here.

    But we might not be absolutely sure of the supporting evidence! Do you understand my point yet?
    But not being "absolutely sure" has no bearing on the outcome of the conclusion Caco. We aren't saying "The premises are absolutely true and therefore so is the conclusion." We are saying "Given the premises, and presuming they are true, then it follows that the conclusion is necessarily true." The conclusion of any sound deductive argument is always necessarily true by virtue of the deductive argument being sound. That's the consequence of a sound deductive argument.

    Of course I understand that the premises of the deductive argument may not be true...as well as the fact that we may not be absolutely sure of their veracity. But that doesn't change the fact that working WITHIN the boundaries of the premises, the conclusion will always be 100% true...always always always. There is no escaping that point. It is logically impossible bro. Can't happen.

    What is the boundary of the argument? Exactly what the premises are saying, nothing more nothing less. What are the qualifiers of the argument being sound? The premises are true and the conclusion properly following them.

    Apok, please, this is what I mean by condescending. I have studied logic;
    Great. Have you studied critical thinking? If so...then why the protest? If not, then here's an explanation: When there is an area of contention or seeming misunderstanding, it's important to focus on the simple details so that all parties are on the same playing field. This leaves little chance to open interpretation and chance and prevents unstated assumptions from entering where they shouldn't as they only cloud meaning and create confusion.\

    Secondly...do I know you? How much of your understanding about X do I possess? If little to nothing, then how am I being condescending to cover the basics just to be sure we are both on the same page? I am not a mind reader nor do I possess magical powers. I do have however, a confident understanding of the elements of critical thinking and the understanding that before more complex issues are evaluated, the ball field in which they are played must be decided and agreed upon by all players.

    But this quote mentions nothing of "deductive" arguments, which I have taken to mean valid arguments.
    Now how can you claim such authority to say "There is no need to speak in simple terms we can both agree on" yet make that statement right there??

    A deductive argument is not synonymous with a valid argument Cac.

    Deductive arguments can be both valid or invalid. All valid arguments are deductive, but not all deductive arguments are valid. Did you just misspeak here?

    But in any valid argument, we might consider the premises somewhat true, entailing the conclusion is somewhat true.
    Not at all. Conclusion of any valid (and sound) argument will always be true, always, no exception.

    I think the confusion here is that you took what I said about inductive vs deductive (probabilities of the conclusion being true vs being necessarily true) and are thinking for some reason that I said we can only speak of probabilities in inductive arguments. I never said any such thing. I spoke only of the truth of the conclusion.

    You aren't talking about the truth of the conclusion, but rather the truth of the statement IN the conclusion.


    Consider this color label system:

    P1. If the clouds clear, there is a 75% chance of sun today.
    P2. The clouds have cleared.
    P3. Therefore, there is a 75% chance of sun today.

    P Q
    P
    Q.


    Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself may not be true or has a probability of not being true.

    What is the conclusion? "[It is 100% true that] there is a 75% chance of sun today."


    At this point, I don't think the rest needs to be addressed because it would appear this is where the source of the confusion lies. It seems you mistakenly took my objection to apply to the statement CORRESPONDING to reality vs guarantee of the truth of a conclusion. I never said any such thing.

    However, just a couple other issues (and let me know if there is anything else I need to respond to)...

    Let W = A witness said he saw John murder Sophie.
    Let M = John did, in fact, murder Sophie.


    1. W P
    2. P(W|M) = 0.2 P
    3. P(M) = 0.05 P
    4. P(W|ŽM) = 0.01 P
    5. P(ŽM) = 0.95 From 3 - highlighting for clarity
    6. P(M|W) = (20/39) approx 51.3% 1-5
    3 issues...

    1) It is 100% true that P(M|W) = 51.3%
    2) The conclusion contains the observation about reality. And that conclusion is 100% true: "It is 100% true that the chances of John being the murderer are 51.3%."

    I never once claimed that John absolutely has to be the murderer. In fact, I explained it in simple terms than this was not the case so you should know by now, what my position actually is (yet you continue to misrepresent it and argue against it - strawman).

    3) In what way did you fulfill the express purpose of making the argument so that if these statements are correct, then it's very probable that John committed the murder? It was already done in the inductive argument. For what purpose should we "transform" the argument?



    Hang on a second here. I never said we should always change our inductive arguments into deductive ones. I simply said we could.
    1) Hence the rest of my statement:

    You claimed we should or at least we can, go from inductive --> deductive and for the purpose stated above. That purpose already exists (it's fulfilled).


    2) What was that "purpose stated above"?

    Make the argument so that if these statements are correct, then it's very probable that X is the case.


    So again, I have to ask, what is the purpose of doing so if the purpose is already fulfilled? You are saying:

    Because I want to make the argument so that if these statements are correct, then it's very probable that X is the case, I will transform the inductive argument into a deductive argument.

