...Logicians have an answer to the above charge, and the answer is perfectly tight and logically consistent. That is part of the problem! Consistency is not enough. Logic should be not just a mathematically consistent system but a human instrument for understanding reality, for dealing with real people and things and real arguments about the real world. That is the basic assumption of
the old logic.
...The conclusion ("Lassie is a dog") may be true, but it has not been proved by this argument. It does not "follow" from the premises.
Now in Aristotelian logic, a true conclusion logically follows from, or is proved by, or is "implied" by, or is validly inferred from, only some premises and not others. The above argument about Lassie is not a valid argument according to Aristotelian logic. Its premises do not prove its conclusion. And common sense, or our innate logical sense, agrees. However, modern symbolic logic disagrees. One of its principles is that "if a statement is true, then that statement is implied by any statement whatever."
This principle is often called "the paradox of material implication." Ironically, "material implication" means exactly the opposite of what it seems to mean. It means that the matter, or content, of a statement is totally irrelevant to its logically implying or being implied by other statements.
Logician: So, class, you see, if you begin with a false premise, anything follows.
Student: I just can't understand that.
Logician: Are you sure you don't understand that?
Student: If I understand that, I'm a monkey's uncle.
Logician: My point exactly. (Snickers.)
Student: What's so funny?
Logician: You just can't understand that.
The relationship between a premise and a conclusion is called "implication," and the process of reasoning from the premise to the conclusion is called "inference" In symbolic logic, the relation of implication is called "a tnith-functional connective," which means that the only factor that makes the inference valid or invalid, the only thing that makes it true or false to say that the premise or premises validly imply the conclusion, is not at all dependent on the content or matter of any of those propositions, but only whether the premise or premises are true or false and whether the conclusion is true or false.
But is something accidental if it not only could have but should have been forseen? — Pantagruel
Yes. No one would say I intentionally killed someone by drunk driving if they knew for certain that I genuinely did not foresee the serious possibility of killing or injuring someone by drunk driving. For example, a severely cognitively challenged person who gets their hands on some alcohol and ends up drunk driving probably isn’t capable of foreseeable (sic) the obvious possibility that they may injure or kill someone. — Bob Ross
In practicality, most people cannot get away with claiming they did not foresee it (because we do not believe them) or, if they can, we hold them responsible for their negligence (as opposed to their intentions). — Bob Ross
* A parallel equivocation occurs here on 'false' and 'absurd' or 'contradictory'. Usually when we say 'false' we mean, "It could be true but it's not." In this case it could never be true. It is the opposite of a tautology—an absurdity or a contradiction. — Leontiskos
((a→b)∧(a→¬b))↔¬a is valid — Lionino
↪Michael
I guess you're asking what "obligation" is supposed to be adding to the act of uttering a promise. — frank
Your points about the difference between two versions of contradiction was interesting and I was thinking about it then got sidetracked in reading the back-and-forth. — Moliere
6 pages too many on this thread. — Lionino
Yeah, looking at OP at least, I can see how there's ambiguity there: whether material implication, or some other meaning, was meant isn't specified in the OP and so whatever meaning was meant there's still ambiguity there (which may explain some of the divergence here that I'm surprised to find) — Moliere
The part where "A" is used as a variable is what made me jump to propositional logic. — Moliere
Your points about the difference between two versions of contradiction was interesting and I was thinking about it then got sidetracked in reading the back-and-forth. — Moliere
Can anyone think up a real world example where you would point out that A implies both B and not-B except for saying something along the lines of:
"A implies B and not-B, therefore clearly not-A." — Count Timothy von Icarus
The way you would usually use it in any sort natural language statement would be to say: "Look, A implies both B and not-B, so clearly A cannot be true." You don't have a contradiction if you reject A, only if you affirm it.
