• Do (A implies B) and (A implies notB) contradict each other?
    It depends upon the values given to the variables. — creativesoul

    Hello, creative. How are the fish hooks?

    It exactly does not depend on the values given to the variables. That's kinda the point of using variables - you get to put different things in and get the same result.

    So a+b = b+a regardless of what number you stick in to the formula, and a^(a→b)⊢b regardless of what statement you put in, too. Or so it is supposed to go.
  • Do (A implies B) and (A implies notB) contradict each other?
    ..we end up with ¬(a→(b∧¬b)), and this can't be read as "It is not the case that a implies a contradiction" — Lionino
    Why not? I'm not seeing the issue here.
  • Do (A implies B) and (A implies notB) contradict each other?
    So, since ¬◇(a→(b∧¬b)) would be read by many as "It is not possible that A implies a contradiction", is that the same thing as "It is necessary that not-A implies a contradiction"? — Lionino

    □¬(a→(b∧¬b)) would be "It is necessarily not the case that A implies a contradiction"
  • Do (A implies B) and (A implies notB) contradict each other?
    ↪Lionino


    Isn't it something like that "if it is not possible that A implies a contradiction, then A is necessarily true"?

    Or "If in no possible world A implies a contradiction, then A is true in every possible world"?
  • Do (A implies B) and (A implies notB) contradict each other?
    ↪flannel jesus
    Yep.

    ↪Lionino
    I gather you worked through this? Nice.

    ↪flannel jesus
    Leo does that sort of thing - claims you have said something you haven't, if it suits his purposes.
  • Do (A implies B) and (A implies notB) contradict each other?
    (It would seem that you are wrong in claiming that classical logic treats contradictions as false. — Leontiskos
    Again, no.

    Pasted-Graphic-1.png

    F's all the way down.
  • Do (A implies B) and (A implies notB) contradict each other?
    Here's another outright error.
    A reductio is not truth-functional. — Leontiskos

    Given a proof of B and ~B from A as assumption, we may derive ~A as conclusion — Lemmon

    Or if you prefer: φ→(ψ^~ψ)⊢~φ

    Or if you think it is only truth-functional if it fits in a truth-table,
    Pasted-Graphic.jpg

    At some point one has to realise that Leo has such an odd notion of logic that he is unreachable.
  • Do (A implies B) and (A implies notB) contradict each other?
    I have already responded to these charges. — Leontiskos
    Maybe not as much as you think.

    At this point you either have an argument for "∴¬A" or you don't. Do you have one? If not, why are you still saying that ¬A is implied? — Leontiskos
    I'm not seeing a salient point here. Pretty demonstrably, you have made a series of claims that have been shown to be in error.

    At this stage it is unclear what your general point concerning "metalogic" might be, beyond an "esoteric mystery".
  • Do (A implies B) and (A implies notB) contradict each other?
    ...but they have no way of knowing when their logic machine is working and when it is not. — Leontiskos

    "Machine", singular. So back to my point, that
    Each of these systems sets out different ways of dealing with truth values. How the truth value of a contradiction is treated depends on which of these systems is in play. — Banno
    and so
    Asking, as you do, how to treat the truth value of a contradiction apart from the system that sets out how a truth value is to be dealt with makes little sense. — Banno

    What I hope to have done over the last page is to show that you are mixing logics, resulting in your own confusion. You do not succeed in showing that "...something and its negation can both be false" in classical propositional logic.
  • Do (A implies B) and (A implies notB) contradict each other?
    A reductio is as much a proof in classical propositional logic as is modus tollens. — Banno
  • Do (A implies B) and (A implies notB) contradict each other?
    ↪Leontiskos
    I seem to have reduced you to reciting gobbledygook. My apologies.
  • Do (A implies B) and (A implies notB) contradict each other?
    ↪Leontiskos
    What?

    The reductio shows that A→(B∧¬B)⊢~A. As
    ↪hypericin
    pointed out.

    It could equally be used to show that A⊢~A→(B∧¬B); but that was not the issue you raised.

    Edit: correction
  • Do (A implies B) and (A implies notB) contradict each other?
    a reductio is an indirect proof which is not valid in the same way that direct proofs are. — Leontiskos
    A reductio is as much a proof in classical propositional logic as is modus tollens.
    In your conclusion you reject (2) instead of (1). Why do you do that? — Leontiskos
    Simply because I matched your example, which has
    A→(B∧¬B)
    ∴ ¬A     — Leontiskos
    and not ~A⊢A→(B∧¬B).