    But that is not a meaningful or reasonable purpose...it's already been done for you via the inductive argument!

    It's like saying "I am not hungry right now because I ate chicken. And because I do not want to be hungry right now, I will eat steak."

    or

    "I am at my house. And because I want to be at my house, I wil go there."

    ...dude...you are already there. You have already fulfilled your intention.

    So there must be something else...a different reason to transform the inductive into a deductive. What is it?
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    Re: Is a purely logical argument for/against God possible?

    Not at all. Conclusion of any valid (and sound) argument will always be true, always, no exception.

    I think the confusion here is that you took what I said about inductive vs deductive (probabilities of the conclusion being true vs being necessarily true) and are thinking for some reason that I said we can only speak of probabilities in inductive arguments. I never said any such thing. I spoke only of the truth of the conclusion.

    You aren't talking about the truth of the conclusion, but rather the truth of the statement IN the conclusion.


    Consider this color label system:

    P1. If the clouds clear, there is a 75% chance of sun today.
    P2. The clouds have cleared.
    P3. Therefore, there is a 75% chance of sun today.

    PQ
    P
    Q.


    Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself may not be true or has a probability of not being true.

    What is the conclusion? "[It is 100% true that] there is a 75% chance of sun today."


    At this point, I don't think the rest needs to be addressed because it would appear this is where the source of the confusion lies. It seems you mistakenly took my objection to apply to the statement CORRESPONDING to reality vs guarantee of the truth of a conclusion. I never said any such thing.
    When talking about probabilities, the statement "the probability that p holds is r%" is often interpreted as meaning "We have a confidence of r% that p holds". (This is referred to as Bayesian statistics.) So if new evidence comes to light, you update your confidences in light of that evidence.


    Consider the following principle:
    (*) For any deductive argument that has a set of premises (the conjunction of which denote as P) and a conclusion (denote as Q), one's confidence that Q is true is at least as good as one's confidence that P is true.

    That is, the probability of Q is at least as big as the probability of P.

    A valid deductive argument is such that if its premises are true, its conclusion necessarily follows.

    So, for example:

    (1) If it's raining outside, the streets will be wet.
    (2) It's raining outside.
    (3) Therefore, the streets are wet.

    So let's say you're 100% confident in (1), but only about 50% confident in (2). Then (assuming independence, which might not be a safe assumption), your confidence that the streets are wet outside should be at least 50% (since in addition to rain, the streets could get wet from other sources, but you know at least there's a 50% chance that one of the causes of street-wetness occurs).


    The nice thing about this principle is that if we assign a confidence of 100% to P, then we should assign no less than 100% confidence to Q.


    Note, however, that a deductive argument whose premises are not held with 100% confidence is distinct from an inductive argument.

    An inductive argument is not such that its conclusion necessarily follows from its premises; as Wikipedia puts it, "...inductive reasoning allows for the possibility that the conclusion is false, even if all of the premises are true."

    A typical inductive argument goes something like this:

    (1) Every swan we've seen so far is white.
    (2) We've seen a lot of swans.
    (3) Therefore, all swans are white.

    Note that even if we assign 100% confidence to (1) and (2), we cannot assign 100% confidence to (3).


    Merely because a conclusion is probabilistic does not mean that its argument is inductive. For example:

    (1) The probability of a particular outcome on a 6-sided die is 1/6.
    (2) "1" is a particular outcome on a 6-sided die.
    (3) Therefore, "1" is unlikely to occur.

    This is a deductive argument, even though its conclusion is a statement of probability.
    Last edited by CliveStaples; September 13th, 2013 at 07:00 PM.
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    Re: Is a purely logical argument for/against God possible?

    How does any of that respond to what you are quoting Clive?

    You seem to merely be defining types of arguments. Which is great, but I don't see the relevance (since it's already been done and it seems redundant to restate what's already been stated). Are you agreeing with me and trying to explain it in different terms for him?

    Or is it the case that you are making the same mistake of confusing the the statement corresponding to reality vs guarantee of the truth of a conclusion? I've already explained how he made the mistake so I'm not sure how you could be doing the same thing.

    In addition, I've not argued against those types of deductive/inductive arguments (making the claim that all things dealing with probability = inductive argument). So it seems there are only 2 possibilities...you agree with me and are attempting to explain it to him in different language that what I used (but this is a little confusing because you are quoting me not him)...or you made the same mistake as he, which has already been addressed.
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Apokalupsis View Post
    How does any of that respond to what you are quoting Clive?
    Well, I was trying to interpret what you meant by a statement like "P is r% true". You could be doing fuzzy logic, but the interpretation I offered in my post gave a classical interpretation.

