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4 very easy arguments. Are they valid?

No.

It is saying 10 + 50 = a million.

Addition is not subjective.
I told the guy to leave his girlfriend with me and that he could take his $20 and shove it; in fact, to just go away, I exclaimed (jokingly) what he could do: to go deposit it into his account; indeed, I followed up and said that for every one of those dollars he deposited that I would add $100. She came and sat with me.

My uncle (flirtatious devil) and so exquisitely rich and with no hint of joking told me for a single dance with her that he’d put $100,000 in my account for each dollar up to $20 I deposited. Well, not needing the money, I took $10 bought a drink and left a $60 tip; for shits and giggles, I deposited $10.
 
Modus Ponens’ if p, then q, p; therefore q is intuitively valid.

If I smile at her, then she’ll like me
I smiled at her
Therefore, she likes me

Never mind if the premises are true. Just ask yourself, if they are true, does the conclusion follow. The answer is yes.

Contradictions’ p and not p is unintuitivly valid

There’s some logically based reason (something to do with an explosion) that sounds like when two rocket propelled contradictory statements meet, a tear in the fabric of space and time unleashes every statement conceived by mankind and they all fit nice and neat in a big ocean we call C

P1: it is the case that dogs bark
P2: it is not the case that dogs bark
C: there’s a three-legged unicorn dancing in your kitchen wearing a yellow polka dot bikini

Valid

Unintuitive as hell, but valid.

I still don't understand why. :confused:

I get the first one, about smiling.

Same. The relationship between smiling and liking is clear, but not necessarily true.....she may smile politely without emotion. A courteous response with no like or dislike as the motive to smile in return.


''a three-legged unicorn dancing in your kitchen wearing a yellow polka dot bikini'' while being a coherent sentence, has nothing to do with dogs or anything else.
 
Modus Ponens’ if p, then q, p; therefore q is intuitively valid.

If I smile at her, then she’ll like me
I smiled at her
Therefore, she likes me

Never mind if the premises are true. Just ask yourself, if they are true, does the conclusion follow. The answer is yes.

Contradictions’ p and not p is unintuitivly valid

There’s some logically based reason (something to do with an explosion) that sounds like when two rocket propelled contradictory statements meet, a tear in the fabric of space and time unleashes every statement conceived by mankind and they all fit nice and neat in a big ocean we call C

P1: it is the case that dogs bark
P2: it is not the case that dogs bark
C: there’s a three-legged unicorn dancing in your kitchen wearing a yellow polka dot bikini

Valid

Unintuitive as hell, but valid.

I still don't understand why. :confused:

I get the first one, about smiling.

Same. The relationship between smiling and liking is clear, but not necessarily true.....she may smile politely without emotion. A courteous response with no like or dislike as the motive to smile in return.


''a three-legged unicorn dancing in your kitchen wearing a yellow polka dot bikini'' while being a coherent sentence, has nothing to do with dogs or anything else.
The relationship doesn’t have to be necessarily true. That was just a premise, not an argument. One might want an argument to accept the premise, but that would be a separate argument.

If I smile at her, she will shoot me. That is not necessarily true, but IF it’s true, and IF I smile at her, then the argument is taking a valid form such that if both premises are indeed true, then the conclusion she will shoot me must be true. There’s no if’s, and’s, but’s, or half naked maybe’s about it. The structure is such that it’s impossible for there to be any other conclusion. It’s deductively valid, and the only thing keeping it from being sound is the possibility the premises are not true; yet, if they are indeed true, there’s no doubt about it.
 
P1: Joe is a cat.
P2: Joe is not a cat.
C: Joe is a cat and Joe is not a cat.

This is where formal logic comes in, when informal logic fails.

P1 a
P2 !a
P3 a & !a

Logically P3 (TRUE) AND (Not TRUE) will always be false
truth table for P3
a !a (a AND a!)
true false false
false true false
 
Same. The relationship between smiling and liking is clear, but not necessarily true.....she may smile politely without emotion. A courteous response with no like or dislike as the motive to smile in return.


