Yeah, this is weird stuff. Much of it goes back to what I said earlier, "When we talk about contradiction there is a cleavage, insofar as it cannot strictly speaking be captured by logic. It is a violation of logic" ().

A contradiction is a contradiction. It is neither true nor false. It is the basis for both truth and falsity.

Thus one can’t pretend to represent a contradiction in the form of a proposition and then apply the LEM to it as if it makes sense to call a contradiction true or false. As soon as a reified contradiction is allowed to enter logical discourse, a wrinkle is introduced which can never ultimately be ironed out. It is hazardous to try to answer the OP's question with a formal proof, because formal proofs cannot represent the notion of contradiction in its entirety. Granted, natural language also cannot do this, but it is at least capable of not-trying to do this. It is capable of apophaticism.

The tokens "(b∧¬b)" and "¬(b∧¬b)" are neither true nor false if by 'true' and 'false' we are talking about something that goes beyond validity and invalidity (i.e. something which the logical system presupposes and is transcended by). The first is invalid but not false. The second is valid but not true. Too often in logic we conflate validity with truth.

But, as my second phrase in this post, I got confused as to whether ¬(a→(b∧¬b)) means a variable that is in contradiction with (a→(b∧¬b)) or simply that (a→(b∧¬b)) is False. — Lionino

Yes, exactly.

¬(a→(b∧¬b)) is only ever True (meaning A does not imply a contradiction) when A is True. But I think it might be we are putting the horse before the cart. It is not that ¬(a→(b∧¬b)) being True makes A True, but that, due to the definition of material implication, ¬(a→(b∧¬b)) can only be True if A is true. — Lionino

Right, one could approach it from two different directions. This is what I was trying to get at earlier, "I think Lionino was somehow seeing this through the overdetermination of the biconditional with respect to ¬¬A" ().

Material implication is supposed to prescind from the reason why the implication is true or false, and therefore it is supposed to prescind from causal and temporal considerations. But in this case the temporal order in which one evaluates a complicated material conditional affects its outcome,* and I can't see how this would ever happen without having that contradiction in the "interior logical flow" of the argument. Similarly, in my last post:

When are we supposed to reduce a contradiction to its functional truth value, and when are we supposed to let it remain in its proposition form? The mind can conceive of [claims] like (b∧¬b) and ¬(b∧¬b) in these two different ways, the manner in which we conceive of them results in different logical outcomes, and symbolic logic provides no way of adjudicating how the [claims] are to be conceived in any one situation. — Leontiskos

* Or perhaps it is not the temporal order, but rather the simple decision of whether to conceive of the different things as propositions or as truth values. A problem of ordering rather than temporal ordering, as it is the combinations that affect the outcome rather than the succession-order in which they are applied. If this is the nub then the problem is, as I said earlier, that truth-functional logic does not give us any instruction for how to handle contradictions. ...and again, there is no such thing as "handling contradictions," so this is to be expected. The problem is that we are trying to handle something that cannot be handled.

Here is something I wrote when my internet was out, and before I was able to read this post of yours. I will read what you have written after posting this (and therefore there may be overlaps or redundancies):

———

If (a→b)∧(a→¬b) is False, ¬A is False, so A can be True or not¹. — Lionino

Note, too, how the LEM operates here.

On the LEM, (a→b)∧(a→¬b) must be either true or false, and therefore a→(b∧¬b) must be either true or false. If a→(b∧¬b) is true then ¬a must be true and (b∧¬b) must be indeterminate. It must be this way in order to avoid affirming the contradiction (and never mind the odd question of whether, in this case, saying “¬a must be true” is the same as saying “a must be false”).

But on the other side of the LEM, if a→(b∧¬b) is false then by material implication (a) must be true and (b∧¬b) must be false. This is different from (b∧¬b) being indeterminate. It is to affirm ¬(b∧¬b), which is the same as (¬b∨b) with an inclusive-or. The inclusive-or provides the second-order possibility of a true contradiction.

Another way this comes out is seen by comparing the truth table of (p→q) with the truth table of a→(b∧¬b). If you run the table “forward,” by using the value of (b) to compute the value of (b∧¬b), then (b∧¬b) is always necessarily false. But if you run the table “backwards,” by using the value of (p→q) to compute the values of (p) and (q), then in that singular case where the entirety of the conditional is false we get (a ^ ¬(b∧¬b)), which again results in the inclusive-or (¬b∨b).