    Again, don't blame me for your problems.

    edit: corrected A⊢A→(B∧¬B)/~A⊢A→(B∧¬B)
  • Do (A implies B) and (A implies notB) contradict each other?
    This answer proves that you do not understand the questions that are being asked. If one wants to understand what is being discussed here they will be required to set aside their ready-made answers. — Leontiskos
    Ah, so it's an esoteric mystery. :wink:

    Nowhere in that post do you affirm (B∧¬B).
    — Banno
    I never said I did. Read again what you responded to. "     — Leontiskos
    The consequent is (B∧¬B)
    The negation of the consequent is ~(B∧¬B)
    Affirming the negation of the consequent is ⊢~(B∧¬B)
    if you don't affirm the negation of the consequent, you affirm (B∧¬B).

    Nowhere do you do this. Nowhere in these examples is it the case that "...something and its negation can both be false". That is, you do not show that somehow classical propositional logic affirms both
    ~(B∧¬B) and (B∧¬B).

    Indeed, while your second example is a case of modus tollens, this is not clear for the first.

    (The second is
    1. A→(B∧¬B) assumption
    2. ¬(B∧¬B) assumption
    3. ¬A 1,2 modus tollens)

    Modus Tollens tells us that "Given ψ→ω, together with ~ω, we can infer ~ψ". In the first example you do not have ~ω. It might as well be a Reductio, although even there it is incomplete. It should be something like:

    1. A→(B∧¬B) assumption
    2. A assumption
    3. B∧¬B 1,2, conditional proof
    4. ~A 2, 3 reductio

    ans so A→(B∧¬B)⊢~A

    _________________
    And yes, A→FALSE is not well-formed in classic propositional logic. So if your first example is to be understood as using MTT, it is not an example from classic propositional logic. Again, that is not something I have supposed, and you misattribute it.

    Which takes us back to what I pointed out earlier - you are mixing various logical systems. The equivocation here is on your part. Don't put the blame for your poor notation on to me.

    (Edit: Actually, Open Logic builds propositional logic from, amongst other things, ⊥. (Definition 7.1). And v(⊥) = F - the valuation of ⊥ is "false" - in Definition 7.15. In this sort of build, φ → ⊥ could be well formed. @TonesInDeepFreeze might be able to clarify.)
  • Do (A implies B) and (A implies notB) contradict each other?
    I've been ignoring Tones... — Leontiskos
    Your loss.

    I think the thread shows that this is not true. — Leontiskos
    Then the thread is in erorr. (p ^ ~p) is false in classical propositional logic.

    The problem here is that your answer lacks specificity — Leontiskos
    Not at all. A contradiction in first order predicate logic is an expression of the form (φ ^ ~φ). It is not an expression of the form ~φ. The lack of specificity here is your attempt to make use of a notion of contradiction that is not found in classical propositional logic.

    How is it that something and its negation can both be false? — Leontiskos
    Whether or not we affirm the negation of the consequent... — Leontiskos
    Nowhere in that post do you affirm (B∧¬B).
  • Do (A implies B) and (A implies notB) contradict each other?
    So far as I can see, it was you who proffered
    the notion of contradiction in its entirety — Leontiskos
    I'm puzzling over what this might be.

    pray tell how a contradiction is to be dealt with in classical propositional logic? — Leontiskos
    As has been explained at length, in classical propositional logic contradictions are false.

    ...you seem to be implying that, according to the logic, one person is right and one person is wrong when they disagree about whether a given instance of (b∧¬b) should be treated as a proposition/variable or as a simple truth value. — Leontiskos
    Another example of your practice of misattributing stuff to your interlocutors - as you did with
    ↪TonesInDeepFreeze
    . What I said is that the disagreement here is as to which system is in play. Hence there is no absolute answer as to which view is "right".
  • Do (A implies B) and (A implies notB) contradict each other?
    A contradiction is a contradiction. It is neither true nor false. It is the basis for both truth and falsity. — Leontiskos
    This seems to be the source of your difficulties.

    As has been explained, in classical logic a contradiction is false. Dialetheism considers what must be the case if some contradictions are considered to be true.The various paraconsistent logics consider what must be the case if A, ~A ⊨ B; that is, if contradictions are not explosive.

    All this to say that there are various ways to treat truth values, each with its own outcomes. (the list is not meant to be exhaustive - there are other options)

    Each of these systems sets out different ways of dealing with truth values. How the truth value of a contradiction is treated depends on which of these systems is in play.

