They are entirely different statements
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Does "All I know are ..." = "I don't know any ..."?
- Thread starter dybmh
- Start date
Heyo
Veteran Member
And I showed how bad one can be. I'm getting old. I was once the one who answered to "Do you like coffee or tea?" with "Yes.". So, it's also influenced by training how good one is at logic.
But nobody is so useless that he can't at least serve as a bad example. I will definitely refer to this thread when people say that logic is simple and easy.
Alien826
No religious beliefs
I thought it was based on x^1-1, that is x/x. Oh well.
No, that's for other bases. So 3^0 =1 for that reason. But with x=0, you would get 0/0, which is undefined.
Alien826
No religious beliefs
Why Is A Number Raised To Zero One?
Considering the myriad ways in which the exponential function can be defined, one can solve for xº by referring to every single definition, which is really the fairest way to go about it.
This site explains it very well imo. It mentions combinations and gives a good example to understand why there is only one empty set (the only way to combine objects where there are none of them is the empty set). It also gets into fractional exponents and negative exponents. It never suggests that the principle is not correct though. Maybe we have to specify base 0 as an exception to make it generally true?
Edit: Here's something I found on t Khan Academy.
If 2^3 = 1x2x2x2, then 2^0 = 1 times zero twos, which equals 1.
That seems to work for base 0, as it would involve 0X0 which is OK (?) not 0/0.
If 0^3 = 1x0x0x0, then 0^0 = 1 times zero zeros, which equals 1.
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dybmh
דניאל יוסף בן מאיר הירש
dybmh
דניאל יוסף בן מאיר הירש
It is if the speaker doesn't know any. You've already confirmed this.
"theist" = "Not atheist"
"Q AND/OR Not Q" = "Atheist or not"
"or" in english = "AND/OR" in logic
Because of this, If the speaker does not know any Jews, "All the Jews I know are atheist" is *actually* "All the Jews I know are ( atheist or not ).
And I'll point out "Not P" does NOT tell us anything about "P --> Q". That's the whole point of the method you are employing. "Not P" is irrelevant to "P --> Q" because "P --> Q" is ASSUMED to be true unless it is proven false.
Yup. It is. And there can be no objections to changing the original statement. You are completely butchering the original statement so that the lowest standards of "truth" can be used.
Here's the "truth" table you are using.
You are attempting to translate "All the Jews I know are atheists" into a material conditional "not P or Q". Where is the "Not" and where is the "Or" in "All the Jews I know are atheists"? And "If ... Then" in logic does not mean "If ... Then" in english. So trying to force the original statement into "If ... Then" in english does not mean that it can be translated into "If ... Then" in logic.
This is a known problem with the "material conditional", but you seem to be ignoring it. Not intentionally. People who are good at math are notriously bad at communicating.
Material implication is used in all the basic systems of classical logic as well as some nonclassical logics. It is assumed as a model of correct conditional reasoning within mathematics and serves as the basis for commands in many programming languages. However, many logics replace material implication with other operators such as the strict conditional and the variably strict conditional. Due to the paradoxes of material implication and related problems, material implication is not generally considered a viable analysis of conditional sentences in natural language.
Material conditional - Wikipedia
The entire quote above is extremely important. I would have liked to bold and emphasize every word! The method you are employing works in math and in math only. It does not work when it leaves its context. Trying to use it in the real world results in paradoxes. And... AND!!!! MANY logics replace it.If a person searches for anwers regarding the bizarre so-called logical-truth of statements like "If it's noon then God is real", they will eventually come to answers which confirm that "consequence" "implication" and "If ... Then" in english do not mean "consequence" "implication" and "If ... Then" in logic. In english these words communicate causation or correlation. In logic these words communicate neither of these.
If this method causes paradoxes, and it is only useful in a math context, and many replace it with something better, why is it being used here? Because it permits word-play. Double-speak. And some people think that's fun and funny. It's math-turbation. I still have not rec'd an answer to the question I asked about the purpose of logic. I suspect that this sort of word-play ( math-turbation ), is not consistent with anyone's understanding of the purpose of logic.
It is the lowest standard for truth that exists. "It's true because it cannot be proven false." Clearly you know the difference between what is vacuously true and what is actually true. Why are you avoiding making that distinction clear? Any time you omit the word "vacuous" that is essentially cherry picking the word "true".
Important information has been omitted. Your answers have been incomplete.
Above, you said "It is logically true". That is incomplete.
"It is logically true, but that does not mean actually true in any real world situation." is complete.
As a professional I would expect you to know that the material conditional does not *actually* mean "If .. then" in english. And I would expect that you would know that it causes problems, catagory errors, when it leaves the math context. But you have omitted that, or ignored it, or forgotten it, or maybe never knew it all. Which is it?
