Does "All I know are ..." = "I don't know any ..."?

[mikkel_the_dane]

If you want all meaningful propositions to be either true or false, and you want some basic logical surrender to hold, then the truth table for implication has to be that for material implication, which makes it the same as not(p) or q.

In particular, if p is false, the implication is true. That is the case of a vacuous truth (the implication).

Yeah, this is such fun, because depending of the definitions of meaningful and all the other words, you are right, even to the point if I think differently, my thinking is illogical.

The joke is what makes the bold proposition meaningful and true, because it says something about a part of the world.

 

[dybmh]

No, it is viable except when the language isn't logical. This happens a lot in natural languages.

Well, there you go. You agreed that the statement "All the Jews I know are atheists AND I don't know any Jews" is meaningless gibberish. That means the language being used here is not logical, and the methods you are using isn't viable.

I disagree. You can ask any philosopher of the subject and see what they say about this specific case.

Listen to that exaggeration... you can ask any philosopher. This is completely ignorant. The concensus of philsophers denies the principle of explosion.

The consensus among the majority of philosophers is descriptively a denial of trivialism, termed as non-trivialism or anti-trivialism. This is due to it being unable to produce a sound argument through the principle of explosion and it being considered an absurdity (reductio ad absurdum).​

​

Trivialism - Wikipedia

en.m.wikipedia.org

The concensus rejects this.

How is looking in an empty-box, not finding something, then ASSUMING that by some math-god-magic, the not-finding has filled the empty-box with everything logical?

What is the purpose of logic? ASSUME everything is true?

I am quite aware of the difficulties of natural language. And it is generally recognized that natural language isn't logical. So, when you asked for the *logic* of a particular situation, I gave it using the *logic* definitions.

Again, equivocation, misrepresetation, ambiguity.

We are talking about the "material conditional". That is one tiny little fraction of "logic". It is included in semantic deduction which has many flaws, primary among them, it ignores relevance. That means trying to claim something is "consistent" is impossible using this method.

You keep calling it "implication". That is ambiguous. "Implication" means correlation. But the "material conditional" the truth-table you anre employing DOES NOT communicate correlation. Continuing to use a word which has a double meaning, and knowing it has a double meaning is dishonest.

It's the same for using the word "logic" when there are many "logics" and you are using the one with the lowest, rock-bottom standards. it is equivocation, misrepresentation, and ambiguous.

 

[dybmh]

I don't. I intend to make it into the statement
"for all x, if x is known and x is a Jew, then x is an atheist.

Since there's no correlation or causation in your method, If ... then doesn't work.

If you want to use the not(p) or q version, it would read (after negating the 'and'),
for all x, either I don't know x, or x is not a Jew or x is an atheist.

Brilliant! Except you left out an english word for 'x'. X=Jews. Now let's compare:

"All the Jews I know are atheists"
"For all Jews, either I don't know any Jews, or Jew is not a Jew, or Jews are atheists"

WOW! That's a huge difference in meaning! HUGE! That's the proof right there that this method invalid.

You had to add 3 Ors and 2 Nots, and none of that is in the original statement.

Now, notice that if I don't know any Jews, this is TRUE since, then 'I don't know x or x is not a Jew' is always true (for all x).

Sure. But since the mistranslated version completely changes the meaning, then the you cannot use ( not P or Q ) in this case.

You asked for the *logic* of a particular situation. I gave it. Enlgish isn't a logical language (no natural language is). It is full of contradictions and non-sequiturs and flat-out ambiguities.

Hee. Full of contradictions, non-sequiturs, and ambiguities...

If today is Tuesday then God exists. Is logically true? You can't prove it false, it MUST be true. By your version of "logic".

 

[Alien826]

It's math-turbation.

Here's what this means.

"1, 2, 3, 4, ..... 95, 96, 97, 98, 99, change hands, 101, 102, ....."

 

[dybmh]

First, it is an 'all' statement. That puts it into quantifier logic (not simple propositional logic).

If you want to use the 'or' version, the statement is equivalent to

For all x, either I do not know x, or x is not a Jew, or x is an atheist.

So, any particular that you pick will fall into one (or more) of those three categories: not known, not a Jew, or an atheist.

OR, if you want to eliminate the 'all', we can say equivalently,

There is nothing which is known, a Jew, and not an atheist.