In one way, in saying that the inclusive-or is true we are admitting the possibility that both disjuncts could be true, which would be impossible. Put differently, negating this conjunction results in an exclusive-or rather than the usual inclusive-or, just as affirming the special conditional of (a→(b∧¬b)) results in (a) automatically being false, even though there is obviously no rule that ((p→q)→¬p). Special cases and special exceptions are popping up.

What is happening, I think, is that the two different kinds of falsity are coming into play, for there are two different ways of calling (b∧¬b) false. We can mean that it is false inherently, even without a negation (and this is reflective of the first argument I gave <here>).* Or else by saying it is false we can mean that we logically negate it, viz. ¬(b∧¬b) (and this is reflective of the second argument I gave <here>). When are we supposed to reduce a contradiction to its functional truth value, and when are we supposed to let it remain in its proposition form? The mind can conceive of propositions symbol-strings like (b∧¬b) and ¬(b∧¬b) in these two different ways, the manner in which we conceive of them results in different logical outcomes, and symbolic logic provides no way of adjudicating how the propositions symbol-strings are to be conceived in any one situation. When we introduce contradictions into the logic—even in minor ways such as in the consequents of conditionals—the logic becomes underdetermined. Different people are legitimately interpreting the propositions symbol-strings in different ways.

* This is reflective of what I have been calling “falsity incarnate”

What is the definition 'analogical equivocity'? — TonesInDeepFreeze

It is the kind of equivocity present in analogical predication, where a middle term is not univocal (i.e. it is strictly speaking equivocal) but there is an analogical relation between the different senses. This is the basis for the most straightforward kind of metabasis eis allo genos. The two different senses of falsity alluded to above are an example of two senses with an analogical relation. I was using the term earlier because I believe @Count Timothy von Icarus has an understanding of it.

I know you want a strict definition, but the wonderful irony is that someone like yourself who requires the sort of precision reminiscent of truth-functional logic can't understand analogical equivocity or the subtle problems that attend your argument for ¬A. As we have seen in the thread, those who require such "precision" tend to have a distaste for natural language itself.

Isn't this a fairly big problem given that (¬¬A↔A)? I take it that this is the same thing I have pointed out coming out in a different way? Namely the quasi-equivocation on falsity? — Leontiskos

Compare:

• A→(B∧¬B)
• ∴ ¬A

With:

• A→(B∧¬B)
• ¬(B∧¬B)
• ∴ ¬A

Whether or not we affirm the negation of the consequent, the antecedent still ends up being false. In the first case the consequent is pre-false, in the second case our explicit negation makes it false. In the first case it is treated as "falsity incarnate," whereas in the second it is treated as a proposition. This demonstrates the analogical equivocity with respect to falsity that I pointed out earlier, with help from . I think Lionino was somehow seeing this through the overdetermination of the biconditional with respect to ¬¬A, but it's slippery to grab hold of.

Note that we could also do other things, such as treat the second premise as truth incarnate, but this is harder to see:

• A→(B∧¬B)
• ¬(B∧¬B), but now conceived as "true"
• ∴ ¬A does not follow

...that is, if we conceive of the consequent as a proposition and the second premise as truth incarnate, then ¬A does not follow from the second premise (or from the consequent, absent a premise that negates the consequent qua proposition).

-

Around a third of folk hereabouts who have an interest in logical issues cannot do basic logic. — Banno

And about two thirds of folk hereabouts who are good at manipulating symbols "have no way of knowing when their logic machine is working and when it is not" ().

Aristotle always wins in the long run, as he could both use the machine and understand when it was misbehaving. :wink:

If (a→b)∧(a→¬b) is False, ¬A is False, so A can be True or not¹. — Lionino

But (a→b)∧(a→¬b) being False simply means that A does not imply a contradiction, it should not mean A is True automatically. — Lionino

Isn't this a fairly big problem given that (¬¬A↔A)? I take it that this is the same thing I have pointed out coming out in a different way? Namely the quasi-equivocation on falsity?

...Or is it simpler: ¬(a→(b∧¬b)) → a

Back to material implication:

As noted in my original post, your interpretation will involve Sue in the implausible claims that attend the material logic of ~(A → B), such as the claim that A is true and B is false. Sue is obviously not claiming that (e.g. that lizards are purple). The negation (and contradictory) of Bob's assertion is not ~(A → B), it is, "Supposing A, B would not follow." — Leontiskos

Given material implication there is no way to deny a conditional without affirming the antecedent, just as there is no way to deny the antecedent without affirming the conditional.