    You seem to merely be defining types of arguments. Which is great, but I don't see the relevance (since it's already been done and it seems redundant to restate what's already been stated). Are you agreeing with me and trying to explain it in different terms for him?
    I'm trying to distinguish clearly between:

    (1) Deductive arguments;
    (2) Deductive arguments with uncertain premises;
    (3) Inductive arguments

    Or is it the case that you are making the same mistake of confusing the the statement corresponding to reality vs guarantee of the truth of a conclusion? I've already explained how he made the mistake so I'm not sure how you could be doing the same thing.
    I'm not sure I understand the kind of mistake you're talking about. You mean distinguishing a true statement from a logically valid argument? Yes, I understand the distinction. I don't think I confused to two anywhere in my post.

    In addition, I've not argued against those types of deductive/inductive arguments (making the claim that all things dealing with probability = inductive argument). So it seems there are only 2 possibilities...you agree with me and are attempting to explain it to him in different language that what I used (but this is a little confusing because you are quoting me not him)...or you made the same mistake as he, which has already been addressed.
    I felt that you were talking about probability in a very haphazard way. I wrote my post in an attempt to clarify how probability theory interacts with these kinds of arguments.
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by CliveStaples View Post
    Well, I was trying to interpret what you meant by a statement like "P is r% true". You could be doing fuzzy logic, but the interpretation I offered in my post gave a classical interpretation.
    Interpretation of what? Of what a deductive or an inductive argument is?

    I'm trying to distinguish clearly between:

    (1) Deductive arguments;
    (2) Deductive arguments with uncertain premises;
    (3) Inductive arguments
    OK...not sure why this is a source of confusion though.

    For example, what is unclear about the following:



    Consider this color label system:

    P1. If the clouds clear, there is a 75% chance of sun today.
    P2. The clouds have cleared.

    P3.
    Therefore, there is a 75% chance of sun today.

    P
    Q
    P

    Q
    .
    Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself may not be true or has a probability of not being true.

    What is the conclusion? "[It is 100% true that] there is a 75% chance of sun today."

    I'm not sure I understand the kind of mistake you're talking about. You mean distinguishing a true statement from a logically valid argument? Yes, I understand the distinction. I don't think I confused to two anywhere in my post.
    No...confusing between the following issues:

    1) a conclusion in a sound argument is always necessarily true

    vs

    2) the statement of the conclusion can contain a probability

    In other words, if we were to soundly conclude "There is a 75% chance of sun today"...what we take away from this is "It is 100% true/applicable that there is a 75% chance of sun today."

    That's a true statement, and will be 100% of the time if it is a conclusion of a sound argument. This is not saying however, that there is a 100% chance of sun today. It's saying that it is true, that there is a 75% chance.

    I felt that you were talking about probability in a very haphazard way. I wrote my post in an attempt to clarify how probability theory interacts with these kinds of arguments.
    I'm not talking about probability. I'm talking about the nature of deductive and inductive arguments. Merely because the word "probability" is mentioned does not make it the subject of what is being said. Regardless, I'm not seeing how anything I wrote was haphazard in any way. Can you be more specific? What was wrong, unclear,"fuzzy," disorganized, or less than accurate?

    But in the end, it is of little importance to me as it is just a subjective opinion (and one that has little to do with what is actually being discussed: nature of deductive and inductive arguments), and everyone has one. I'm more interested in what would be objectively true or false. And if someone else conveys what is objectively true or false in a way that others understand but didn't before, that's fine and is a good thing.
    Last edited by Apokalupsis; September 14th, 2013 at 07:54 AM.
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Apokalupsis View Post
    Interpretation of what? Of what a deductive or an inductive argument is?
    No, my interpretation of what "P is r% true" means.


    OK...not sure why this is a source of confusion though.

    For example, what is unclear about the following:



    Consider this color label system:

    P1. If the clouds clear, there is a 75% chance of sun today.
    P2. The clouds have cleared.

    P3.
    Therefore, there is a 75% chance of sun today.

    P
    Q
    P

    Q
    .
    Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself may not be true or has a probability of not being true.

    What is the conclusion? "[It is 100% true that] there is a 75% chance of sun today."
    That's the unclear portion. What does it mean for a proposition P to be "r% true"?

    No...confusing between the following issues:

    1) a conclusion in a sound argument is always necessarily true

    vs

    2) the statement of the conclusion can contain a probability

    In other words, if we were to soundly conclude "There is a 75% chance of sun today"...what we take away from this is "It is 100% true/applicable that there is a 75% chance of sun today."

    That's a true statement, and will be 100% of the time if it is a conclusion of a sound argument. This is not saying however, that there is a 100% chance of sun today. It's saying that it is true, that there is a 75% chance.
    Okay, so "P is r% true" means "If P is the conclusion of a sound argument, it will be true in r% of the cases"?