OK. So you have given 2 options, lets compare. ( you didn't define 'x', that's ambiguous. 'x' are Jews. )

"All the Jews I know are atheists"
"For all Jews, either I don't know any Jews, or Jew is not a Jew, or Jews are atheists"

That's a huge difference. It has completely different meaning.

"All the Jews I know are atheists"
"There is nothing which is known, a Jew, and not an atheist."

That's a huge difference. It has a completely different meaning.

So why are you using ( not P or Q ) in this case?

No, there is more here than simply the truth table for implication. There is also the quantifier (all). That needs to be taken into account. And it is easy to do so.

"implication" is ambiguous, it has two meanings. Please use the specific term, "material conditional". Since the material conditional cannot be used without changing the meaning of the statement it is not viable. This has been shown. You kinda-sorta admitted it. But phrased it backwards.

If you want to use quantifier logic, that's fine. But it shows that there are zero Jewish-atheists known. That is the opposite of what you're saying. You are saying, "they're all atheists, and theists, and marvel super-heros, weeeeeee isn't this fun."

If I know no Jews, then every Jew I know is an atheist. But it is also the case that every Jew I know is a theist.

But you don't *actually* know any. You just flip-flopped. Are you using quantifier logic, or not.

The statments given are consistent, but not equivalent.

How do you evaluate "consistent" without evaluating relevance?

The joke, as far as I can see, it that the implication is vacuously true.

Praise the math-gods, you are starting to distinguish between vacuous truth and actual truth! Or are you?

 

[dybmh]

Here's what this means.

"1, 2, 3, 4, ..... 95, 96, 97, 98, 99, change hands, 101, 102, ....."

feels like a stranger... it'll be a long long crazy crazy night ...

Spoiler: Lyrics

Inside you're burnin', I can see clear through
Your eyes tell more than you mean them to
Lit up and flashin' like the reds and blues
Out there on the neon avenue
Well, I feel like, feel like a stranger
Well, the music's thunderin', well reckless and hot
You keep firin' glances across the room
And I can't stop wonderin' just what you got
I get the feeling I'm goin' to find out real soon, oh yeah c'mon
I feel like, I feel like, feel like a stranger
Everyone's calling me a stranger
Let's get on with the show, let's go
Yes, and the wheel, it's smoking 'round midnight
You show me a look that says, let's go
Yes, and it feels 'bout like running a red light
There ain't no point in looking behind us, no
Oh, still I feel like, feel like a stranger
You know it's going to get stranger
So I think you just know
I feel like a stranger
I feel like, feel like, feel like a stranger
I just like, just like, just like a stranger
Just, just, just, just like a stranger, stranger
Feel like a stranger
Crazy night, that's right
Feel like a stranger
Long, long, crazy, crazy night
Feel like a stranger
Long, long, crazy, crazy night
Feel like a stranger
Silky, crazy, crazy night
I feel like, I feel like, I feel like, I feel like a stranger

 

[dybmh]

Agreed. I just don't have the time or energy right now to give you a class in basic logic.

Unless and until you are distinguishing between *actual* truth and *vacuous* truth, your classes are not valuable.
Unless and until you are accurately translating real world statements into logical statements your classes are not valuable.

"All Jews I know are atheists" is a judgement not an implication.

 

[mikkel_the_dane]

If no Jews are known, there are no *actual* Jewish-atheists.



What is the purpose of logic?

It depends, but originally it was in the Western tradition a part of practical attempt to understand how the world works.
Today it has several purposes. A formal abstract one, a practical one as relates to science and a political/social one as a word of authority.

 

[dybmh]

@dybmh

Here's an excerpt from the Standford site on philosophy about implication:

No link? Why not?

"The inference is sometimes called ex falso quodlibet or, more colorfully, explosion. Some call it “¬-elimination”, but perhaps this stretches the notion of “elimination” a bit. We do not officially include ex falso quodlibet as a separate rule in D, but as will be shown below (Theorem 10), each instance of it is derivable in our system D
.

Some logicians object to ex falso quodlibet, on the ground that the sentence ψ may be irrelevant to any of the premises in Γ. Suppose, for example, that one starts with some premises Γ about human nature and facts about certain people, and then deduces both the sentence “Clinton had extra-marital sexual relations” and “Clinton did not have extra-marital sexual relations”. One can perhaps conclude that there is something wrong with the premises Γ. But should we be allowed to then deduce anything at all from Γ? Should we be allowed to deduce “The economy is sound”?

A small minority of logicians, called dialetheists, hold that some contradictions are actually true. For them, ex falso quodlibet is not truth-preserving."