- He confuses what is achievable with what is deemed to be achievable in the same way that he earlier confused what is wrong with what is deemed to be wrong in the conversation about penalty/punishment. This is standard Moorean confusion.

- Thanks Lionino. Good reminders and clarifying points.

Edit: I underestimated your post. Like your first post, this is far above and beyond anything else that is occurring in this thread.

Much like it would be rational for me to appeal to the Bible if he were a Christian. But the Bible is still bullshit. — Michael

The Bible has a very high view of promising, a very high view of God's word (dabar):

So shall my word be that goes forth from my mouth;
it shall not return to me empty,
but it shall accomplish that which I purpose,
and prosper in the thing for which I sent it. — Isaiah 55:11 RSV

God's word is associated with his power. Why? Because the one who has power over his word is the one who has power over the future. It is the one who can make and fulfill promises who has power over the future. The one who is not able to make and fulfill promises has no power over himself or his surroundings, and he a fortiori has no power of the future. He is a shitty man:

Why is it bad to go back on promises, not only for others but also for oneself? It is bad because it is to be a shitty man, in the same way that to continually try to do something and fail at it is to be a shitty man. "By promising he directs what he himself is to do for another," and someone who continually reneges or simply fails in his promises is a failure. He is unable to direct himself. He is unable to do what he promises—and yes, also intends—to do. To fail to understand why promises involve obligations is a bit like failing to understand why reaching out to turn on the light involves turning on the light. "If it turns on, it turns on. If not, not. It has nothing to do with my reaching out." :scream: — Leontiskos

Aka: everybody is a realist when they walk out of the door. — Lionino

Yep. :up:

Because he told me to, and it's rational to pay less if the person asking you for money asks for less. — Michael

Then suppose you invoke the promise and he says, "Oh sorry, I forgot about that. Never mind."

Is he being irrational in this? Is he deluded and engaged in bullshit?

You say that his word is good enough to write the check for $975, but it is not good enough for you to invoke when he says you underpaid. You are contradicting yourself. You wrote the subsidized check on the basis of a promise - a real promise that involved obligations. Without those obligations it would make no sense to write the subsidized check, and given the promise it makes no sense not to invoke it when he says you underpaid.

The point here is not that the landlord must, of absolute necessity, honor his promise. That is a strawman form of obligation. The point is that it is rational for him to do so, and therefore it is rational for you to invoke the promise when he says you underpaid, and therefore it is rational for you to write the check for $975 in the first place.

This sort of thing happens all the time in real life. Compare this to a different person who writes a check for $975 for no reason. Do they have recourse? Of course not. They are in an entirely different situation. The only difference between the two cases is an obligation.

If there's reason to believe that it will work then yes. Much like it would be rational for me to appeal to the Bible if he were a Christian. But the Bible is still bullshit. — Michael

If you think the obligation is bullshit then how can you tell me that it was rational to pay him $975?

He told me to only pay him $975. So I believed that he is only expecting me to pay him $975. So I only pay him $975. — Michael

That's right, and so I ask again: would it be rational for you to invoke his promise when he tells you that you underpaid?

No. I was told to only pay $975 by my landlord, so that's what I did. — Michael

Right, but how would it be rational to depend on his promise if obligations don't exist? If it is rational to write the check for $975, then it must be plausible that reminding him of his promise will produce an effect.

Because, like you, he might believe in obligations. — Michael

So was it irrational to write the check for $975 rather than for $1000? Are you claiming that you would never have written the check for $975?

Yes, if I thought it would work. — Michael

And why is it plausible that it might work? Why would this move plausibly convince him to do as you wish?

Perhaps, and to convince him not to ask me for more money? — Michael

So you would invoke his promise in order to convince him that he should not require an additional $25?

I don't understand what kind of answer you want to a question like that. — Michael

I am wondering if I have recourse. What would you do in that situation? Would you invoke the promise he made? Why?

Speak to a lawyer. — Michael

Whenever your position falls apart you bury your head in the sand.

I tell my landlord that I replaced the furnace filters. He tells me, "Thanks, go ahead and deduct that from your rent." At the beginning of the next month I pay $975 rather than $1000 for my rent. My landlord informs me that I have underpaid, as the rent is $1000. Do I have recourse? Why?

People use the phrase "I promise to do so-and-so". That's all a promise is; the use of those words with honest intentions. — Michael

Honest intentions to do what!? This completely begs the question.