    I'm not talking about probability. I'm talking about the nature of deductive and inductive arguments. Merely because the word "probability" is mentioned does not make it the subject of what is being said. Regardless, I'm not seeing how anything I wrote was haphazard in any way. Can you be more specific? What was wrong, unclear,"fuzzy," disorganized, or less than accurate?

    But in the end, it is of little importance to me as it is just a subjective opinion (and one that has little to do with what is actually being discussed: nature of deductive and inductive arguments), and everyone has one. I'm more interested in what would be objectively true or false. And if someone else conveys what is objectively true or false in a way that others understand but didn't before, that's fine and is a good thing.
    Your use of the "100%" proportion was unclear. To what proportion does it refer? Your statements seem to indicate that the proportion you're referring to is "the number of sound arguments having P as a conclusion where P is true" divided by "the number of sound arguments having P as a conclusion".
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by CliveStaples View Post
    No, my interpretation of what "P is r% true" means.

    . . . . That's the unclear portion. What does it mean for a proposition P to be "r% true"?
    That it is necessarily the case. That it is guaranteed given the argument is sound. That is what in fact, the conclusion of a sound deductive argument is. It's merely a different way of saying that "it will necessarily be the case that..." It's an indiom (or in some cases used, a hyperbole) in the English language. Saying "x is 100% true" or "That is 100% correct" are not referring to probabilities or odds...but just a way to emphasize that x is true or x is correct.

    It isn't about probability whatsoever.

    Okay, so "P is r% true" means "If P is the conclusion of a sound argument, it will be true in r% of the cases"?
    Yes. It is guaranteed to be true, it necessarily follows.

    In the example given above re: sound argument about the chance of sun today, there are various ways we can phrase the conclusion:


    • "It is 100% true that there is a 75% chance of sun today."
    • "It is 100% correct that there is a 75% chance of sun today."
    • "It is guaranteed that there is 75% chance of sun today."
    • "It is necessarily the case that there is 75% chance of sun today."
    • "It is true that there is a 75% chance of sun today."


    I chose to use "100% true that..." because Cacon wasn't making a distinction between probabilities of the outcome and the guarantee of the truth of the conclusion. This was explained earlier in my response to him (post #25):

    Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself may not be true or has a probability of not being true.

    What is the conclusion? "
    [It is 100% true that] there is a 75% chance of sun today."

    At this point, I don't think the rest needs to be addressed because it would appear this is where the source of the confusion lies. It seems you mistakenly took my objection to apply to the statement
    CORRESPONDING to reality vs guarantee of the truth of a conclusion. I never said any such thing.

    Your use of the "100%" proportion was unclear.
    That's because you are thinking in terms of math instead of terms of common English.

    • "It is 100% true that..."
    • "That is 100% correct!"
    • "I'm going to give it 100%."
    • "He gave it 110%."
    • "I'm 99% sure that..."
    • "It's totally true that..."
    • It's completely true that...}


    None have anything to do with probability or statistics Clive. They are just different ways to emphasize something using numbers (or stated percentages)...none of which are intended to be literal or mathematically applicable/accurate. This just comes down to using a little bit of common sense and an understanding of the English language.

    Still not a believer in this common form of expression?

    Google +"100% true" or +"100% correct". 36M and 19M hits respectively.

    You have made a mountain out of a molehill here my friend...one that didn't need to be if only those "math goggles" were removed long enough to have an ordinary discussion using ordinary language.
    Last edited by Apokalupsis; September 16th, 2013 at 04:41 PM.
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Apokalupsis View Post
    That it is necessarily the case. That it is guaranteed given the argument is sound. That is what in fact, the conclusion of a sound deductive argument is. It's merely a different way of saying that "it will necessarily be the case that..." It's an indiom (or in some cases used, a hyperbole) in the English language. Saying "x is 100% true" or "That is 100% correct" are not referring to probabilities or odds...but just a way to emphasize that x is true or x is correct.

    It isn't about probability whatsoever.


    Yes. It is guaranteed to be true, it necessarily follows.
    So if P is 50% true, then for half of the sound arguments with P as a conclusion, P is true?

    In the example given above re: sound argument about the chance of sun today, there are various ways we can phrase the conclusion:


    • "It is 100% true that there is a 75% chance of sun today."
    • "It is 100% correct that there is a 75% chance of sun today."
    • "It is guaranteed that there is 75% chance of sun today."
    • "It is necessarily the case that there is 75% chance of sun today."
    • "It is true that there is a 75% chance of sun today."


    I chose to use "100% true that..." because Cacon wasn't making a distinction between probabilities of the outcome and the guarantee of the truth of the conclusion. This was explained earlier in my response to him (post #25):

    Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself may not be true or has a probability of not being true.

    What is the conclusion? "
    [It is 100% true that] there is a 75% chance of sun today."