    Asking, as you do, how to treat the truth value of a contradiction apart from the system that sets out how a truth value is to be dealt with makes little sense. It does not make much sense to speak of "the notion of contradiction in its entirety".
  • Do (A implies B) and (A implies notB) contradict each other?
    "The car is green" and "The car is red" is not a contradiction. But if we add the premise: "If the car is red then the car is not green," then the three statements together are inconsistent. That's for classical logic and for symbolic rendering for classical logic too. — TonesInDeepFreeze
    Yep. Worth noting that parsing this correctly shows that the original was incomplete - implied nothing.

    More generally, parsing natural languages in formal languages, while not definitive, does occasionally provide such clarification. That's kinda why we do it.

    Also worth noting that (A → B) ^ (A → ¬B), while not a contradiction, does imply one, given A:

    (A → B) ∧ (A → ¬B)→(A→(B∧¬B))

    So in answer to the OP
    Do (A implies B) and (A implies notB) contradict each other? — flannel jesus
    Taking "implies" as material implication, they are not contradictory but show that A implies a contradiction.

    I'd like to see what formation rules you come up with. — TonesInDeepFreeze
    I had the same thought when I read that. It's wellformed. It is also invalid: A∧¬A

    This thread is bringing out some rather odd attitudes towards the relation between logic and natural languages.
  • A Case for Moral Anti-realism
    ...but are refusing to make sense of them... — Michael

    An obligation is simply something you ought to do. Your inability to make sense of obligation is not our problem. Eventually this reduces to a personal psychological issue.

    But I wonder how widespread this inability is, and what place it plays in odd political ideals.

    Edit: I was unable to make anything of this:

    So the proper comparison would be:

    1. You were given an order
    2. Do this

    I have no problem with (1). Is this all "you ought do this" means?     — Michael
  • A Case for Moral Anti-realism
    1. You ought do this
    2. Do this
    The first appears to be a truth-apt proposition, whereas the second isn’t. But beyond this appearance I cannot make sense of a meaningful difference between them. The use of the term “ought” seems to do nothing more than make a command seem like a truth-apt proposition.     — Michael

    You conclude that there are no such thing as obligations.

    Compare:
    1. You were asked to give an answer to what we get when we add six and five.
    2. What is six and five?
    The first appears to be a truth-apt proposition, whereas the second isn’t. Beyond this appearance is there a meaningful difference between them? Will you say that the use of the term "asked" seems to do nothing more then make a question seem like a truth-apt proposition?

    Do you also conclude that there are no such things as answers?

    I think not. Answers are brought about by asking questions, just as obligations are bought about by (amongst other things) commands and promises.

    Or this:
    1. She greeted you
    2. "Hello"

    The use of the term "greeted" seems to do nothing more than make "Hello" seem like a truth-apt proposition?

    Will you conclude that there is no such thing as a greeting?

    We bring answers and greetings into existence; they are things we do with words, and a part of our social life. As are obligations.

    Anscombe argued against the moral "ought" found in ethics, but was very clear that there was a place for "non -emphatic ought" apart from a moral sense:
    I will end by describing the advantages of using the word "ought" in a non-emphatic fashion, and not in a special "moral" sense; of discarding the term "wrong" in a "moral" sense, and using such notions as 'unjust'. — MMP, p.13
    There follows a passionate defence of the justice. Your girlfriend did you an injustice when she reneged on the promise she made. It was an injustice because she undertook an obligation to you, which she did not fulfil. One ought fulfil one's obligations, since that is what an obligation is.

    To my eye, this and my last post answer your objection.

    Heading back a few days and a few pages, this was all in answer to your attempted defence of
    There is nothing that exists beyond the act. — AmadeusD
    I will maintain that questions, greetings and obligations are examples of things that exist "beyond the act", along with property, currency, marriage, incorporation, institutionalisation, legality... and a few other things.
  • Banno's Game.
    Well, I'm only too pleased to provide you with the raw material.
  • Banno's Game.
    But if you want to do something interesting in mathematics, or the philosophy of mathematics, this is not the way to go about it. — unenlightened

    But yet again, here you are…. :wink:
  • A Case for Moral Anti-realism
    I don't think so. — Leontiskos
    I re-read MMP this morning and was again in awe of the complexity of her thinking. Better not to assume, so I went with "may". She almost certainly would have had much more to say on the issue, and I don't think she had a soft spot for Austin.
  • Banno's Game.
    So the thread itself is badly set up as a game that doesn't have much interest or significance — unenlightened
    And yet it lives, five years on.

    If the King is in check then the other player can swipe away the peices, but this is rude — Moliere

    Some rules ruin the game, others make it more interesting.