Cherry picked. You omitted the next paragragh which is important.

Deductive systems that demur from ex falso quodlibet are called paraconsistent. Most relevant logics are paraconsistent. See the entries on relevance logic, paraconsistent logic, and dialetheism. Or see Anderson and Belnap [1975], Anderson, Belnap, and Dunn [1992], and Tennant [1997] for fuller overviews of relevant logic; and Priest [2006a,b], for dialetheism. Deep philosophical issues concerning the nature of logical consequence are involved. Far be it for an article in a philosophy encyclopedia to avoid philosophical issues, but space considerations preclude a fuller treatment of this issue here. Suffice it to note that the inference ex falso quodlibet is sanctioned in systems of classical logic, the subject of this article. It is essential to establishing the balance between the deductive system and the semantics (see §5 below).​

​

Hmmmmmmm. The method you are using is irrelevant. There are deep philosophical issues, but the article you chose didn't have the space to address them. ( And you conveniently ignore those issues and omit mentioning them in your answers. ) From falsehood anything follows is **sanctioned**. Sanctioned where? In "Classical logic". Not "Standard logic". Classical. Sanctioned? What does that mean?

Sanctioned is a decree.

"Hear-ye, Hear-ye, by proclamation of the math-gods as written in our holy scripture, from falsehood anything follows!"

Your "logic" is amazing. { sarcasm }

Notice the key words: "some object" and "a small minority". The vast majority hold to the truth table I gave.

Only in "Classical logic". You omitted that part. The article you quoted is on "Classical logic". You are ignoring relevance logic, and connexive logic. Both are much better in real world situations. The small minority is just one fraction of thoe who object to "from fallsehood -> anything". Not giving the link obscures this. Don't you know by now that I will look up and verify everything you post? And when you omit details, you're going to get caught?

 

[Polymath257]

Well, there you go. You agreed that the statement "All the Jews I know are atheists AND I don't know any Jews" is meaningless gibberish. That means the language being used here is not logical, and the methods you are using isn't viable.



Listen to that exaggeration... you can ask any philosopher. This is completely ignorant. The concensus of philsophers denies the principle of explosion.

The consensus among the majority of philosophers is descriptively a denial of trivialism, termed as non-trivialism or anti-trivialism. This is due to it being unable to produce a sound argument through the principle of explosion and it being considered an absurdity (reductio ad absurdum).​

​

Trivialism - Wikipedia

en.m.wikipedia.org

The concensus rejects this.

And I reject trivialism as well. But that has nothing to do with the truth table for implication.

How is looking in an empty-box, not finding something, then ASSUMING that by some math-god-magic, the not-finding has filled the empty-box with everything logical?

Nope. Nothing like that is going on.

What is the purpose of logic? ASSUME everything is true?

Nope. Nothing close to that is going on.

Again, equivocation, misrepresetation, ambiguity.

Nope. I have been quite clear about my meaning and scope.

We are talking about the "material conditional". That is one tiny little fraction of "logic". It is included in semantic deduction which has many flaws, primary among them, it ignores relevance. That means trying to claim something is "consistent" is impossible using this method.

You keep calling it "implication". That is ambiguous. "Implication" means correlation. But the "material conditional" the truth-table you anre employing DOES NOT communicate correlation. Continuing to use a word which has a double meaning, and knowing it has a double meaning is dishonest.

One of the many names for this is implication.

It's the same for using the word "logic" when there are many "logics" and you are using the one with the lowest, rock-bottom standards. it is equivocation, misrepresentation, and ambiguous.

I am using standard, classical logic. More specifically, propositional and quantifier logic, which is what is appropriate here.

Since there's no correlation or causation in your method, If ... then doesn't work.



Brilliant! Except you left out an english word for 'x'. X=Jews.

Nope. That is NOT what I am doing.

Now let's compare:

"All the Jews I know are atheists"
"For all Jews, either I don't know any Jews, or Jew is not a Jew, or Jews are atheists"

Nope. If you want to go that route, the appropriate version is
for all Jews, if I know them, then there are atheist.

WOW! That's a huge difference in meaning! HUGE! That's the proof right there that this method invalid.

Yes, that is a change in meaning. But that the previous also not what i said, nor is it equivalent to what I said. The current sentence
(there is notthing that is a Jew, known, and not an atheist)
IS equivalent to
(All Jews I know are atheist).