    At this point, I don't think the rest needs to be addressed because it would appear this is where the source of the confusion lies. It seems you mistakenly took my objection to apply to the statement
    CORRESPONDING to reality vs guarantee of the truth of a conclusion. I never said any such thing.


    That's because you are thinking in terms of math instead of terms of common English.

    • "It is 100% true that..."
    • "That is 100% correct!"
    • "I'm going to give it 100%."
    • "He gave it 110%."
    • "I'm 99% sure that..."
    • "It's totally true that..."
    • It's completely true that...}


    None have anything to do with probability or statistics Clive. They are just different ways to emphasize something using numbers (or stated percentages)...none of which are intended to be literal or mathematically applicable/accurate. This just comes down to using a little bit of common sense and an understanding of the English language.

    Still not a believer in this common form of expression?

    Google +"100% true" or +"100% correct". 36M and 19M hits respectively.

    You have made a mountain out of a molehill here my friend...one that didn't need to be if only those "math goggles" were removed long enough to have an ordinary discussion using ordinary language.
    Don't give me the anti-intellectual "ordinary language" schtick. You were specifically talking about probabilities--which are proportions, by the way, since they take values between 0 and 1--and then you made a statement about a proposition being "100% true". If you're gonna go with the "aw, shucks" colloquialisms, you should avoid the ones that overlap with the technical terms you're using.


    Also, while your statement to the effect that conclusions of sound arguments can involve statements of probability is undoubtedly true, I think it failed to capture the kind of doubt that Caconym was having. I thought that distinguishing between the probability representing one's confidence in the truth of the premises and the probability referred to in the propositional content of the argument itself.

    Which apparently was so troubling to you that I had to defend my motivation for writing the post in a 4-post exchange with you. And I'm the one making mountains of molehills.
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by CliveStaples View Post
    So if P is 50% true, then for half of the sound arguments with P as a conclusion, P is true?
    ...what?

    Clive, there is no "50% is true." Nor is there "X% is true."

    How could you possibly even think that after the explanation of how the phrase was being used??

    Don't give me the anti-intellectual "ordinary language" schtick. You were specifically talking about probabilities
    No. I was not Clive. And as I said previously, just because there is a statement involving a probability does not mean that the statement was about probability. You are having a knee-jerk reaction presumably because your field of vision is far too narrow (which has been the case in several threads as of late as almost every discussion has resorted to some mathematical equation).

    I was talking about the nature of deductive and inductive arguments and how the former results in a certainty of truth of the proposition since it is contained within the premises (and it is thusly, necessarily true), while the latter cannot be as it goes beyond the truth of the given premises.

    And I'm the one making mountains of molehills.
    Abso-frickin-lutely you are. Instead of using common sense and remaining in common English...you seemingly believe that all language can be evaluated and expressed in mathematical terms. And that is just silly.


    Personal observation...
    You do this in almost every thread (that I've seen) as of late. Discussion, believe it or not...does not revolve around the world of mathematics. It's a conveyance of ideas in a format that the audience can understand. When we are speaking of modal logic or physics, we use the language of math to evaluate and discuss those topics. But these types of languages are not necessary in all discussions or about all topics Clive. And I think you've been working with numbers so long that you see all conversations as symbols or equations...and that is just going to cloud the message being conveyed as well as the proper understanding of it.
    Last edited by Apokalupsis; September 16th, 2013 at 06:44 PM.
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    Re: Is a purely logical argument for/against God possible?

    Apok, as I said before, I was merely trying to distinguish clearly between:

    (1) Deductive arguments;
    (2) Deductive arguments with uncertain premises;
    (3) Inductive arguments

    Inductive arguments, uncertainty, and confidence are in the domain of probability theory and statistical inference.

    If there was an error in my original post, please point it out. I have no interest in continuing to have a discussion about my motivations for writing that particular post, or any further analysis of the pedagogical effectiveness of your posts.
    Last edited by CliveStaples; September 16th, 2013 at 06:59 PM.
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by CliveStaples View Post
    So you just declared that "P is r% true" means "If P is the conclusion of a sound argument, it will be true in r% of the cases". Take r = 50.
    Right...but with my explanation r can only be 100%. I'm not talking probability of being true, and this should be evident by its explanation of what I meant by the expression.

    At no time ever...can the conclusion of a sound argument ever be true half the time. A conclusion of a sound argument must be true all of the time. OR....

    A conclusion of a sound argument is true 100% of the time.
    A conclusion of a sound argument is necessarily true.
    A conclusion of a sound argument is guaranted to be true.

    Take your pick.

    There is no half, middle, quarter, some, x%.

    The message was about always being true by virtue of being the conclusion of a sound argument. There is no other possible outcome for that conclusion Clive. This isn't hope that it is the case, this isn't speculation. It's the necessary consequence of its premises being true and it following properly from them.