Do you admit that promises have an enormous impact on day to day life?

And they all just baselessly assert "promises are more than just intentions". There's no justification for this assertion... — Michael

Oh really? So when I tell my friend, "I intend to marry that woman over there," who holds my promise? Who is the promisee? You haven't even figured out that a promise involves a relation between two people and an intention does not. You seem to be clueless as to what a promise is.

No there isn't. — Michael

Focusing only on the last few pages, and ignoring the 'penalty' conversation which you seem to have in large part already conceded:

Well, no. She also committed to marrying you. She did not just intend to do so... — Banno

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... — Banno

To promise and to intend are two different things. We intend to do things in the future all the time, but it does not follow from this that we are making promises. — Leontiskos

"I intend to marry that woman over there." "Do you believe it will happen?" "Yes, I believe it with all my heart."

On your account he has just promised to marry the woman, which is obviously false. It is false because it has no relation to another (i.e. it does not regard something that he is to do for another). It is also false because he has not bound himself. — Leontiskos

"Honey, do you think we will ever get married?" "I fully intend to eventually." "So that's to say that you're not ready to propose?"

A man can tell a woman that he intends to marry her, and he can affirm his belief in this future act to the maximal degree, and yet not propose (promise) to marry her.* On your view this would not be possible.

* Technically a proposal is a mutual promise. — Leontiskos

This is all just meaningless word games... — Michael

I'm glad we're on the same page! (And I'm also glad you threw in the towel on your attempt to remove fault from punishment.)

Here is some of the crazy stuff you have been peddling:

• Obligations are commands
• To intend something is to promise
• To intend something while especially believing it is to promise
• To penalize or punish is to take something of value
• To penalize or punish is to take something of value as a response to an action

The thread is filled obvious refutations of all of these bizarre ideas.

I can only take the unwillingness of anyone to actually make sense of obligations as evidence that Anscombe was right. — Michael

I can only take the above to mean 1) you are deeply unintelligent, or 2) you are not trying to understand obligations, or promises, or penalties, etc. You don't strike me as unintelligent, so I conclude that you must not be trying to understand these things.

So then what is going on here? Presumably you are playing a kind of game where you throw away the dictionary, common use, and social practice; you redefine a whole swath of terms in accordance with your anti-obligation dogma; and then you see if you can give short, noncommittal answers to all of the objections that get directed against your project. I can't believe that you are actually trying to understand promises, because you accounts of promises have frankly been silly. What you are trying to do is defend a thesis at all costs.

Any attempts so far to show otherwise have amounted to nothing more than the bare assertion that "obligations exist". — Michael

As I have pointed out many times in the past, the answer is simple: obligation is simple, it is not complex. It is not reducible to other kinds of realities. All your arguments ever amount to is something like, "Show me how to derive obligation from my quasi-materialistic premises. You can't. I win." An obligation is not a product of quasi-materialistic premises. You may as well say, "I hold that everything is made of wood, and I deny that metal exists. If you cannot show me how wood is transmuted into metal I will not accept the existence of metal." The answer you usually get is, "Metal is not made of wood, but it does exist. Look around."

Criminals have punished people who testified against them in court. Was it wrong of them to testify against the criminal in court? What does "wrong" even mean? — Michael

For something to be seen to be a punishment it must be seen to be in response to wrongdoing. So as I said:

If you break a contract you should say, "They think they are punishing or penalizing me, but really they are just taking away something that I value." — Leontiskos

Criminals have punished people who testified against them in court. — Michael

The mafia who does so may be punishing or else merely using negative conditioning. Negative conditioning does not require punishment, although that is more subtle.

It's a punishment because it was done in response to something I did. — Michael

You're missing the word "wrong" at the very end of your sentence.

You left your garage door open. The thief stole your car (because of something you did). He did not punish you.

I mean that I will be put in prison or executed. — Michael

As I've said, taking away something you value is not punishment. If it was then the thief who stole your car has necessarily punished you.

It is just the case that if you murder then you will be punished. — Michael

And by "punished" you presumably do not mean what every dictionary in the world says, because then we would be right back to the equivocation on "penalty."

If you break a contract you should say, "They think they are punishing or penalizing me, but really they are just taking away something that I value." To punish or penalize presupposes wrongdoing, and wrongdoing presupposes obligation. Without obligation there exists no penalization, only the mistaken impression of penalization.