You had to add 3 Ors and 2 Nots, and none of that is in the original statement.

I said they are logically equivalent. And they are.

Sure. But since the mistranslated version completely changes the meaning, then the you cannot use ( not P or Q ) in this case.

Nope, what I said is completely equivalent, What you said above is not.

Hee. Full of contradictions, non-sequiturs, and ambiguities...

If today is Tuesday then God exists. Is logically true? You can't prove it false, it MUST be true. By your version of "logic".

Well, today *is* Tuesday, so the statement is false. *smiles*.

 

[Polymath257]

No link? Why not?



Cherry picked. You omitted the next paragragh which is important.

Deductive systems that demur from ex falso quodlibet are called paraconsistent. Most relevant logics are paraconsistent. See the entries on relevance logic, paraconsistent logic, and dialetheism. Or see Anderson and Belnap [1975], Anderson, Belnap, and Dunn [1992], and Tennant [1997] for fuller overviews of relevant logic; and Priest [2006a,b], for dialetheism. Deep philosophical issues concerning the nature of logical consequence are involved. Far be it for an article in a philosophy encyclopedia to avoid philosophical issues, but space considerations preclude a fuller treatment of this issue here. Suffice it to note that the inference ex falso quodlibet is sanctioned in systems of classical logic, the subject of this article. It is essential to establishing the balance between the deductive system and the semantics (see §5 below).​

​

Hmmmmmmm. The method you are using is irrelevant. There are deep philosophical issues, but the article you chose didn't have the space to address them. ( And you conveniently ignore those issues and omit mentioning them in your answers. ) From falsehood anything follows is **sanctioned**. Sanctioned where? In "Classical logic". Not "Standard logic". Classical. Sanctioned? What does that mean?

You do realize that the term 'relevant logic' is a technical terms, right? In particular, relevance logics allow contradictions. Are you sure you want to do that?

Sanctioned is a decree.

"Hear-ye, Hear-ye, by proclamation of the math-gods as written in our holy scripture, from falsehood anything follows!"

Your "logic" is amazing. { sarcasm }

OK, if you want to reject the usual logic, that is your right. Just don't expect to be taken seriously.

Only in "Classical logic". You omitted that part. The article you quoted is on "Classical logic". You are ignoring relevance logic, and connexive logic. Both are much better in real world situations. The small minority is just one fraction of thoe who object to "from fallsehood -> anything". Not giving the link obscures this. Don't you know by now that I will look up and verify everything you post? And when you omit details, you're going to get caught?

Yes, while I think paraconsistent logic is amusing, I do reject it. So do most people who study logic.

But hey, if you want to go that route, I have some reading for you to do.

Paraconsistent Logic

Paraconsistent logics are those which permit inference from inconsistent information in a non-trivial fashion. Their articulation and investigation is a relatively recent phenomenon, even by the standards of modern logic. (For example, there was no article on them in...

link.springer.com

Handbook of Philosophical Logic

such questions for centuries (unrestricted by the capabilities of any hard ware). The principles governing the interaction of several processes, for example, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based effective but rigid...

books.google.com

 

[dybmh]

And I reject trivialism as well. But that has nothing to do with the truth table for implication.

You're changing the subject. The claim was "ask any philosopher and they agree /accept the principle of explosion". That is false. The concensus reject the principle of explosion. The concensus reject "from falsehood anything follows".

Regarding the "material conditional" which you are labeling "implication" eventhough that word has a double meaning, it is not applicable because using it changes the meaning of the english language statement.

Nope. Nothing like that is going on.

Nope. Nothing close to that is going on.

Then there are no known Jewish-atheists, which is the opposite of all the Jews I know are atheists.

Nope. I have been quite clear about my meaning and scope.

Not even close. As I've shown. You keep claiming "logic" as if it's the only one. You keep claiming "consitency", which cannot be evaluated without relevance. You claimed that *actual* truth is equal to "vacuous truth*. If "true" can mean both, then anytime you said "true" it is ambiguous.

One of the many names for this is implication.

Does this version of "implication" require causation or correlation? If not, then "implication" has a double-meaning which needs specificity. Why are you refusing to use a specific term which is not ambiguous?

I am using standard, classical logic. More specifically, propositional and quantifier logic, which is what is appropriate here.

Which ignores relevance, correct? So how are you using this to evaluate consistency? You are *actually* using semantic deduction. The weakest lowest standard for truth that exists.