    One way to fix the game might be to oblige players to list the rules they are making use of, and hence have them construct a tree.

    Hence,

    Players take turns to add rules. — Banno
    The sum of any two integers is zero. — jgill
    The product of any two integers is omega. (Where omega is the first number bigger than any integers). — Pfhorrest
    Then integers takes on a use that is peculiar to this game. — Banno
    Conclusion:
    0=Ω — Banno
    Let's call them Gill integers. — Banno
    Let's call them Fhorrest Integers. — Banno

    Question: prove that Fhorrest integers are the same as Gill integers

    Theorem 1: Any two integers are the opposite of each other
    a=-b     — Lionino
    (from JGill's rule)
    Conclusion:
    There is only one integer, 0. — Lionino

    An adding: If there is only one integer, then Fhorrest integers are the same as Gill integers.

    New rule: There is an integer that is neither a Fhorrest integers nor a Gill integer.

    Your turn...
  • The Principle of Double Effect
    ↪Moliere
    One of the failings of 'mercan English is its inability to distinguish it's ass from its arse.
  • The Principle of Double Effect
    ↪Bob Ross
    Yeah, good point. I did that too quickly.
  • A Case for Moral Anti-realism
    Which still needs to be explained. Why won't you ever explain this? — Michael

    I think I have explained the situation at some length, but perhaps more can be said.

    Thanks for this topic, one more interesting than most. I think you make an ostensible point, and I suspect Anscombe may have agreed with you, but I think there is more going on here that needs attention.

    In Modern Moral Philosophy Anscombe talks of a sort of "ought" that has a "...special so-called 'moral' sense... a sense in which they imply some absolute moral verdict". From about p.11 she lists and dismisses various "standards" which might permit one to infer an ought. The list includes the following:
    There is another possibility here: "obligation" may be contractual. Just as we look at the law to find out what a man subject to it is required by it to do, so we look at a contract to find out what the man who has made it is required by it to do. Thinkers, admittedly remote from us, might have the idea of a foedus rerum, of the universe not as a legislator but as the embodiment of a contract. Then if you could find out what the contract was, you would learn your obligations under it. Now, you cannot be under a law unless it has been promulgated to you; and the thinkers who believed in "natural divine law" held that it was promulgated to every grown man in his knowledge of good and evil. Similarly you cannot be in a contract without having contracted, i.e. given signs of entering upon the contract. Just possibly, it might be argued that the use of language which one makes in the ordinary conduct of life amounts in some sense to giving the signs of entering into various contracts. If anyone had this theory, we should want to see it worked out. I suspect that it would be largely formal; it might be possible to construct a system embodying the law (whose status might be compared to that of "laws"of logic): "what's sauce for the goose is sauce for the gander," but hardly one descending to such particularities as the prohibition on murder or sodomy. Also, while it is clear that you can be subject to a law that you do not acknowledge and have not thought of as law, it does not seem reasonable to say that you can enter upon a contract without knowing that you are doing so; such ignorance is usually held to be destructive of the nature of a contract. — Anscombe, Modern Moral Philosophy, p.12
    I've bolded the part that caught my eye. I think Austin and Searle are embarked on just the enterprise described. But they are not interested so much in prohibiting murder and sodomy - so far as I know - so much in providing a description of the social role played by our utterances, of how we do things with words.

    Your girlfriend may well have intended to marry you, and this may have been so were it expressed or not. But she went further, making a promise, and thereby she also committed to marrying you, undertook doing so, binding herself to marrying you and placed herself under an obligation.

    And all of that is a result of her having made the promise. It was an act done by her in making the utterance. One amongst many, many other acts we perform in making utterances - naming ships, asking questions, issuing demands or orders - and undertaking obligations.

    We enter into these "contracts" by our participation in, and understanding of, these social facts.

    Now I don't think this will convince you. You have a leaning towards notions of individualism that lead you to deny such social facts. But for me that's neither here nor there.

    There is something of Moore's paradox here, the insincerity that English speakers see in "it is raining but I do not believe that it is raining". What would we make of your girlfriend saying "I promise to marry you, but I do not undertake an obligation to marry you"? Perhaps only that she has not understood what it is to promise.
  • Do (A implies B) and (A implies notB) contradict each other?
    I'm not sure what you mean: I was considering the two statements separately and it still seems to me, that regardless of the soundness or relevance of their content, that, taken informally as statements, they contradict one another. — Janus
    Note
    ↪unenlightened
    's testimony.
  • The Principle of Double Effect
    I would say that one’s duty to what is good comes first... — Bob Ross
    Looks a lot like deontology to me. You are suggesting that we ought be virtuous because it is our duty.