    You were specifically talking about probabilitistic statements--statements about probability--such as, "It is 75% likely to rain tomorrow." Those are probabilities.
    You are missing the container. The container is what was being discussed. The container is the subject. The container is the focus.

    So what is the container?

    The proposition of a sound argument that is referred to as the conclusion. That is...there is a distinction here...the conclusion proposition of the sound argument and the contents of it (or the statement about reality that the conclusion proposition holds).

    I helped illustrate the distinction between the container and what is being contained, by using color codes.

    "75% chance of sun" is the statement that corresponds to reality...it is what is being contained.

    How true is the conclusion/container that holds this contained statement? That is..."how true" is it the case that "there is a 75% chance of sun today"?

    Well...this depends on what type of argument we find the conclusion in.

    If it is an inductive argument...then we have x% chance. We could know x% or we may not know (depending upon the data provided and that which we are aware of).

    We could reasonably (and justifiably) say that "There is a good chance that there is a 75% chance of sun today." We may also be able to say (depending upon available data and knowledge) that "There is a 75% chance that there is a 75% chance of sun today."

    We can do that in an inductive argument. The conclusion (the container its contents) isn't necessarily true by virtue of it being an inductive argument. The truth of the conclusion goes beyond the truth contained in the premises.

    If it is a deductive argument however, it's a completely different story. With the same statement that corresponds to reality...we can say:

    It is necessarily true that there is a 75% chance of sun today.
    It is definitely true that there is a 75% chance of sun today..
    It is absolutely true that there is a 75% chance of sun today.
    It is assuredly true that there is a 75% chance of sun today.
    It is 100% true that there is a 75% chance of sun today.

    Your argument, as I understand it, is that a statement of probability like, "It is 75% likely to rain tomorrow" should not be interpreted as having a lesser degree of certainty merely because the propositional content of the statement involves probabilities.
    Nope. That's not my argument. Never argued anything like it.

    Here's my argument:

    Conclusions of inductive arguments are not guaranteed to be true. Conclusions of deductive arguments are guaranteed to be true. Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself (the container of the statement involving the probability) may not be true or has a probability of not being true. In addition, it makes no sense to change the form of an inductive argument into a deductive argument for the sole purpose of "making the argument so that if these statements are correct, then it's very probable that X is the case." The inductive argument already does this.

    When you're talking about the confidence you have that a conclusion is true, you're making probabilistic statements.
    Where did I talk about confidence of a conclusion being true? That was something you brought up and forced into the discussion...not me. It was never an issue for me.
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  20. #37
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Apokalupsis View Post
    Right...but with my explanation r can only be 100%. I'm not talking probability of being true, and this should be evident by its explanation of what I meant by the expression.

    At no time ever...can the conclusion of a sound argument ever be true half the time. A conclusion of a sound argument must be true all of the time. OR....

    A conclusion of a sound argument is true 100% of the time.
    A conclusion of a sound argument is necessarily true.
    A conclusion of a sound argument is guaranted to be true.

    Take your pick.

    There is no half, middle, quarter, some, x%.

    The message was about always being true by virtue of being the conclusion of a sound argument. There is no other possible outcome for that conclusion Clive. This isn't hope that it is the case, this isn't speculation. It's the necessary consequence of its premises being true and it following properly from them.
    I asked you whether "P is r% true" meant "of all sound arguments concluding with P, in r% of them P holds", and you said yes. You've clarified further and said it is only true for r=100 (that is, the truth values are 0 and 1, not a continuum between them). I note your clarification.


    You are missing the container. The container is what was being discussed. The container is the subject. The container is the focus.

    So what is the container?

    The proposition of a sound argument that is referred to as the conclusion. That is...there is a distinction here...the conclusion proposition of the sound argument and the contents of it (or the statement about reality that the conclusion proposition holds).
    Yes, I've routinely distinguished between statements and their propositional contents in this thread.

    I helped illustrate the distinction between the container and what is being contained, by using color codes.

    "75% chance of sun" is the statement that corresponds to reality...it is what is being contained.

    How true is the conclusion/container that holds this contained statement? That is..."how true" is it the case that "there is a 75% chance of sun today"?

    Well...this depends on what type of argument we find the conclusion in.

    If it is an inductive argument...then we have x% chance. We could know x% or we may not know (depending upon the data provided and that which we are aware of).

    We could reasonably (and justifiably) say that "There is a good chance that there is a 75% chance of sun today." We may also be able to say (depending upon available data and knowledge) that "There is a 75% chance that there is a 75% chance of sun today."

    We can do that in an inductive argument. The conclusion (the container its contents) isn't necessarily true by virtue of it being an inductive argument. The truth of the conclusion goes beyond the truth contained in the premises.