I don't deny future accountability. I have repeatedly said that if I don't do as I'm told, whether it be by some authority figure or by the terms of a contract, then I will be penalised. — Michael

No, you think they will forcibly take some money from you. One is only penalized for having done something wrong, and in denying obligations you deny that you could ever have done anything wrong. Again:

You are recasting the entire social sphere. Your "promises" and "contracts" are not real promises or contracts. Your "penalties" are not real penalties. Your "debts" ("owes") are not real debts. — Leontiskos

Accountability also implies obligation, but you would redefine that word as well. You are redefining words left and right, and at some point this is nothing more than dishonesty.

A contract tells the party what he is to do, and therefore someone who does what the contract tells him to do is more likely to fulfil his contracts. — Michael

Oh really? A contract is like the sergeant who goes around commanding people what they are to do? This is in line with your first harebrained theory that obligations are commands. I hate being ordered around so I'll have to keep a keen eye out for this "contract" you speak of. :roll:

You are recasting the entire social sphere. Your "promises" and "contracts" are not real promises or contracts. Your "penalties" are not real penalties. Your "debts" ("owes") are not real debts — Leontiskos

I knew this discussion would be a joke from the start:

Dictionaries should solve it, but they won't for Michael. Michael will sooner deny every form of future accountability rather than abandon his strange [dogmatic] position. He will deny promises, oaths, contracts, marriages - you name it. The more reductio that is applied, the muddier he is willing to get. — Leontiskos

...but even so, that's enough for me.

I'm still waiting on a reply to this. — Michael

In this context what is the difference between these two propositions?

1. He is more likely to fulfil his obligations
2. He is more likely to complete the contract

If they're the same then I have no objections, except to point out that the introduction of the term “obligation” is unnecessary, and evidently susceptible to misunderstanding.

If they're different then I need (1) explained, and to know why (2) is not a sufficient account. — Michael

A contract establishes an obligation, and therefore someone who is more likely to fulfill his obligations is more likely to fulfill his contracts. You are falsely assuming that promises and contracts do not involve obligations, and that obligations are an unnecessary add-on. See my post <here>.

The point about the contractor is that the reason you prefer the reliable contractor over the unreliable contractor has to do with obligations. It has to do with the fact that he is a man of his word, and when he says that he will do something he does it. You can dance around this all day, but in fact you do prefer reliable contractors to unreliable contractors, and the only reason you prefer them is because they honor their obligations. Yes, you want your house built on time, and therefore you want a contractor who honors his obligations. The one who enters a contract is simply not indifferent to the two outcomes of completion vs. legal settlement. The consequences of breaking a contract are a penalty, not merely a consequence.

The use of "I promise" over "I intend" is just to emphasise the strength of one's belief that it will happen. — Michael

See:

When our father says, "Yes, I intend for us to go on vacation next summer, and more than that, I promise you that we will go on vacation come hell or high water!," does the latter part of that sentence change nothing at all? As I have said in many ways, the sort of directing involved in promising extends over the temporal duration of the promise. We can "hold him to it." If summer is near and there is no sign of travel arrangements, we have a right to apply a pressure to our father in a way that we would not if he had not promised. — Leontiskos

The first difference between intending and promising, as Aquinas says, is that "by promising he directs what he himself is to do for another." A mere intention has no necessary relation to another.

As a further example, consider something like "I'll try to do this, but I can't promise that I will". This isn't me saying that I intend to but am not obligated to; it is me saying that I am not certain that I will. — Michael

I don't think trying is the same as intending.

Note that we have a number of different ideas from you. Intending that something will happen, believing that something will happen, and trying to make something happen. You say:

The use of "I promise" over "I intend" is just to emphasise the strength of one's belief that it will happen. — Michael

"I intend to marry that woman over there." "Do you believe it will happen?" "Yes, I believe it with all my heart."

On your account he has just promised to marry the woman, which is obviously false. It is false because it has no relation to another (i.e. it does not regard something that he is to do for another). It is also false because he has not bound himself.

"Honey, do you think we will ever get married?" "I fully intend to eventually." "So that's to say that you're not ready to propose?"

A man can tell a woman that he intends to marry her, and he can affirm his belief in this future act to the maximal degree, and yet not propose (promise) to marry her.* On your view this would not be possible.

* Technically a proposal is a mutual promise.