    That's not how I understand virtue ethics. It's claim is more like that we ought be charitable, we ought be courageous, we ought be forgiving, and that's an end to it; there is no further step to duty, no "because".
  • A Case for Moral Anti-realism
    She intended to marry me. That’s all there is to it. — Michael
    Well, no. She also committed to marrying you. She did not just intend to do so, she undertook doing so. She said she would. She bound herself to you. She placed herself under an obligation.

    But we are now in the usual tediously circular posture of so many of our chats. No blame, just no progress.
  • The Principle of Double Effect
    ↪Fire Ologist
    Cheers. I don't see anything here that has not already been addressed.

    Have a read of PI §201 and consider if a single principle ever implies a certain action, or whether a given action can be explained by any principle, given suitable ad hoc hypothesises.

    Or look at the discussion between Lakatos and Feyerabend about what constitutes a rational methodology, and apply it to choosing what to do.

    Or consider how the Duhem–Quine thesis might apply to explaining an action in terms of a principle.
  • A Case for Moral Anti-realism
    my girlfriend promises to marry me, but several weeks later changes her mind.

    Is my girlfriend obligated to marry me?     — Michael
    Yes. She undertook to marry you. Either she reneged on that obligation or you allowed her to leave it.

    Just because obligations cease to be doesn't mean they never were, right? — Moliere
    yep.
  • A Case for Moral Anti-realism
    Yes. I've been very clear on that. This is true even using Searle's definition of a promise. Your claim that if S promises to do A then S has undertaken an obligation to do A is as of yet unsupported. — Michael
    Well, what is a promise, if not the undertaking of an obligation?

    Presumably, nothing, and there are no such things as promises.

    Yet there are promises.

    Which forms a neat reductio to show that you are mistaken.
  • A Case for Moral Anti-realism
    There's sunshine, for the first time an a few weeks, so later.
  • A Case for Moral Anti-realism
    I am saying that Searle's conditions – even with conditions (7) and (8) – do not entail that when one promises to do something one is agreeing to undertake an obligation. — Michael

    So what do you think - if someone undertakes an obligation, are they thereby obligated?

    If so, then you seem to be claiming that making a promise is not undertaking an obligation. And that does not appear right.
  • A Case for Moral Anti-realism
    Even with (8) it doesn't count as undertaking an obligation. — Michael
    If you do not agree that someone who undertakes an obligation is not thereby obligated, then I have no more to offer you.
  • A Case for Moral Anti-realism
    Failure to commit.
  • A Case for Moral Anti-realism
    Searle's conditions 1-6 that you linked me to. — Michael

    Without (8), the promise does not count as undertaking an obligation. And that, apparently to all except your good self, is the very point of making a promise.
    I don't even know what an obligation is, if something more than a command. — Michael
    Perhaps an obligation is a binding of an individual to the performance of an act. It can be brought about by, amongst other things, promising and commanding.

    If you do not consider yourself to be bound to enact those things that you promise, then it seems to me that you have simply misunderstood the nature of making a promise.
  • A Case for Moral Anti-realism
    Searle’s conditions 1-6 seem sufficient. But again, even 7 and 8 don’t entail the existence of an obligation. — Michael

    Sorry - can you give an account of what making a promise is, that does not involve placing oneself under an obligation? Is it your contention that one ought not keep one's promises?

    The problem with this claim is that I cannot make sense of the difference between “do this” and “you ought do this”. At best it just claims that “do this” entails “do this”. — Michael
    Then perhaps you ought not get a job waiting on tables? It is beginning to look as if you are describing a peculiarity of your own psychology rather than something of general interest.

    It appears we disagree as to the nature of "obligation".
  • A Case for Moral Anti-realism
    I’m asking you to justify this claim. — Michael
    Well, that's what promising is. I'm at a loss to explain it any further.

    Can you offer an alternative meaning for "promise"

    Here are two sentences:

    1. You ought do this
    2. Do this

    The first appears to be a truth-apt proposition, whereas the second isn’t. But beyond this appearance I cannot make sense of a meaningful difference beyond them. The use of the term “ought” seems to do nothing more than make a command seem like a truth-apt proposition.     — Michael
    Oh, very nice. I like that.

    As a first response, if you are given a command, by someone with the authority to command you, then "do this" does imply "you ought do this".

    If your boss tells you to take the tray to table five, you ought take the tray to table five.

    It does seem that you are ignoring an important social aspect of language: that we do things with words, including placing ourselves and others under certain obligations.
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