LOL. Simple question.
Is a "vacuously true" statement = an "actually true statement"?
Key word: ambiguous.
Nope. If that were *actually* true "vacuous truth" would not be a necessary concept defined in logic.
Hee-hee. There are 3 and only 3 possibilities:
- They are both irrelevant. ( this is the correct answer )
- They are both equally relevant.
- What I said is vastly more relevant than what you said.
You said, and I agree, "it is never the case that something is both known and a dog." IF "I don't know any dogs". - Post#84
Because of this, the propostion "All the dogs I know are brown." is *actually* one of the three statements below.
All the dogs I know are brown.
All the dogs I know are brown.
All the dogs I know are brown.
I asked how can this possibly be true, and you answered: "Show me a dog that I know that is not brown." Let's compare for relevance.
All the dogs I know are brown.
"Show me a dog that I know that is not brown." is irrelevant. You are talking about dogs, the statement is not.
All the dogs I know are brown.
"Show me a dog that I know that is not brown." is irrelevant. You are talking about knowing, the statement is not.
All the dogs I know are brown.
"Show me a dog that I know that is not brown." is irrelevant. You are talking about a dog and knowing, the statement is not.
What you said is completely irrelevant. And my statement was equally irrelevant for all the same reasons.
Case 2: They are both equally relevant.
You said: "Show me a dog that I know that is not brown." That is incomplete.
"Show me a dog that I know is not brown. If you can't then I MUST know a dog that IS brown" is complete.
Notice, significance, relevance, is linked to whether or not the dog is brown. If we look at the so-called truth table you are using. The only time that Q ( is brown ) is signficant is if P ( all the dogs I know ) is true.
p | q | p-->q
T | T | T
T | F | F
F | T | T
F | F | T
The rows in blue show that "is brown" is significant ONLY when "all the dogs I know" is true. The rows in red show that if "all the dogs I know" is false, then "is brown" could be either true or false. If your so-called proof that "All dogs I know are brown" IS relevant, then "all the dogs I know" is assumed to be true.
Because of this, my statement is equally relevant. If you can look for a dog that is NOT brown, and not finding, this "proves" that one exists, then I can look for a dog that IS brown, and not finding one "proves" that one does not exist. You are assuming the success condition based on a lack of information. I am assuming a failure condition based on a lack of information. Fair is fair. Your method cuts both ways. If your "proof" is relevant, mine is equally relevant. If you can assume P is true, then I can assume P is true.
Case 3: What I said is vastly more relevant that what you said.
If "All the dogs I know are brown" AND "I don't know any dogs" is true, how is "All the dogs I know are brown" possibly true?
Your answer: "Show me a dog that I know that is not brown" is ONLY relevant if you are expecting to find one.
My answer: "Show me a dog that I know that is brown" is ONLY relevant if I am not expecting to find one.
Why in the world would you expect to find a brown dog if you don't know any dogs? That is one of the dumbest assertions I have ever heard. There is NO reason at all to expect to find one. My "proof" expects not to find one which is obviously true if you don't know any dogs. Because of this my statement is vastly more relevant that yours. You are drawing a conclusion based on a condition that cannot exist. There is no maybe, there is no middle ground. Expecting to find one and not finding one is meaningless / worthless / useless. Since I am not expecting to find one, when I don't find one that is consistent with the necessary condtion: "I don't know any dogs."
My statement is consistent with the necessary condition. Your statement is not. My statement is vastly more relevant that yours.
Case 1: "Neither of what we said is relevant" is the correct answer.The only reason to "look for a dog that you know" is if the person is ignorant or pretending that they know any dogs. So you were ignoring a necessary condition of the statement. This is precisely what happens in all the so-called proofs regarding the empty-set obtaining any property. The individual has completely forgotten or is intentionally ignoring the necessary condition: the empty-set is empty.
This is why this case is the correct answer answer. Neither of what we said is relevant. Looking for dogs that are known is meaningless / worthless / useless with the necessary condition "I don't know any dogs."
No class is needed. Your standards for proof and truth are simply ridiculously low and you are not ready, willing, or able to admit it.
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dybmh
דניאל יוסף בן מאיר הירש
This is incomplete. Paraconsistent logic is not the ONLY way to avoid the principle of explosion. What you have said here can be easily misunderstood. "Standard logic"??? What does that even mean?
The easiest way to avoid the principle of explosion is to do what virtually every sane logical person does. They use natural deduction. That is a much better defintion of "Standard logic". What you are talking about is not "Standard logic", you are talking about the popular version of logic that is employed by mathematicians because it permits the most amount of creativity. And, I can appreciate that. But, it often doesn't work in the real world.