Logic, on the other hand, focuses on the deductive relation of logical consequence between the premises and the conclusion or how people should draw inferences. There are different ways of conceptualizing this relation. According to the semantic approach, an argument is deductively valid if and only if there is no possible interpretation of this argument where its premises are true and its conclusion is false. The syntactic approach, on the other hand, holds that an argument is deductively valid if and only if its conclusion can be deduced from its premises using a valid rule of inference.​

So, the *actual* truth is you are giving 1 of 2 options. 50% of the answer, and ignoring the other. The rules of inference are what define logical falacies. Your method ignores all of those. If nothing is falacious that lowers the standards of a "logical consequence" to the point where the entire concept is meaningless.

Nope. That is NOT what I am doing.

Denial is more than a river in egypt.

Nope. If you want to go that route, the appropriate version is
for all Jews, if I know them, then there are atheist.

Fine, let's compare:

"All the Jews I know are atheists" is a certain judgement.

"For all the Jews, if I know them, then they are atheist." is an uncertain propostion.

Certain is the opposite of uncertain. You are still mistranslating the original statement.

Yes, that is a change in meaning. But that the previous also not what i said, nor is it equivalent to what I said. The current sentence
(there is notthing that is a Jew, known, and not an atheist)
IS equivalent to
(All Jews I know are atheist).

Let's look at the together:

"All Jews I know are atheist." is a positive assertion.
"there is nothing that is a Jew, known, and not an atheist" is a negative assertion.

a positive assertion is the opposite of a negative assertion.

You are still mistranslating the oiginal statement.

I said they are logically equivalent. And they are.

Using semantics and grand assumptions.

Nope, what I said is completely equivalent, What you said above is not.

Completely? Hah! They're opposites. You are living in bizarro-world.

Is certain = uncertain?
Is a positive assertion = a negative assertion?

Let me help you.

Contradiction (Stanford Encyclopedia of Philosophy)

plato.stanford.edu

If Socrates doesn't exist, “Socrates is wise” and its contrary “Socrates is not-wise” are both automatically false (since nothing—positive or negative—can be truly affirmed of a non-existent subject), while their respective contradictories “Socrates is not wise” and “Socrates is not not-wise” are both true. Similarly, for any object x, either x is red or x is not red—but x may be neither red nor not-red;​

​

The negative assetions are true, but the positive assertions are ... say it with me ... AUTOMATICALLY FALSE. Because of this making any positive assertion about the empty-set, is automaticaly false. Any positive assertion about knowing the unknown... false.

​

Well, today *is* Tuesday, so the statement is false. *smiles*.

Show me God that doesn't exist... if you can't then it must be true. That's the logic you're employing. Of course, you'll never admit it.

 

[dybmh]

You do realize that the term 'relevant logic' is a technical terms, right? In particular, relevance logics allow contradictions. Are you sure you want to do that?


OK, if you want to reject the usual logic, that is your right. Just don't expect to be taken seriously.


Yes, while I think paraconsistent logic is amusing, I do reject it. So do most people who study logic.

But hey, if you want to go that route, I have some reading for you to do.

Paraconsistent Logic

Paraconsistent logics are those which permit inference from inconsistent information in a non-trivial fashion. Their articulation and investigation is a relatively recent phenomenon, even by the standards of modern logic. (For example, there was no article on them in...

link.springer.com

Handbook of Philosophical Logic

such questions for centuries (unrestricted by the capabilities of any hard ware). The principles governing the interaction of several processes, for example, are abstract an similar to principles governing the cooperation of two large organisation. A detailed rule based effective but rigid...

books.google.com

Since I'm advocating natural deduction and connexive logic, all of this is irrelevant.

The point is, your method ignores all falacies, and does not evaluate relevance, assumes it's true unless it is proven false, and none of that is logical. So I ask again,

How do you evaluate consistency without evaluating relevance?
What is the purpose of logic?
What is the meaning of a logical consequence if there is no causation and no correlation?

If you cannot answer these questions, why should I take what you're saying seriously?

 

[dybmh]

If you want all meaningful propositions to be either true or false, and you want some basic logical surrender to hold, then the truth table for implication has to be that for material implication, which makes it the same as not(p) or q.

The point is, and you have admitted:

All the Jews I know are atheists AND I don't know any Jews is meaningless.

So, by your own standards, if you are consistent, if you are able to distinguish between consitent and not, if you care about precision, the material conditional does not apply. You are talking about meaningful propostions. This is a meaningless propostion.

