Poll 2 on the validity of a more complex argument

Discussion in 'General Philosophy' started by Speakpigeon, Jan 18, 2019.

?

Is the argument valid?

Poll closed Feb 17, 2019.
  1. No

    25.0%
  2. Yes

    37.5%
  3. I don't know

    0 vote(s)
    0.0%
  4. The argument doesn't make sense

    37.5%
  1. Speakpigeon Valued Senior Member

    Messages:
    1,123
    Who says?
    Please produce empirical evidence for your claim.
    Here is what a dictionary says of argument:
    Which is exactly what this thread is about.
    I hope you understand this is a different sense of the word "argument". In your definition here, it's argument in the sense that x is argument of f(x).
    EB
     
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  3. Speakpigeon Valued Senior Member

    Messages:
    1,123
    Thanks, at least you're showing it's possible to do something else than obfuscate as most other posters have done.
    There are two problems in what you say.
    First, my argument says "may", not "might" as you keep asserting wrongly throughout your post. That's obviously not the same thing at all.
    "Might" signals a remote possibility, something we've good reasons to think is unlikely.
    "May" just signals possibility.
    I might win the lottery but we all know that it's more probable that I won't win.
    It may well be that God exists and it may well be that God doesn't exist. No clues as to probability.
    I hope you see how this is crucial and why you're wrong about my argument being "weak".
    Further, your notion of weakness only makes sense when discussing soundness. With validity, we don't care. An argument is valid or not.
    But with soundness, you usually have to assess for yourself how likely the premises are to be true.
    So, that makes most of your post essentially irrelevant. May, not might. Might would be a different argument.
    Ah, this bit is much better.
    This is the gist of what some people here have referred to as "undistributed middle", but you explain your point, they didn't.
    So, yes, it's true, there's no guarantee that the unknown part of B in premise 1 is the same as the unknown part of B in premise 2.
    Still, that doesn't make the argument invalid. If you take the two premises to be true, as worded, and not redacted as some posters did, then the conclusion is true and couldn't be false.
    First, there are no ifs as to validity. The argument is valid or it isn't. No ifs.
    As for soundness, there are only two ifs, i.e. premise 1 and premise 2. Please note this is exactly the same situation as for any argument having two premises, including for example the argument about Socrates being mortal.
    So, yes, two ifs. If premise 1 is true and if premise 2 is true, then the conclusion is true, and this precisely because the argument is valid.
    And then, it is up to you to decide whether you believe that the premises are true or not. And then, no ifs left.
    And if you believe that any of the premises is false, I'd be very interested to know why, because anybody able to prove them false would be eligible to the Nobel Prize.
    Note that nobody did, yet.
    EB
     
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  5. Baldeee Valued Senior Member

    Messages:
    2,122
    The weakness of your argument is not a matter of the semantic difference between "may" v "might", but in the fact that it's validity relies on only a non-zero possibility contained within the "may" of the conclusion.
    The actual strength of the possibility is unknown, whatever probability you place on the "may" in the first premise, due to the parts of B being referenced in the two premises being unknown, and the overall size of B being unknown (are the parts 50% of the whole, or a thousandth, or a quadrillionth?).
    So the chance that they are referencing the same thing is unknown, and thus the possibility of the conclusion from true premises is unknown other than it being non-zero (and thus true), and thus would be considered weak.
    Probably as weak as it is possible to be, actually.
    I mean, at least with the lottery I know what my chances are when I say "I may win the jackpot".
    With your conclusion you don't know what probability, other than non-zero, to ascribe to it.

    Compare that to a valid syllogism with certain premises.
    In such cases we know that if the premises are true then the conclusion is certain - i.e. as strong as it can be.
    The issue then is what probability we ascribe to the premises being true, but at least the argument is strong.
    Your argument seems to have premises that can be more easily agreed upon, but at the expense of the weakest of possible conclusions, albeit more likely to be true.
    If you are referring to Sarkus, you are mistaken in that they did explain their point, and quite clearly.
    Don't confuse your lack of understanding of an explanation with there being a lack of explanation.
     