Because obligations are everywhere in human culture and they dictate a great deal of behavior. They show up everywhere, in economics, in law, in finance, in ethics, in dramas. — Count Timothy von Icarus

Money, oaths of office, marriage, contracts, the possibility of perjury, internet trust certificates, banking, fiduciary responsibilities, the list goes on... All of society would collapse in about 0.2 seconds without obligations and promises. I wonder why it doesn't...

---

- Yes, thank you! I could not agree more. :lol:

Hume's claims about the skeptic also come to mind:

And though a Pyrrhonian may throw himself or others into a momentary amazement and confusion by his profound reasonings; the first and most trivial event in life will put to flight all his doubts and scruples, and leave him the same, in every point of action and speculation, with the philosophers of every other sect, or with those who never concerned themselves in any philosophical researches. When he awakes from his dream, he will be the first to join in the laugh against himself, and to confess, that all his objections are mere amusement, and can have no other tendency than to show the whimsical condition of mankind... — David Hume, An Enquiry Concerning Human Understanding, § xii, 128

It has been some time since I studied formal logic, but I would want to say something along the lines of this, "A proposition containing (p∧¬p) is not well formed." — Leontiskos

The obvious objection to this idea is to note that this restriction goes beyond the typical syntactical requirements for a formula being well formed. I do see this, and it is possible that in rejecting this I am doing irreparable damage to modern symbolic logic. Perhaps my idea is that if someone engages in these sorts of inferences then there should be added an asterisk to their conclusion on account of the fact that this form of metabasis is highly questionable. I mostly want attention to be paid to what we are doing, and to be aware of when we are doing strange things.

- Yes, in fact I had forgotten the bit you quoted. I have only done a close read of MMP once and then skimmed it a few times afterwards, but skimming Anscombe doesn't really work.

A = a cat is sleeping outstretched on the threshold of the entry door to a house.
B = the cat is in the house
notB = the cat is not in the house

In this example, how does A not imply both B and notB in equal measure? — javra

Yes, this is similar to 's vampire argument.

As I so far see things, this addresses the principle of the excluded middle. But the fault would then not be with this principle of itself but, instead, with faulty conceptualizations regarding the collectively exhaustive possibilities in respect to what happens to in fact be the actual state of affairs. — javra

Right: another way of putting it is that you are expressing a phenomenon which is not able to be captured by the logic at hand.

This same type of reasoning can then be further deemed applicable to well enough known statements such as “neither is there a self nor is there not a self”. — javra

This reminds me of the reasoning and forms of denial that both Buddhists and Pyrrhonic Skeptics developed, for similar reasons.

This latter proposition would be contradictory only were both the proposition’s clauses to simultaneously occur in the exact same respect. Otherwise, no contradiction is entailed by the affirmation. — javra

Right: if the terms of the argument are equivocal then the conclusion does not follow, and in this case the conclusion is the claim that a contradiction is occurring.

Asking this thinking I (as a novice when it comes to formal modern logics) might have something to learn from any corrections to the just articulated. — javra

It seems accurate to me. I see it as a heavier critique of bivalent logic than the one I was trying to give, but there are a lot of similarities.

Presumably the objection would be something like, "If you hear dogs barking outside and your roommate asks you if the cat is in the house, isn't he asking a question with only two mutually exclusive answers?" Or in other words, I think someone like Wittgenstein might say that the sense of "in the house" should be traced back to the purposes of the speaker, and that where the purposes are unclear the answer will also be unclear. If "in the house" means that the cat is locked inside and safe, then there is no ambiguity. I think there is some merit to this objection, but my guess is that there are nevertheless phenomena which bivalent logic struggles with. There are a lot of ways you could go with this sort of topic, and I am not well versed on polyvalent logic.

-

Edit: I sort of forgot to address the way your post interacts with the thing you were quoting. When a symbolic logician writes out (B∧¬B), they are not thinking of something like, "Yes and no," where the 'yes' applies to one aspect or consideration of the question and 'no' applies to a different aspect or consideration of the question. They are thinking of a formal contradiction, where something is and is not in precisely the same way. It is this formal contradiction which justifies their modus tollens and the affirmation of ¬A. If they are talking about something like your cat then as you rightly say the inferences that they depend on (and that I oppose) are no longer available for use. In that case I have no objection, for what I was objecting to has disappeared.

Note, though, that this problem does not seem to go away on polyvalent logic. It is still possible to syntactically represent an absurdity like (B∧¬B) in more complex logics, such as Buddhist logic. It's just more difficult to do.