In particular, if p is false, the implication is true. That is the case of a vacuous truth (the implication).

Not always. This is incomplete.

" if p is false, the implication is true" is incomplete.
"If p is false, the implication is true, unless the consequent is p." is complete.

"I don't know any Jews" = "I don't know any Jews that are atheists, theists, dogs, cats, birds, lamas..."

"All the Jews I know are atheists AND I don't know any Jews that are athiests."

If "All the Jews I know are atheists" Then "I don't know any Jews that are athiests." is false.

P and Not P is automatically false.

Bye-now. Hope your move goes well.

 

[Polymath257]

You're changing the subject. The claim was "ask any philosopher and they agree /accept the principle of explosion". That is false. The concensus reject the principle of explosion. The concensus reject "from falsehood anything follows".

No, that is NOT the case. Even yoyur own quotes show otherwise. Those that reject the principle of explosion are a minority. The consensus is that the principle is valid.

Regarding the "material conditional" which you are labeling "implication" eventhough that word has a double meaning, it is not applicable because using it changes the meaning of the english language statement.

Then there are no known Jewish-atheists, which is the opposite of all the Jews I know are atheists.

Nope. The two are consistent. If I know no Jews, then all of the Jews I know (0 of them) are atheist.

Not even close. As I've shown. You keep claiming "logic" as if it's the only one. You keep claiming "consitency", which cannot be evaluated without relevance. You claimed that *actual* truth is equal to "vacuous truth*. If "true" can mean both, then anytime you said "true" it is ambiguous.

Nope. Vacuously true statements are those implications where the hypothesis is false. It is not a separate version of truth, just a particular subcategory.

Does this version of "implication" require causation or correlation? If not, then "implication" has a double-meaning which needs specificity. Why are you refusing to use a specific term which is not ambiguous?

In logic, the term implication means the material conditional.

Which ignores relevance, correct? So how are you using this to evaluate consistency? You are *actually* using semantic deduction. The weakest lowest standard for truth that exists.

Logic, on the other hand, focuses on the deductive relation of logical consequence between the premises and the conclusion or how people should draw inferences. There are different ways of conceptualizing this relation. According to the semantic approach, an argument is deductively valid if and only if there is no possible interpretation of this argument where its premises are true and its conclusion is false. The syntactic approach, on the other hand, holds that an argument is deductively valid if and only if its conclusion can be deduced from its premises using a valid rule of inference.​

And, according to Godel, the syntactic and the semantic are equivalent.

So, the *actual* truth is you are giving 1 of 2 options. 50% of the answer, and ignoring the other. The rules of inference are what define logical falacies. Your method ignores all of those. If nothing is falacious that lowers the standards of a "logical consequence" to the point where the entire concept is meaningless.


Denial is more than a river in egypt.



Fine, let's compare:

"All the Jews I know are atheists" is a certain judgement.

It is a proposition. it has a truth value. It is true if every Jew I know is an atheist.

"For all the Jews, if I know them, then they are atheist." is an uncertain propostion.

It is equivalent, so I'm not sure what sort of distinction you are trying to make. The truth values of the two propositions are the same.

Certain is the opposite of uncertain. You are still mistranslating the original statement.

There is no uncertainty. Either the two are both true or they are both false. The condition for falsity is that there is a Jew that I know that is not an atheist.

Let's look at the together:

"All Jews I know are atheist." is a positive assertion.
"there is nothing that is a Jew, known, and not an atheist" is a negative assertion.

So? They are still equivalent statements.

a positive assertion is the opposite of a negative assertion.

You are still mistranslating the oiginal statement.

Nope.

Using semantics and grand assumptions.

Actually, using syntactics and standard assumptions. Do you want me to list the assumptions?

Completely? Hah! They're opposites. You are living in bizarro-world.You havre asked

Is certain = uncertain?
Is a positive assertion = a negative assertion?

Let me help you.

Contradiction (Stanford Encyclopedia of Philosophy)

plato.stanford.edu

If Socrates doesn't exist, “Socrates is wise” and its contrary “Socrates is not-wise” are both automatically false (since nothing—positive or negative—can be truly affirmed of a non-existent subject), while their respective contradictories “Socrates is not wise” and “Socrates is not not-wise” are both true. Similarly, for any object x, either x is red or x is not red—but x may be neither red nor not-red;​

​

The negative assetions are true, but the positive assertions are ... say it with me ... AUTOMATICALLY FALSE. Because of this making any positive assertion about the empty-set, is automaticaly false. Any positive assertion about knowing the unknown... false.