    If it is a deductive argument however, it's a completely different story. With the same statement that corresponds to reality...we can say:

    It is necessarily true that there is a 75% chance of sun today.
    It is definitely true that there is a 75% chance of sun today..
    It is absolutely true that there is a 75% chance of sun today.
    It is assuredly true that there is a 75% chance of sun today.
    It is 100% true that there is a 75% chance of sun today.
    Those are all statements about the proposition, "There is a 75% chance of sun today". You are saying of that proposition, "It is necessarily true."

    You are talking about probabilistic statements; specifically, that if P is a probabilistic statement, and P is the conclusion of a sound argument, then P is true.

    Nope. That's not my argument. Never argued anything like it.
    Really?

    Here's you:

    Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself may not be true or has a probability of not being true.

    Here's my characterization of your argument:

    Your argument, as I understand it, is that a statement of probability like, "It is 75% likely to rain tomorrow" should not be interpreted as having a lesser degree of certainty merely because the propositional content of the statement involves probabilities.

    Those seem pretty close to me!

    Here's my argument:

    Conclusions of inductive arguments are not guaranteed to be true. Conclusions of deductive arguments are guaranteed to be true. Just because we have a premise that CONTAINS a statement about a probability, it does not mean that the conclusion itself (the container of the statement involving the probability) may not be true or has a probability of not being true. In addition, it makes no sense to change the form of an inductive argument into a deductive argument for the sole purpose of "making the argument so that if these statements are correct, then it's very probable that X is the case." The inductive argument already does this.


    Where did I talk about confidence of a conclusion being true? That was something you brought up and forced into the discussion...not me. It was never an issue for me.
    Yes, you didn't use the word "confidence". But you were talking about the (lack of a) probability of a conclusion being false, and the guarantee or certainty of a conclusion being true. You caution against being uncertain of a sound argument's conclusion. It seemed to me that your arguments were closely aligned with Bayesian statistics, so I thought I'd formulate my own argument on the matter since Caconym seems to like the language of probability.




    Apok, you're free to ignore Bayesian statistics and inferences. You're free to ignore probability theory. You're free to cast your arguments in language that doesn't borrow from mathematical philosophy, probability theory, or set theory. You're free to think that my post was superfluous. But unless you have an argument that my post was wrong, this whole tangent has been completely off-topic navel-gazing.
    If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard
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  22. #38
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    Talking Re: Is a purely logical argument for/against God possible?

    I would just like to state my agreement with Clive; he has managed to state much more succinctly and clearly the heart of what I was attempting to get at. Also, I'd like to interject with a little bit of Fuzzy Logic. The purpose of this isn't to counter anything that anyone has said. Rather it is to explore what we mean when use the words "sound argument" and "100% certainty". I'll use the &-operator to be min(x,y), and the V-operator to be max(x.y) [these are common definitions].

    Let Ax = X is tall.
    Let Bx = X is a human.
    Let s = Simon.

    In Normal First-order Logic

    1. As P
    2. Bs P
    3. As & Bs 1,2 Conjunction

    This is a fine, valid deductive argument. If the premises are definitely true, then the conclusion is necessary. However, can it be sound? Well, if Simon is 6 foot and a human, yes. Or is it? Sure, 6 foot is pretty tall, but 10 foot is way taller! So we have a problem with the definition of tall. We can't simply define tall as "greater than or equal to 5 foot 10 inches". This would mean that someone 5'10" is tall, whilst someone an inch shorter at 5'9" isn't.

    The problem is that, in normal propositional logic, we have to be 100% certain of the premises before we can say anything about the truth value of the conclusion. This is irritating. What if I'm kind of sure that Simon is tall, but not really, because he's only borderline tall? I still want to be able to make the conclusion; I still want the argument to be sound. But in propositional logic, the only way to do this is:

    Let KAx = X is kind of tall.
    Let Bx = X is a human.
    Let s = Simon.

    1. KAs P
    2. Bs P
    3. KAs & Bs 1,2 Conjunction

    But "kind of tall" is really vague. And it's of no use to me to be absolutely certain that someone is "kind of tall and a human being". We don't care about the set "kind of tall" - we want to know about the set "tall". Therefore, we need to invent a system of logic which allows us to make comments about "kind of X", where "kind of X" isn't a set in its own right, but rather "kind of X" describes some property about the set X.

    We need a scale:



    Fuzzy logic allows there to be a degree of membership to the set of "tall". Now we can realistically talk about arguments being sound or not, because the premises are no longer statements like "Simon is (absolutely) tall". We can now have "Simon is (to some degree of membership) tall". That means that instead of talking about whether an object belongs in the set "kind of tall", we are talking about the degree of membership an object has in the set "tall". We've done it! As we will see later, this doesn't now pose the problem of returning to "Necessarily, Simon is (to X degree of membership) tall". But I'll come onto that later.