Everything you've said in this thread is depending on the "material conditional". As I have shown, it is not viable for real world usage. It is a poor method. The standard of truth is weak and meaningless. Not proven false =/= true to any normal sane person in any normal real world setting. The reasons to avoid the "material conditional" are: 1) the language used does translate properly into english. And 2) it causes paradoxes.
The paradoxes of material implication are a group of true formulae involving material conditionals whose translations into natural language are intuitively false when the conditional is translated as "if ... then ...". A material conditional formula P ---> Q is true unless P is true and Q is false. If natural language conditionals were understood in the same way, that would mean that the sentence "If the Nazis had won World War Two, everybody would be happy" is vacuously true. Given that such problematic consequences follow from a seemingly correct assumption about logic, they are called paradoxes. They demonstrate a mismatch between classical logic and robust intuitions about meaning and reasoning.
Paradoxes of material implication - Wikipedia
Notice: Translating the material conditional into "if ... then" is NOT a proper method. Is NOT. The conflict is between a "vacuous truth" and "robust intuitions about meaning and reasoning." Vacuous is empty, weak and worthless. Robust is strong, consistent, and useful. Would you rather build a house on a vacuous foundation or a robust foundation? Any sane logical person would avoid the vacuous and seek out the robust. Valuing robust intuitions over vacuous statements is "Standard logic". Valuing vacuous statements over robust reasoning is not "Standard".This is "Standard logic".
A judgment is something that is knowable, that is, an object of knowledge. It is evident if one in fact knows it. Thus "it is raining" is a judgment, which is evident for the one who knows that it is actually raining; in this case one may readily find evidence for the judgment by looking outside the window or stepping out of the house. In mathematical logic however, evidence is often not as directly observable, but rather deduced from more basic evident judgments. The process of deduction is what constitutes a proof; in other words, a judgment is evident if one has a proof for it.
The most important judgments in logic are of the form "A is true".
Natural deduction - Wikipedia
"All the Jews I know are atheists" is a judgement. It is not an implication. You have been translating this incorrectly the entire time.
A judgement is knowable if one has proof for it. It is not assumed true if it is not proven false. In math, if evidence is not observable, it is deduced from things that are. By using natural deduction, the principle of explosion is avoided, naturally. And that is the standard for most sane logical intelligent people. Accepting the principle of explosion is the minority position, and it is only useful in a minority of real world circumstances.
Zooming in from "Standard logic" employed by most logical sane intelligent people, your incomplete answer can be easily misunderstood to mean that acceptance of the principle of explosion is somehow "standard" among philosophers, and logicians. That is completely false.
Aristotle strongly opposed the principle of explosion. For thousands of years many many great thinkers opposed the principle of explosion, it was only adopted by a significant number of academics in the past 100ish years. The reason? They couldn't work around paradoxes. I'm not sure why? But they couldn't. So, they lowered their standards on what is "true", started writing axioms ( creating a religion ), and the rest is history. Readers can explore this topic in the below link. The information goes on for pages and pages. There is so much good thought and research put into this idea that "Nothing follows from falsehood."
Connexive Logic (Stanford Encyclopedia of Philosophy)
plato.stanford.edu
So, as usual. In this thread your answer was woefully incomplete. Your referral to paraconsistent logic is ignorant of Aristotle's thesis, and Connexive logic. I haven't even mentioned that your so-called version of true comes from semantic deduction, which is one of two major groupings of deduction. It is the one with the lowest standards for truth, and because of this it is the easiest to use. Most people know that arguments relying on "semantics" are weak arguments that are generally useless. None the less, people like easy answers. And for mathematicians, if all they care about is "T" or "F", the easy way is the best way.
Editted to add link.
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dybmh
דניאל יוסף בן מאיר הירש
OK. I didn't give it a lot of thought. It's cards on a table, I don't see it translating to a real world situation other than finding loopholes in rules and exploiting them.
Parent to child: "Did you do your homework?"
Child to parent: "Yes."
Parent to child: "Let me see it."
Child hands homework to parent.
Parent to child: "I can't read any of this. It's too messy."
Child to parent: "You didn't ask if I did my homework neatly."
dybmh
דניאל יוסף בן מאיר הירש
Never under-estimate a Jew on a mission opposing falsehood.
@Polymath257 has been defeated here. He has been mistranslating the statement "All the X I know are Y" this entire time. It's a known problem which he is either ignoring or never knew. And he is not distinguishing between a "vacuous" truth and an "actual" truth which is absolutely required when considering real-world phenomena.