''a three-legged unicorn dancing in your kitchen wearing a yellow polka dot bikini'' while being a coherent sentence, has nothing to do with dogs or anything else.
The relationship doesn’t have to be necessarily true. That was just a premise, not an argument. One might want an argument to accept the premise, but that would be a separate argument.

If I smile at her, she will shoot me. That is not necessarily true, but IF it’s true, and IF I smile at her, then the argument is taking a valid form such that if both premises are indeed true, then the conclusion she will shoot me must be true. There’s no if’s, and’s, but’s, or half naked maybe’s about it. The structure is such that it’s impossible for there to be any other conclusion. It’s deductively valid, and the only thing keeping it from being sound is the possibility the premises are not true; yet, if they are indeed true, there’s no doubt about it.

Sure, no dispute, that much is clear. But some of the examples given in these threads by several posters appear to drift somewhat beyond what you happen to be saying here.
 
P1: Joe is a cat.
P2: Joe is not a cat.
C: Joe is a cat and Joe is not a cat.

This is where formal logic comes in, when informal logic fails.

P1 a
P2 !a
P3 a & !a

Logically P3 (TRUE) AND (Not TRUE) will always be false
truth table for P3
a !a (a AND a!)
true false false
false true false
A false conclusion is evidence that a deductive argument is unsound, not invalid.
 
No.

It is saying 10 + 50 = a million.

Addition is not subjective.
I told the guy to leave his girlfriend with me and that he could take his $20 and shove it; in fact, to just go away, I exclaimed (jokingly) what he could do: to go deposit it into his account; indeed, I followed up and said that for every one of those dollars he deposited that I would add $100. She came and sat with me.

My uncle (flirtatious devil) and so exquisitely rich and with no hint of joking told me for a single dance with her that he’d put $100,000 in my account for each dollar up to $20 I deposited. Well, not needing the money, I took $10 bought a drink and left a $60 tip; for shits and giggles, I deposited $10.


P1: If I deposit $10 to my checking account which currently has $50 in it, my new balance will be $1,000,000.

OK. You win.

It's not that I didn't see it but it is not rational to assume things like that will occur in the real world.

It is much more likely the premise is false than true.

It is probably something that has never happened.
 
Occlusion follows from the premise when there are no logical faults in the premise.

A crime occurs. One witness tells a cop the man was very short. Another witness says the man was very tall. The cop gets on the radio and says 'be on the lookout for a very sort very tall man;. . Somebody on the receiving end will think WRF?

Here P2 is !P1 as in the syllogism with a claimed valid conclusion. Contradiction in the premises can not lead to a valid conclusion.
 
Occlusion follows from the premise when there are no logical faults in the premise.

A crime occurs. One witness tells a cop the man was very short. Another witness says the man was very tall. The cop gets on the radio and says 'be on the lookout for a very sort very tall man;. . Somebody on the receiving end will think WRF?

Here P2 is !P1 as in the syllogism with a claimed valid conclusion. Contradiction in the premises can not lead to a valid conclusion.

A conclusion is never valid or invalid. It is not the sort of thing that can be valid or invalid. A deductive argument with contradictory premises is always valid. The conclusion from that is anything you want (or, if you like, everything), so it is not good at providing information - except, of course, in situations in which the information that you are looking for is something like whether one of the premises is true, given that the others are.
 
If valid means ''to prove that something is correct,'' but if the conclusion of a syllogism does not follow from its set of premises, the conclusion has not proven to be correct. So according to the given definition of 'valid' the conclusion is not valid.


to prove that something is correct:
I can see it now! You fail to use your right turn signal and are subsequently issued a traffic ticket. You show up for court and in front of the Flying Spaghetti Monster and everybody in the courtroom, you argue that you didn’t do anything wrong because it wasn’t a left turn that you had made.

Green peanuts are not called green because of their color.

The armored car driver fishing at the bank of the river both did and did not go to the bank—it depends on what is meant by “bank.”

An old man comes back from crabbing and says, “I have crabs.” The young teens chuckle and giggle.

Words are ambiguous, and although your usage is not an incorrect one, using it now is like bringing a soccer ball to a football game. Wrong ball...wrong game...wrong word usage
 
Occlusion follows from the premise when there are no logical faults in the premise.