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  7. Beer w/Straw Transcendental Ignorance! Valued Senior Member

    Messages:
    6,368
    Is the argument "I don't know" a valid argument?
     
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  8. DaveC426913 Valued Senior Member

    Messages:
    16,758
    That's not an argument, but it is a valid response to the poll.
     
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  9. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

    Messages:
    9,491
    I think the option "who cares" is also missing.
     
  10. Yazata Valued Senior Member

    Messages:
    5,608
    This is the fourth thread that Speakpigeon has started on this little argument of his, each one challenging everyone else to tell him whether or not it is logically valid. I don't know why that's so important to him. But he must believe that his argument is extraordinarily good.

    Nor do I know why he hasn't simply produced a validity proof of his own. (My guess is that he probably can't.) So he keeps challenging everyone else and behaving very dismissively when he doesn't like their answers.

    Perhaps it's time for him to answer his own question. (That way we can dismiss him.)

    As for me, it's been more than 30 years since I studied formal logic (in the 1980's). My memory of the subject is exceedingly fuzzy. I don't think that I can produce a formal validity proof any longer. But I can still comment on whether Speakpigeon's argument looks valid to me.

    Here's premise 1:

    For all we know, A may be the state of some unknown part of B

    I'm inclined to think that "For all we know" can simply be eliminated as redundant, since the rest could still be interpreted as being either T or F.

    The "may be" seems to introduce the modal possibility operator. I'm not sure that it is necessary either.

    His 1. would seem to symbolize as something like

    (∃a)(∃b)(possible) S (a,b)

    where

    (∃a) and (∃b) are existential quantifiers
    (possible) is the modal possibility operator (that diamond-shaped thing. I can't find it on my keyboard).
    S is a two place predicate 'is a state of'
    and 'a' and 'b' are Speakpigeon's A and B (more or less) in an ordered pair, such that a is a state of b.

    The existential quantifiers seem to take care of the "some unknown part of", by saying that there exists some a and some b, such that a is a state of b.

    We might be able to drop the possibility operator as well, since (∃a)(∃b)S(a,b) can still be interpreted as T or F. (I suspect that's all that Speakpigeon meant to say.)

    So premise 1 seems to symbolize as

    (∃a)(∃b)S(a,b)

    Something like that. (It's been a long time.)

    Moving on to premise 2:

    C is determined by the state of some unknown part of B;

    (∃c)(∃b)D(c,b)

    Where D is 'is determined by'

    The conclusion is:

    Therefore, for all we know, C may be determined by A

    (∃c)(∃a)D(c,a)

    So the question of the thread (and its four successors) is: Is --

    1. (∃a)(∃b)S(a,b)

    2. (∃c)(∃b)D(c,b)
    _____________________

    C. (∃c)(∃a)D(c,a)

    logically valid? Doesn't look like it, formally speaking, unless we are equating and identifying a with b.

    So, does the 'S' in premise one justify our replacing the 'b' in premise 2 with 'a' in the conclusion?

    (Maybe, but it isn't a strictly logical question, is it?)

    1. a <=> b, a ≡ b, or a := b 'a if and only if b', 'a is identical to', or 'a is defined as b'

    2. (∃c)(∃b)D(c,b)
    _____________________

    C. (∃c)(∃a)D(c,a)

    Might be better.

    It might be helpful to remember the original form of Speakpigeon's argument, before he tried to turn it into a matter of formal logic.

    Premise 1 - For all we know, somebody's mind may be the state of a group of neuron's in this person's brain
    Premise 2 - What somebody does is determined by the state of a group of neurons in this person's brain
    Conclusion - Therefore, for all we know, what somebody does may be determined by the conscious mind of this person

    I don't really have much problem agreeing with that. It might even be logically valid, if premise 1 is actually making "somebody's mind" logically interchangeable with that person's brain states.