    In Fuzzy Logic

    Let T(Xy) = the degree of membership of y to X.

    1. T(As) = 0.7 P
    2. T(Bs) = 1 P
    3. T(As & Bs) = 0.7 1,2 &-operator

    This is great! No longer do we have the irritating conclusion "Simon belongs in the set (kind of tall and human beings)". I mean, what the hell is the set "kind of tall and human beings" and what relevance does it have to the set "tall and human beings"? In fuzzy logic we have "Simon's degree of membership to the set (tall and human beings) is 0.7". This is far better; because we wanted to talk about the set "tall and human beings", not the set "kind of tall and human beings".

    The problem of necessity


    Have we really gotten away from necessity? Surely, for the arguments to be sound here, we still need T(As) to be absolutely true. The answer is yes, but we can get further away from necessity like this:

    -0.7≤p≤0.3
    -1≤q≤0

    1. T(As) = 0.7 + p P
    2. T(Bs) = 1 + q P
    3. T(As & Bs) = Min(0.7+p , 1+q) 1,2 &-operator

    P and Q act like uncertainty analysers. Their values will be close to 0 because we are not that uncertain. And now we can say with confidence that the premises are both true, because they are by definition (they can take membership values 0-1, which is all the possible values). So the element of necessity is still there, but now it's in a place where we can be 100% certain - that the premises have truth values. Thus, this argument is definitely valid and sound.

    Now all we need to do is say that we are not very uncertain, so p and q are too small to be relevant. If we aren't very uncertain, it allows us to say that T(As & Bs) approx 0.7. This is good.

    Is this an improvement?

    Yes, I believe it is. Why? Here is a summary of the reasons I have referenced throughout the post:


    • Our conclusion is still valid and sound, as in the the Propositional case with KAs.
    • Our conclusion no longer talks about the set "kind of tall and a human being", now it talks about the set "tall and a human being" - which is what we wanted in the first place
    • It's no longer the case that being slightly uncertain about whether "Simon is tall" renders our argument not sound
    • We no longer have to use the vague phrase "kind of tall"
    • Now we can be slightly uncertain about our premises, but rather than render our argument not sound, this means that T(As & Bs) = 0.7 is a worse approximation

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  24. #39
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by CliveStaples View Post
    Apok, you're free to ignore Bayesian statistics and inferences. You're free to ignore probability theory. You're free to cast your arguments in language that doesn't borrow from mathematical philosophy, probability theory, or set theory.
    And you are of course, free to ignore the English language and principles of critical thinking and proper rhetoric. But of course, that gets us nowhere now does it?

    You are also free to continue to ignore the distinction between the nature of a conclusion and the statement of which corresponds to reality and misstating my argument. But continuing to do so of course...will always yield an error on your part (strawman), as I have shown.

    And the difference between you and I ignoring things here...is that in me ignoring them (what you have charged me with ignoring) it is because they simply are not applicable to anything I've argued.

    It's like me saying "I like vanilla ice cream" and you saying "Ohhh...yeah...sure, you can just ignore statistics all day long if you want there mister!"

    It leaves no response other than "...wtf?" You are not listening...you are not reading carefully what is being said Clive.

    We aren't leaving anything out that shouldn't be there already.

    I've already explained what my argument is. It has nothing to do with probability Clive. Nothing to do with math. Nothing to do with physics or statistics.

    It's the nature of an inductive vs deductive argument as well as objecting to the idea that we need to (or should) transform inductive into deductive for the reasons Cac gave. You are missing the forest through the trees.


    If you wish to respond to him or something he said in the language of mathematical philosophy, probability, statistics, etc... go for it. But you chose not to...and instead...you responded to me and my argument...which has absolutely nothing to do with any of it.
    Last edited by Apokalupsis; September 17th, 2013 at 07:07 AM.
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  25. #40
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    Re: Is a purely logical argument for/against God possible?

    Quote Originally Posted by Caconym
    I'll use the &-operator to be min(x,y), and the V-operator to be max(x.y) [these are common definitions].
    I'm having a bit of trouble understanding why to use those definitions. Consider the following:

    T(Ax) = .5
    T(Bx) = 1
    T(A&Bx) = min{.5, 1} = .5

    T(Ay) = .5
    T(Bx) = .5
    T(A&By) = min{.5, .5} = .5

    Isn't it a bit strange that y has the same membership in A&B as x does, even though x is "entirely" in B while y is only "partially" in B, and their membership in A is identical?
    If I am capable of grasping God objectively, I do not believe, but precisely because I cannot do this I must believe. - Soren Kierkegaard
    **** you, I won't do what you tell me

    HOLY CRAP MY BLOG IS AWESOME

 

 
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