The other relevant matter is whether we are thinking about speakers or whether we are thinking about propositions in the abstract. There are strong arguments for the idea that a conclusion requires at least two premises, and although the argument I am taking issue with is arguably an enthymeme (with a hidden premise), there is still a strange way in which the conclusion has only one premise insofar as nothing additional needs to be independently affirmed. This moves quickly away from a speaker-conception idea of propositions and logic, as if arguments could be self-proving, with no middle term. What is at stake, then, is not a logical inference in the psychological sense but rather a formal identity between the truth tables of two propositions. It is a case where the "inference" is based on nothing more than the regrettable idiosyncrasies of the logical system, and that could never be made by those who are not privy to the arbitrary conventions of the system.

Just because obligations cease to be doesn't mean they never were, right? — Moliere

A promise establishes an obligation, and that obligation ceases if: 1) it is fulfilled, 2) the promise is "broken", or 3) the promisee releases you from the obligation. There are of course many subcategories of (2). Where legitimate exceptions fit in is arguable, and perhaps this is a fourth category.

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. — Banno

Are we trying to teach Michael how to make a promise so he can have a real girlfriend and really get married? It's sort of a sine qua non quality in a man.

Obviously Michael is mistaken when he claims that to promise to do something is no more than to intend to do something, but if we are to teach him how to make a promise, what more is required than the intention to act in the future? Going back to Aquinas from my earlier post:

For just as a man by commanding or praying, directs, in a fashion, what others are to do for him, so by promising he directs what he himself is to do for another. — Aquinas, ST II-II.88.1 Whether a vow consists in a mere purpose of the will?

(Note that "praying" = "petitioning," i.e. asking someone to do something for you.)

Now if @Michael concedes that commanding and petitioning are real acts that he can really do, then we're only one step away from the act of promising. If a sergeant can successfully command the soldier to scout ahead and the child can successfully petition his mother for a candy, then apparently commands and petitions are alive and well in the world. If Aquinas is right then what is happening here is that the sergeant and the child are directing others, albeit in very different ways. And we can direct others. We can command and petition, both successfully and unsuccessfully.

Now if this is all conceded, then is the objector to maintain his position by claiming that although it is true that we can direct others, nevertheless we cannot direct ourselves vis-a-vis some other? If the mother can receive a petition from her child, cannot she also promise her child that the petition will be fulfilled? When our father says, "Yes, I intend for us to go on vacation next summer, and more than that, I promise you that we will go on vacation come hell or high water!," does the latter part of that sentence change nothing at all? As I have said in many ways, the sort of directing involved in promising extends over the temporal duration of the promise. We can "hold him to it." If summer is near and there is no sign of travel arrangements, we have a right to apply a pressure to our father in a way that we would not if he had not promised.

The reason I never really think Michael is being sincere is because he is never willing to do any of the leg work. How many times have we told him that to intend something is not yet to promise it, only to be met with mute silence? He is not the sort of person who would ever say, "Oh hey, you're right! Give me some time to revise my understanding of what a promise is and then get back to you." The eristic is too heavy. It seems to be a game where he tries to be as slippery as he can.

I suspect Anscombe may have agreed with you — Banno

I don't think so. I assume Anscombe understood what a promise is and how to make one. A promise is a special kind of obligation in that it is conditional and voluntarily entered into, and I don't think Anscombe's arguments cut against this form of obligation.

Edit: I am reminded of a "promissory note," which is what money is, or at least was. Or the simpler example of a coupon given out by the grocery store.

I woke in the middle of the night and realized there is an alternative interpretation of the above in natural language. I remain convinced that reading the two propositions as "B follows from A" and "B does not follow from A" means that they contradict one another. — Janus

That makes sense to me (even though symbolic logicians must interpret all such things as material implication, as they have no alternative). Related:

Yet in natural language when we contradict or negate such a claim, we are in fact saying, "If lizards were purple, they would not be smarter." We say, "No, they would not (be smarter in that case)." The negation must depend on the sense of the proposition, and in actuality the sense of real life propositions is never the sense given by material implication. — Leontiskos

Janus' point about natural language is something like this:

Supposing A, would B follow?
Bob: Yes
Sue: No

Now Sue has contradicted Bob. The question is, "What has Sue claimed?" — Leontiskos

It seems to me that it is key to understand that, "The negation must depend on the sense of the proposition..." Material implication is the way it is for much the same reason that humans are the way they are given Epimetheus' mistake. When the logic gods got around to fashioning material implication they basically said, "Well if the antecedent is true and the consequent is true then obviously the implication is true, and if the antecedent is true and the consequent is false then obviously the implication is false, but what happens in the other cases?" "Shit! We only have 'true' and 'false' to work with! I guess we just call it 'true'...?" "Yeah, we certainly can't call it 'false'."