    It's a pretty strong mind-brain identity theory. I'm more inclined personally to identify our psychologistic vocabulary (ideas, emotions, beliefs, memories, perception etc.) with kinds of information processing behavior that might be performed in a variety of different physical ways, by brains (whether human or nonhuman), by computers with different sorts of architectures, and so on.

    Making that kind of functionalist move weakens the identity that premise 1 is seemingly intended to establish, and hence weakens the formal validity of Speakpigeon's argument. Nevertheless, I still agree with his version in broad outline.

    I make a similar move myself in defending compatibilism in the free-will/determinism argument.
     
    Last edited: Jan 20, 2019
    James R likes this.
  11. Speakpigeon Valued Senior Member

    Messages:
    1,123
    You're sure doing a nice bit of special pleading here on insisting only on modal "may" being compatible with near zero probability. You're pleading so you choose to ignore that "may" is just as compatible with 99% probability.
    And "might" isn't. So, no, "may" isn't the same at all as "might". Yes or no?
    And your point is irrelevant to validity.
    So, thanks for your expert derail.
    EB
     
  12. Speakpigeon Valued Senior Member

    Messages:
    1,123
    That's obviously not a good formalisation.
    The relation is a bit more specific than S(A, B). The argument says A is the state of B, meaning that A is identical ( ≡) with the state of B: A ≡ S(B)
    And it's not "There exist a person's conscious mind such that...", but "For all persons, their conscious mind...".
    So, ∀ not ∃.
    So, the first premise is as follows: ◇ ∀A, ∃X/ P(X, B) ∧ A ≡ S(X) i.e. For all we know, A may be (◇) the state (S) of some unknown (X) part (P) of B
    The rest is easy.
    Yeah, your argument here is not valid. I agree.
    So, what about mine?
    Yes, it's better.
    Yes, it's not just strong, it's as strong as you could ever make it. There's nothing above identity.
    And, as the argument, shows, it may be true.
    EB
     
  13. Baldeee Valued Senior Member

    Messages:
    2,122
    There's no derail.
    There is no special pleading.
    There is the observation that the best you can say about your conclusion is that it is a non-zero probability.
    I don't insist on this being near zero or near certainty.
    Due to the premises, and the unknowns within, being non-zero is all that can be said.
    And as such the conclusion is weak.

    You can either deal with that or, as your tendency is, close your eyes to it, ignore it, and try to evade the issue.
    I'm not referring to your may/might semantic quibble.
    I am dealing with your argument as you wrote it.
    "May" expresses a non-zero probability: a possibility.
    Your conclusion, as I stated previously, seems valid.
    But all you can say about the conclusion is that it has non-zero possibility, irrespective of how much confidence one has in premise one.
    As such, valid or not, it is exceptionally weak.
     
  14. Speakpigeon Valued Senior Member

    Messages:
    1,123
    No.
    EB
     
  15. Jeeves Valued Senior Member

    Messages:
    5,028
    I said.
    If you argue about nothing, or solve and equation for no value, you do neither, merely waste your own and other people's time.
    Fortunately, I had some to waste.
     
  16. Speakpigeon Valued Senior Member

    Messages:
    1,123
    If you can't get yourself to argue what you claim, I won't do it for you.
    EB
     
  17. Baldeee Valued Senior Member

    Messages:
    2,122
    Valid doesn't equate to being good, though, as I'm sure you agree.
    One can create valid syllogisms that are of no value at all beyond being expressions of their form.

    The way the argument is worded seems to exchange acceptability of the premises for lowering the strength of the conclusion.
    And because of what would seem to be in more classical deductive logic a case of undistributed middle, the conclusion is far weaker in terms of probability than the merely the product of the premises.

    For example, in classical logic one may argue:
    A is the state of B.
    C is the state of B.
    Therefore A is C.
    This is valid, and if you apply probability to the premises - as in their chance of being true - you can arrive at the probability of the conclusion being true.
    So if each premise has 50% chance of being true, the conclusion has a 25% chance.