Sure, if the topic is numbers and symbols, or maybe a puzzle with cards and numbers and colors, I would not win. But when it comes to applying these ideas to the real world, @Polymath257 is not untouchable, not inerrant. He is human and not a god.
dybmh
דניאל יוסף בן מאיר הירש
If you want to make this relevant to the debate, the game needs to be adjusted.
There are NO cards on the table, which cards do you turn over to show that the rule "if a card shows an even number on one face, then its opposite face is blue" is valid?
Answer: The rule cannot be tested. The question "is it true" cannot be answered. It is neither true nor false using your method. And that is what I have shown in ths thread.
I am proposing a simple solution to this problem. The question can be answered, "It is false" because "there are no cards" contradicts with "which cards do you turn over", and this renders the answer "false" because all contradictions are false. The question is not actually a question.
Alien826
No religious beliefs
Blasphemy!
Alien826
No religious beliefs
As Pharaoh discovered to his cost!
I have a strong feeling that the problem may be that the two of you are approaching this from different directions. @Polymath257 is answering from a position of pure mathematics, where everything is strictly defined and words like "true" have a meaning that may not be the same as what you might find in a dictionary. You are taking the actual words of the example and applying everyday "common sense" to them.
Maybe you are both right according to your own suppositions. I'll go back into the audience and see how it pans out.
dybmh
דניאל יוסף בן מאיר הירש
As Pharaoh discovered to his cost!
I have a strong feeling that the problem may be that the two of you are approaching this from different directions. @Polymath257 is answering from a position of pure mathematics, where everything is strictly defined and words like "true" have a meaning that may not be the same as what you might find in a dictionary. You are taking the actual words of the example and applying everyday "common sense" to them.
Maybe you are both right according to your own suppositions. I'll go back into the audience and see how it pans out.
As I have shown, "the material condition" which @Polymath257 is employing is not viable for assessing true/false in natural language statements. Not viable. It's supposed to be generally known.
"All the Jews I know as atheists" is a natural language statement, in a natural language context. It is better understood as a logical judgement, not a logical implication. The method employed is improper, and that is why it delivers an incorrect conclusion.
That's all there is to it. Does baking a cake prove that Bob's your uncle?
If this is generally known, then I don't need to take class. I was right all along. I think @Polymath257 should be posting in here with an admittance that he was wrong. But that doesn't happen very often on RF. So, I'll accept his lack of rebuttal as a concession. He has walked away from the debate, because he cannot refute any of this.
The question is: did he know it wasn't viable, or did he know it and hope no one would figure it out?
Heyo
Veteran Member
Then Aristotelian logic isn't right for real-world problems. It is a binary logic, the rule of the excluded middle applies.
There is no difference between a real truth and a vacuous truth.
Once again, what I said is correct and applies. If you have problems with that, go take a class in logic.
I am going to be moving to another state this week, so I have a LOT to do. I may be back in a couple of weeks.
I am going to be moving to another state this week, so I have a LOT to do. I may be back in a couple of weeks.
dybmh
דניאל יוסף בן מאיר הירש
Nope. The material conditional is not viable for real world phenomena. It's on multiple wiki pages. Are you saying they're wrong? I've found other sources backing them up. They're wrong too?
If you want to try to pound that square peg into a round hole here's the statement, and try to reform it into ( ~P OR Q ).
"All the Jews I know are atheists". How do you intend to make that into "Not P or Q"?
( hint: you can't without changing the meaning of the statement ).
Edit: to accomplish this, the resulting statement MUST be in english. No logical notation that can be misunderstood. E-N-G-L-I-S-H. English. It should take less than 5 minutes. Surely you can accomplish that before you toddle away.
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dybmh
דניאל יוסף בן מאיר הירש
All that law means is: For every proposition P, there exists a true statement in the form of ( P or not ). That has nothing to do with trying to make "Not P or Q" useful in real world situations.
Then why does the term vacuous truth exist? This is from the wiki article referenced earlier.
... a statement is vacuously true because it does not really say anything. For example, the statement "all cell phones in the room are turned off" will be true when no cell phones are in the room. In this case, the statement "all cell phones in the room are turned on" would also be vacuously true, as would the conjunction of the two: "all cell phones in the room are turned on and turned off", which would otherwise be incoherent and false.
Notice: the negative "all cell phones are off ( are not on )" is true. The negative assertion is true. The positive assertion "all cell phones are on" is vacuously true. As well as the conjunction; it's vacuously true. So there is a difference. The vacuous truth permits incoherence and making positive assertions about things that don't exist.
dybmh
דניאל יוסף בן מאיר הירש
"I'm right. You're wrong" is not a valid argument in a debate.