Sorry, but your claims that they are false is no better than my claims that they are true *except* that I can give you the assumptions and deduction is you want.

Show me God that doesn't exist... if you can't then it must be true. That's the logic you're employing. Of course, you'll never admit it.

No, it is not the logic I am applying.

You have asked what the purpose of logic is. It is to avoid talking nonsense. It is to go from assumptions to conclusions in a way such that no errors creep in.

Here are a couple of pages describing the axioms and a few deductions based on them:

Hilbert system - Wikipedia

en.wikipedia.org

List of axiomatic systems in logic - Wikipedia

en.wikipedia.org

And, if you want to go for paraconsistent logic, which of the following do you reject?
1. If P is true, then (P or Q) is true
2. If (P or Q) is true and Q is false, then P is false.

Notice that the second is the same as proof via contradiction

 

[Polymath257]

The point is, and you have admitted:

All the Jews I know are atheists AND I don't know any Jews is meaningless.

I did not say that. If you thought that I did, you misunderstood me. It is consistent *if* I know 0 Jews.

So, by your own standards, if you are consistent, if you are able to distinguish between consitent and not, if you care about precision, the material conditional does not apply. You are talking about meaningful propostions. This is a meaningless propostion.

Two statements are consistent if they can both be true at the same time.

Not always. This is incomplete.

" if p is false, the implication is true" is incomplete.
"If p is false, the implication is true, unless the consequent is p." is complete.

Nope. it is NOT incomplete and adding the rest changes the meaning.

If p is false, the implication p-->p is still true. In fact, it is always true.

"I don't know any Jews" = "I don't know any Jews that are atheists, theists, dogs, cats, birds, lamas..."

True.

"All the Jews I know are atheists AND I don't know any Jews that are athiests."

True. That implies I know 0 Jews.

If "All the Jews I know are atheists" Then "I don't know any Jews that are athiests." is false.

That is a true deduction.

P and Not P is automatically false.

Good. In that case, you reject paraconsistent logic, which allows for both p and not p.

Bye-now. Hope your move goes well.

It's crazy. Right now, I am waiting for the guys to load the truck.

 

[dybmh]

No, that is NOT the case. Even yoyur own quotes show otherwise. Those that reject the principle of explosion are a minority. The consensus is that the principle is valid.

But not sound. Just because it's valid doesn't mean it's actually true or has value in real world situations.

Nope. The two are consistent. If I know no Jews, then all of the Jews I know (0 of them) are atheist.

How are you evaluating consistent without evaluating relevance?

Nope. Vacuously true statements are those implications where the hypothesis is false. It is not a separate version of truth, just a particular subcategory.

If I grant that, then using generic "true" is ambiguous. There are subcatagories? Should they all have the same value in the real world?

The negative assertion has much more value because it is *actually* true.

In logic, the term implication means the material conditional.

But without causation and correlation, the word is ambiguous.

And, according to Godel, the syntactic and the semantic are equivalent.

But, they're not. Semantics do not account for relevance or logical fallacies. Most people know that semantic argument have zero value in real world circumstances.

It is a proposition. it has a truth value. It is true if every Jew I know is an atheist.

It is has no value. It is vacuously true. What does vacuous mean? Empty. It is lacking all truth value.

It is equivalent, so I'm not sure what sort of distinction you are trying to make. The truth values of the two propositions are the same.

Nope. Read your own source. The negative assertion is true. The positive assertion is vacuously true. I'll color code it for you and emphasize the difference.

Vacuous truth - Wikipedia

en.m.wikipedia.org

​

It is sometimes said that 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​

​

In the empty room, the cellphones are off

• is a negative assertion about an empty room,
• it is true.

In the empty room, the cellphones are on

• is a positive assertion about an empty room,
• it is considered vacuously true.

In the empty room, the cellphones are on and off,

• is an incohernet contradiction about an empty room,
• it is considered vacuously true.

And this is confirmed by the snippet from Stanford University Philosophy library: Contradiction (Stanford Encyclopedia of Philosophy)

​

If Socrates doesn't exist, “Socrates is wise” and its contrary “Socrates is not-wise” are both automatically false (since nothing—positive or negative—can be truly affirmed of a non-existent subject), while their respective contradictories “Socrates is not wise” and “Socrates is not not-wise” are both true. Similarly, for any object x, either x is red or x is not red—but x may be neither red nor not-red;​

There really isn't anyway around it. It is illogical to make a positive assertion about something that doesn't exist.