    If we rewrite the premises to build in the sense of probability then:
    A may be the state of B.
    C may be the state of B.
    Therefore A may be C.
    Valid, as before, and the probability of A actually being C can be calculated in the same way.

    However, if you look at what would be a case of undistributed middle:
    A is a part of B.
    C is a part of B.
    Therefore A is C.
    This is invalid.
    One could change the conclusion to "Therefore A may be C" and it would seem to be now be valid.
    But here we have a conclusion with an inherent probability from premises that are certain, and is thus weaker than a valid argument that is certain in its conclusion.

    In this same way the conclusion of speakpigeon's argument is weaker than merely the product of the probability within the premises.
    How much weaker?
    Due to the premises themselves referring to "unknown part", it is not possible to say, so at best we can say that the "may" within the conclusion is referring to a non-zero probability, irrespective of the confidence in the first premise.

    As such, while the premises may be more readily accepted due to the probability inherent within them, the conclusion seems incredibly weak.
    Children have a habit of doing that.
    Dismissing him isn't an issue: his manner will result in us doing that in due course.
    As yet he's offered nothing to dismiss in terms of content.
    It still needs strengthening with regard the various references to "a group of" otherwise the conclusion is weak, as per above.
    But the argument doesn't get you there with any confidence.
    Sure, the strong theory would be that what we do is determined by the conscious mind.
    At the moment the argument results in merely a non-zero possibility of it.
    And in my view if that's all that can be said then it is weak.
     
  18. Speakpigeon Valued Senior Member

    Messages:
    1,123
    Unsupported opinion and all logicians would disagree. All valid syllogisms compel you to accept the conclusion of true premises. Once validity is recognised, that's it. All pairs of true premises engage our rationality to accept the conclusion. That has to be very good.
    You're merely making stuff up. There are no probabilities at all associated with the argument, as it is worded, and even if you substitute A, B and C with concrete things, as in my example with the conscious mind.
    You're merely making stuff up. There are no probabilities at all associated with the argument.
    You're merely making stuff up. There are no probabilities at all associated with the argument
    Non-zero possibility?! What's that?!
    You're really making stuff up as you go.
    EB
     
  19. Baldeee Valued Senior Member

    Messages:
    2,122
    See how you introduced the qualification of true premises?
    I.e. You're arguing a straw man.
    Yes, once validity is recognised that is it, but it is only as good as the soundness of the premises in terms of making the argument good.
    With unsound premises you are left with nothing but an example of form.
    - All Quoots are Zargs.
    - Berz is a Quoot.
    - Therefore Berz is a Zarg.
    How is this good beyond being an expression of the form?
    Answer: it's not.
    End of.
    If you say "something may be the case" then you are asserting there to be a non-zero probability associated with it being the case, I.e. a degree of uncertainty.
    If you didn't intend to express uncertainty then you should use "is" instead of "may be".
    By using "may be" you are are saying that it could be the case, or it could not be the case.
    The likelihood of it being the case is indeterminate, but there is a non-zero probability of it being so.
    I.e. it can be conceived that in at least one possible world it is the case, even if it turns out not to be the case in our own.

    And by applying probability more mathematically one can clearly show how the indeterminate possibility in your conclusion is much weaker than the indeterminate possibility in your first premise.

    And even if you do substitute for concrete things there remains probability associated with it.
    To wit:
    My initials may be written on a brick my house is made of.
    The letters ZZZ are written on a brick my house is made of.
    Therefore my initials may be ZZZ.