I haven't thought about this problem in some time, but last time I did I decided that calling the vacuous cases of the material conditional 'true' is like dross. In a tertiary logic perhaps they would be neither true nor false, but in a binary logic they must be either true or false, and given the nature of modus ponens and modus tollens 'true' works much better. It's a bit of a convenient fiction. This is not to say that there aren't inherent problems with trying to cast implication as truth-functional, but it seems to me that an additional problem is the bivalence of the paradigm.

Yet some here have interpreted the OP in such a way that this 'dross' gets repackaged and marketed as gold. The undesirable behavior of material implication is basically supposed to be ignored, not utilized for logic parlor tricks.

That's my kindergarten contribution for what it's worth. — Janus

I think your basic intuition is correct. It resists the crucial methodological error of "trusting the logic machine to the extent that we have no way of knowing when it is working and when it is not" (). We need to be able and willing to question the logic tools that we have built. If the tools do not fit reality, that's a problem with the tools, not with reality ().

There is no "standard" of foreseeability. — Pantagruel

Therefore...?

Some people act carefully. Others act recklessly. — Pantagruel

How would you know, given your curious claim that, "There is no 'standard' of foreseeability"?

Many people think that they know what they are doing and do not. We do not live in a world where we go around executing "transactional" events that are over and done with. — Pantagruel

Obviously.

It isn't realistic. — Pantagruel

What isn't realistic? Constant ignoratio elenchus?

It is an invalid abstraction to view intentional action in this "A causes B and over" sense. — Pantagruel

I don't think you've managed to understand what you are attempting to critique, because you surely haven't managed to contradict it. If you want to substantially disagree with the classical view of intention you will have to argue for the absurd conclusion that someone who causes an unforeseeable effect has intended that effect.

This is exactly the kind of false "insular causality" reasoning that leads to the debacle of externalized costs destroying the biosphere. — Pantagruel

When you commit an equivocation by pretending that a company which intentionally ignores foreseen consequences is somehow supposed to be acting unintentionally, you are whipping up faux disagreement and enmity. The question is not whether some person or some company professes that an effect was unforeseen or unforeseeable, the question is whether it actually was.

Intentional causality is often done with an imperfect knowledge and therefore, even when it "works" often has additional unexpected effects. This is exactly what companies who choose to disregard "externalized costs" do. — Pantagruel

This is to ignore foreseen effects (and also to ignore foreseeable effects). Bob's point is presumably that unforeseeable effects are not intentional. The business you are talking about is intentionally ignoring a foreseen effect. The person who strikes out in anger is ignorant of a foreseeable effect, and therefore possibly guilty of negligence. An unforeseeable effect is a pure accident, and cannot be intentional. I still think you two are talking past each other.

You might be interested in relevance logic, which tries to deal with the paradoxes of material implication: https://plato.stanford.edu/entries/logic-relevance/ — Count Timothy von Icarus

Thanks, I may check this out in time. My sense, though, is that you can't fully formalize reasoning. In particular Aristotle's final condition for demonstrative knowledge at 71b22 of the Posterior Analytics is something that I think can never be fully formally modeled, "[demonstrative understanding depends on things that are...] explanatory (aitia) of the conclusion." To understand why something is the way it is requires more than symbol-manipulation, and to understand why B follows from A requires understanding why B is the way it is.

There is a section in Tractatus where Wittgenstein declares that belief in a causal nexus is a "superstition" and holds up logical implication as sort of the "real deal." I think this is absolutely backwards. — Count Timothy von Icarus

That sounds like classic Humean backwards-reasoning. :lol:

In that very same paragraph of Posterior Analytics Aristotle points out that in order for an argument to produce knowledge the premises must be better-known than the conclusion, which strikes me as indicative Hume's significant error. Hume takes premises that are very implausible and leverages them to disprove beliefs that are highly plausible, and this is also why his arguments are rightly dismissed even by those who cannot offer a point-for-point refutation.

Or one that isn't horrifically complex. I actually think that is what gets people more than the "paradoxes of implication." People can learn that sort of thing quite easily. What seems more confusing is the way in which fairly straightforward natural language arguments can end up requiring a dazzling amount of complexity to model. — Count Timothy von Icarus

Right.