There is no uncertainty. Either the two are both true or they are both false. The condition for falsity is that there is a Jew that I know that is not an atheist.

Nope, that's the material conditional. All Jews I know are atheists is a judgement not an implication. Adding the "if then" and 2 "nots" and 3 "ors" is completely changing the meaning of the statement.

So? They are still equivalent statements.

So? Your mistranslation changes the meaning. They cannot be equivalent if they do not mean same thing.

Nope.

I showed you the difference between a negative assertion and a positive assertion. That's the whole point of the thread. Look at the votes.

"All I know are..." is a positive assertion.
"I don't know any ... " is a negative assertion.

The one is the contrapositve of the other. You should know these things. Why deny it?

Actually, using syntactics and standard assumptions. Do you want me to list the assumptions?

I'm not sure I can trust you to give complete answers.

Sorry, but your claims that they are false is no better than my claims that they are true *except* that I can give you the assumptions and deduction is you want.

Not true.

My claim is equally irelevant to yours if we are both looking for non-existent Jews when none can exist. This means that the method you are using cannot develop a true/fale conclusion without some sort of faith-based-decree. You're calling them assumptions. That's true. But really relying on that assumption and calling it "true" is nothing more than a leap of faith.

Because of this, it makes sense to abandon that silly, looking for non-existent Jews, method, and instead look for a better way. It's obvious there is a contradiction here. And contradictions are always false.

No, it is not the logic I am applying.

Oh? Great! Then I guess the material condition is out. Bah-bye.

You have asked what the purpose of logic is. It is to avoid talking nonsense. It is to go from assumptions to conclusions in a way such that no errors creep in.

Agreed. So let's agree to reject the meaningless gibberish "All the Jews I know are atheists AND I don't know any Jews".

Deal? Calling it true is acceptance, and that is counter to the stated purpose of logic.

Here are a couple of pages describing the axioms and a few deductions based on them:

Hilbert system - Wikipedia

en.wikipedia.org

List of axiomatic systems in logic - Wikipedia

en.wikipedia.org

The Church of logic? Axioms? OK, I'll look at it. Thanks.

And, if you want to go for paraconsistent logic, which of the following do you reject?
1. If P is true, then (P or Q) is true
2. If (P or Q) is true and P is false, then Q is true.

I'll go with natural deduction for now. Is there any evidence for P? Is there any evidence for Q? Are P and Q correlated? Does P actually cause Q? Those are questions and answers have value in the real world.

Notice that the second is the same as proof via contradiction

I have not advocated for paraconsistent logic. That is a red hering.

 

[dybmh]

I did not say that. If you thought that I did, you misunderstood me. It is consistent *if* I know 0 Jews.

Is gibberish meaningful?

You said that the material condition is necessary for evaluating meaningful statements into true/false. If gibberish is not meaningful, then the material condition is not useful.

Two statements are consistent if they can both be true at the same time.

"All I know are athiests" is not consisten with "I don't know any that are atheists"

Nope. it is NOT incomplete and adding the rest changes the meaning.

Of course it's incomplete. What you said is not true in all cases. You need to be more precise. Yes, it changes the meaning, what you said is unqualified and false.

You said: "if p is false, the implication is true" For all implications? What if the consequent is P? I didn't say "Not P" is the consequent.

If p is false, the implication p-->p is still true. In fact, it is always true.

That's not what I said.

"Not P ---> P" is false.
"P ---> Not P" is false.

True.

True. That implies I know 0 Jews.

And... It also implies that 0 are atheists.

That is a true deduction.

OK, if folks are following along,

"All the Jews I know are atheists AND I don't know any Jews that are athiests." is considered true.
If "All the Jews I know are atheists" Then "I don't know any Jews that are athiests." is considered false.

"All the Jews I know are atheists" AND "I don't know any Jews that are athiests." should be considered false.

P and NOT P is false.

Because you have agreed that "I don't know any Jews" = "I don't know any Jews that are atheists", I am not chnaging the meaning of the statement in any way. The method being employed delivers both true and false conclusions. There is a better method.

Good. In that case, you reject paraconsistent logic, which allows for both p and not p.

In real world circumstances, reject contradictions as false, and any true judgement requires evidence.

It's crazy. Right now, I am waiting for the guys to load the truck.

Best wishes.