    Concrete examples, and the argument is valid, but there is inherent probability not only in the first premise (unless you can say with certainty one way or another - but then why use "may" when "is" or "is not" would be more accurate?), but also with the distribution of the middle term (brick my house is made of).
    If my house is made of 1 brick then the two bricks referred to are equivalent, and it is with certainty that they are referencing the same thing.
    If my house is made of 2 bricks then the inherent probability that they are referring to the same brick is 50%.
    With 100 bricks it is 1% etc.
    Thus the conclusion not only has the inherent probability associated with the probability of my initials being on a brick at all (i.e. Premise 1) but now the additional probability associated with the bricks referred to in the first two premises being the same one.
    Still keeping up?
    My mistake, that should have read non-zero probability.
    I would correct it but the time limit has expired.
     
  20. Speakpigeon Valued Senior Member

    Messages:
    1,123
    A valid argument produce a true and meaningful conclusion by substituting the terms of the arguments with words referring to actual things and in such a way as to make the premises true. There is an infinity of such substitutions, so that there is an infinity of true and meaningful conclusions a valid argument can produce.
    For example:
    All men are living things.
    All living things are mortal.
    Therefore all men are mortal.
    There is an infinity of similarly true and meaningful conclusions a valid argument can produce.
    Simple, really. And people do that all the time. It's part of what we are and it helps us go through our day. So, Good? You bet. There is just an infinity of true and meaningful conclusions a valid argument can produce.
    This thread is about validity, not soundness. We don't care whether premises are probable or not.
    And "may" signals possibility, not probability. So, even the soundness of my argument is immune to your point about probability. It's just irrelevant.
    Sure, if we could assign a probability to premise 1, that would affect the probability of the conclusion.
    But the "may" signals possibility, not probability. So, even the soundness of my argument is immune to your point about probability. It's just irrelevant.
    And the conclusion is true.
    Probabilities depend on each specific example. We know a house is made of many bricks. Take an example where your initials may be written on one item among two.
    Your choice of an example involving one brick of a house isn't based on good logic. There is an infinity of examples where the probabilities would be 1.
    And my argument isn't about probability but about possibility. So, probabilities are just irrelevant.
    In my example about the conscious mind, we don't have any probability, assuming premise 2 is true. We only have possibility, and possibility is consistent with probabilities above zero including 1. That's why the argument works.
    You're making my point, thanks.
    You've just convincingly demonstrated that the notion of probability is only relevant to cases where we can assume a probability, such as that a house is made of many bricks.
    So, our point is only relevant to cases where where we can assume many "bricks". My example is immune from that because we have no probabilities regarding "a group of neurons", which may well be a small group or a large group. No probabilities. Only possibility.
    At last, something sensible.
    EB
     
    Last edited: Jan 21, 2019
  21. Baldeee Valued Senior Member

    Messages:
    2,122
    None of which counters anything I said.
    Your "good" relies on the premises being true.
    That an argument might be valid doesn't itself make the argument good.
    Until you can address that point, without resorting to the strawman of true premises, you're just being irrelevant.
    You might not care, and clearly you don't, but others do, others have raised the issue of the strength of the conclusion, and I am continuing that line.
    If you don't like it, don't respond to it.
    If you are illiterate enough not to see the inherent notion of probability within the term "possibility" then there is little hope for you.
    Something can be considered either necessary or possible, whether it exists in all conceivable worlds or only some of them.
    If possible then it is a matter of probability as to how likely it is to occur in a specific world.
    Probability is merely the ascribing of quantity to that likelihood, whereas possibility leaves it indeterminate.
    Since your argument deals only in possibility, and is thus valid, it remains the case that the possibility in the conclusion is far weaker than the possibility within the premises.
    I never said that the soundness was affected.
    I have said, and continue to say, that your argument sacrifices weakness in the conclusion by creating uncertainty within the premise, and that the weakness in the conclusion is actually greater than that introduced in the first premise.
    If one accepts the premises as true, yes.
    But it is a weak conclusion.
    Yes, the probability would be 50%.
    If there is but one brick, it would be 100%.
    But any more than two and the probability quickly disappears below 50% and asymptotes to zero.
    Sure, and far more orders of infinities where they are nearer zero.
    Just take the bricks in my house as an example: it takes one brick for the example to yield a probability of 1, yet beyond 2 bricks...?
    And you are ultimately looking to tie this back to "groups of neurons in the brain", so apologies if I example the issue with something far more easily quantified.
    Note that this is even before you take account of the probability inherent within the first premise.
    For validity, yes, that much is not disputed, and has not been.
    I am now talking with the grown ups (as far as being able to hold a civil discussion) and exploring the matter of how strong or weak the conclusion is, and why, even if it is ultimately valid.