This is a fairly common sort of argument. Something like: "if everything Tucker Carlson says about Joe Biden is true then it implies that Joe Biden is both demented/mentally incompetent and a criminal mastermind running a crime family (i.e., incompetent and competent, not-B and B) therefore he must be wrong somewhere." — Count Timothy von Icarus
...and "imply ¬A" as [meaning] the proposition being True means A is False. — Lionino
and when the OP is in the Logic sub-forum it makes sense to default to trained logic — Moliere
EDIT: Also, I ought say: I think it's a good story for highlighting a problem in rationality. That's the real conversation. — Moliere
I think it's a good story to highlight how we can get into a bind about decisions if all we do is follow some rules in the mode of obedience to them — Moliere
The idea is: Don't be an Ass. — Moliere
Which antecedents? — Moliere
Aristotle, Al-Ghazali, Averroes, Aquinas, Spinoza, Bayle, and Leibniz — Leontiskos
It's not a misinterpretation. To say that P is contradictory is to say that P is a contradiction. — TonesInDeepFreeze
First, take out 'would' since subjunctives unnecessarily complicate. — TonesInDeepFreeze
Sue claimed "It is not the case that B follows from the supposition A" — TonesInDeepFreeze
Later writers satirised this view in terms of an ass which, confronted by both food and water, must necessarily die of both hunger and thirst while pondering a decision. — Buridan's Ass | Wikipedia
I take 'the contradictory statement is P' to mean that P is a contradiction, as a contradictory statement is a contradiction. — TonesInDeepFreeze
But maybe you mean it is a contradicting statement. — TonesInDeepFreeze
You changed the sentence. Here is what you wrote: — TonesInDeepFreeze
"If lizards were purple then they would be smarter" is not a contradiction — TonesInDeepFreeze
I know of no context in which that sentence is a contradiction. — TonesInDeepFreeze
There are two separate matters: negation and material implication. — TonesInDeepFreeze
Given the way that common speech differs from material implication, in common speech the two speakers would generally be contradicting one another. — Leontiskos
no - the consequent can only be affirmed as true IF the antecedent is first affirmed as true. It's THAT that is not the case here. — flannel jesus
if you phrase "A -> B" as "from A follows B", then if A is false, you can say "A -> anything", from A anything follows — flannel jesus
From falsehood, anything follows. Have you ever heard of this? — flannel jesus
Another example is that someone might have a sudden and uncontrollable sneezing fit when driving and fail to see the pedestrian on the crossing and run them over and kill them. They will still be punished even though it was not their fault in any moral sense. — Janus
You are conflating the legal with the moral. If someone drinks and drives they are being negligent. If their ability to focus on the task of driving safely and/ or being physically coordinated enough to do it, is sufficiently impaired by the alcohol and they are unlucky enough to kill someone, they will not be excused and will be prosecuted and punished to a far greater extent than if they had not killed someone. — Janus
From the point of view of the law concerning negligence, they have committed a greater crime than if they had merely driven without incident, but this doesn't seem right from a moral standpoint. Call this moral luck (or unluck). — Janus
Again, a contradiction is a statement and its negation. If there is a contradiction then you could show that both a statement and its negation are implied.
Again:
"if lizards are purple, then they would be smarter" and "if lizards are purple, then they would not be smarter" is not a contradiction. — TonesInDeepFreeze
Which is, compared to your citations, a poor translation (apparently). Irregardless, if I take it that his second sentence is a definition (and not an assertion that about what nobility think), then: — Bob Ross
'The good' refers to what is supremely and ultimately good — Bob Ross
If I assume he means to define "good", as opposed to "the good", as "that which all things aim at", then this seems like an incredibly inadequate definition... — Bob Ross
Now as "being" is the first thing that falls under the apprehension simply, so "good" is the first thing that falls under the apprehension of the practical reason, which is directed to action: since every agent acts for an end under the aspect of good. Consequently the first principle of practical reason is one founded on the notion of good, viz. that "good is that which all things seek after." — Aquinas, ST I-II.94.2
People want a contractor who will build them a house; they don't want a contractor who will not build them a house. — Michael
The law simply says "if someone does not fulfil the terms of their contract then they are to be jailed". The judge then rules that I did not fulfil the terms of my contract and so orders the bailiffs to take me to jail.
Again, the existence of some supposed obligation is utterly irrelevant. — Michael
↪Michael So this tells me only that you will not be held to your promises.
OK. You are not a man of your word. — Banno
A vow denotes a binding to do or omit some particular thing. Now one man binds himself to another by means of a promise, which is an act of the reason to which faculty it belongs to direct. 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. Now a promise between man and man can only be expressed in words or any other outward signs; [...] Now a promise is the outcome from a purpose of doing something: and a purpose presupposes deliberation, since it is the act of a deliberate will. Accordingly three things are essential to a vow: the first is deliberation. the second is a purpose of the will; and the third is a promise, wherein is completed the nature of a vow. — Aquinas, ST II-II.88.1 Whether a vow consists in a mere purpose of the will?
The terms of the contract simply say "Michael is to build the house or pay a fine". The law simply says "if someone does not fulfil the terms of their contract then they are to be jailed".
Neither the law nor the contract depend on the existence of obligations, and so arguing that obligations don't existence is an irrelevant argument. — Michael
I can say whatever I want. I doubt it would convince a judge. The contract states that if I do not build the house then I am to pay a fine. The law states that if I do not pay the fine then I am to be jailed. So I build the house, pay a fine, or go to jail. Unless I have very good lawyers, I have to choose between one of these outcomes. — Michael
I can do all of that. And then I will presumably face some further punishment. — Michael
I don't understand the relevance of the question. — Michael
For not doing what I was contracted to do. — Michael
As in, "If I don't build the house on time then some authority will fine me."
This is true if in the terms of the contract. But this proposition does not entail "I ought build the house" (or "I ought pay the fine"). — Michael
I was thinking of it in terms of the conditional "If X doesn't happen then Y will happen", and that this proposition does not entail "I ought X". — Michael
Right, by "owe" you mean "obligated to give you the money"? Again, you haven't told me what it means to be obligated to do something. I just either do it or I don't. — Michael
Well I can certainly change my mind and not give you the money, and then face whatever punishment follows. — Michael
Yes. — Michael
He didn't do what he was contracted to do and so as per the terms of the contract (or the law in general) he is penalized.
That's all there is to it. I don't understand what this additional thing – the "obligation" – is, or what part it plays. — Michael
That depends on what you mean. Here are two propositions:
1. Promises exist
2. People promise to do things — Michael