    So if you want an argument that is valid but offers a weak conclusion, that is what you have.
    If you don't want to concern yourself with how weak your argument is, feel free not to respond.
    It seems valid, but remains weak precisely because it allows any probability above zero up to 1, but analysis of the middle term quickly demonstrates that it doesn't take many "groups" being considered for the probability to drop below 50%, and that's not including the uncertainty inherent in premise 1.
    The notion of probability remains applicable, which is why your's is an even weaker argument than where probability can actually be quantified, because with your argument it remains unknown.
    Your argument is so weak that at best we can say that the valid conclusion results in a non-zero probability.
    It is a stronger argument that can actually quantify that probability.
    And by making itself immune you make the conclusion weaker.
    This was my point earlier that you seem to make the premises as acceptable as true as possible but in doing so you sacrifice the strength of the conclusion.
    And one where the probability associated with the possibility can not be even remotely quantified is as weak as you can seem to get.
    So congratulations on that.
    I await the same from you.
     
  22. Speakpigeon Valued Senior Member

    Messages:
    1,123
    This thread is a poll on the validity of the argument. So, please vote first before you comment.
    And if you can't get yourself to vote, your posts are just a derail.
    Pascal's wager.
    Descartes would have appreciated.

    OK, the rest is just a repeat and we're not here to repeat ourselves.
    EB
     
  23. Yazata Valued Senior Member

    Messages:
    5,608
    Right. It just means that the conclusion follows from the premises such that if the premises are all true, then the conclusion has to be true too. If the premises aren't all true, the conclusion needn't be true either.

    In the case of these four threads, I'll quite happily accept that adopting a strong mind-brain identity theory in the philosophy of mind does seem to suggest that it's just as correct to say that a person's mind causes his or her volitional actions, as it is to say that his or her brain does. (The proposed theory has just equated them ex hypothesi for the sake of argument.)

    All this formal logic stuff just mystifies what might otherwise be a simpler point. How many of us are proficient in modal logic or prepared to do formal validity proofs? I know that I'm not. That's why I voted 'don't know' in the poll above. If Speakpigeon is so eager to have somebody demonstrate the validity or invalidity of his argument (four threads demanding it!!), then perhaps he needs to do it himself (if he can).

    I think that beneath all the formal-logic obfuscation, all that Speakpigeon seemingly wants to do is argue...

    1. Mind is identical to (state of brain) (That's the mind-brain identity theory)
    2. A person's behavior is determined by (state of brain)
    ________________________
    C. A person's behavior is determined by mind

    I don't know why he's laying it on so hard (four threads!). But like I said, I don't have any real objection to that argument. I've argued the same way in the past (see my posts in that never-ending free-will/determinism thread).

    I'm less prepared to opine on its formal validity. For one thing, we don't know that (state of brain) in #1 is the same state as (state of brain) in #2. (I think that to his credit, Sarkus first pointed out that problem several threads ago.) There are countless mental states mapped onto particular members of a set of brain states. And there are countless behaviors, mapped onto particular members of a different set of brain states. So pretty clearly we can't just treat "brain states" as if it was the middle term in an Aristotelian syllogism. The two sets might conceivably be entirely disjoint.

    In order to judge the argument's formal validity, we would have to look closely at its semantics, I think. And that's even before we address the modal stuff.

    It arguably does serve to express a basic philosophical argument about the metaphysics of what might be happening, but I can't speak with any assurance as to its formal validity.
     
    Last edited: Jan 21, 2019

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