A crime occurs. One witness tells a cop the man was very short. Another witness says the man was very tall. The cop gets on the radio and says 'be on the lookout for a very sort very tall man;. . Somebody on the receiving end will think WRF?

Here P2 is !P1 as in the syllogism with a claimed valid conclusion. Contradiction in the premises can not lead to a valid conclusion.

A conclusion is never valid or invalid. It is not the sort of thing that can be valid or invalid. A deductive argument with contradictory premises is always valid. The conclusion from that is anything you want (or, if you like, everything), so it is not good at providing information - except, of course, in situations in which the information that you are looking for is something like whether one of the premises is true, given that the others are.

To add more info, actually there are senses of 'valid' under which a conclusion may be valid: the most closely related one would say that a conclusion is valid if it follows from the premises. But that is not the sense of 'valid' we are considering here. Rather, we are considering validity as a property of arguments, not of conclusions.
 
If valid means ''to prove that something is correct,'' but if the conclusion of a syllogism does not follow from its set of premises, the conclusion has not proven to be correct. So according to the given definition of 'valid' the conclusion is not valid.


to prove that something is correct:

Valid, at least in this context, is not a verb (and I don't know any context in which it is). There are different definitions of validity, but I would say a standard one is given here (in classical logic; there are other notions in other logics, so perhaps a more general one would be that the conclusion follows from the premises according to some logic, but the one in the link holds for the most common cases by far, including I would say for our usual logic, when properly applied).
 
Unlike science definitions on philosophy are not singular and are contextual. Hence the endless debate on meaning and the fall back cliché I use out in the real world 'Define your terms!'.

The more you try to narrow a definition the more fuzzy it gets, a sort of philosophical uncertainty principle borrowing from physics.

Reducing a problem in logic to logical equations with unambiguous rules gets rid of the problem with meaning.
 
Occlusion follows from the premise when there are no logical faults in the premise.

A crime occurs. One witness tells a cop the man was very short. Another witness says the man was very tall. The cop gets on the radio and says 'be on the lookout for a very sort very tall man;. . Somebody on the receiving end will think WRF?

Here P2 is !P1 as in the syllogism with a claimed valid conclusion. Contradiction in the premises can not lead to a valid conclusion.

A conclusion is never valid or invalid. It is not the sort of thing that can be valid or invalid. A deductive argument with contradictory premises is always valid. The conclusion from that is anything you want (or, if you like, everything), so it is not good at providing information - except, of course, in situations in which the information that you are looking for is something like whether one of the premises is true, given that the others are.

You are proffering debate that can never be resolved in philosophy. This is why as science advanced it split from Natural Philosophy and metaphysics as a means to describe reality.The general stent when reading locic in an intro logic class in philosopy is ' a vaild syllogism or argument must floow from the premise'. That is what valid means in the context of the thread.

Along with that there can be no faults in the prmise.

P1 jack is a dog
P2 Jack is not a dog
C Jack is both a dog and not a dog.

Which looks a kittle like the Liar's Paradox. Resorting to symbolic logic

P1 a
P2 !a not a
C a ^ !a

The AND truth table c = a & b
a b c
F F F
F T F
T F F
T T T

In your syllogism the P1 P2 terns appear as the 2nd and 3rd rows in the truth table. The syllogism conclusion can never be logically true or valid in any context.


If Jack says he is Greek and all Greeks are liars the conclusion Jack is both Greek and a liar is invalid. In logic a term can only have 2 possible states true or false derived by the rules and definitions in logic. In math and technology we call them Boolean variables.
 
If valid means ''to prove that something is correct,'' but if the conclusion of a syllogism does not follow from its set of premises, the conclusion has not proven to be correct. So according to the given definition of 'valid' the conclusion is not valid.


to prove that something is correct:
I can see it now! You fail to use your right turn signal and are subsequently issued a traffic ticket. You show up for court and in front of the Flying Spaghetti Monster and everybody in the courtroom, you argue that you didn’t do anything wrong because it wasn’t a left turn that you had made.

Green peanuts are not called green because of their color.

The armored car driver fishing at the bank of the river both did and did not go to the bank—it depends on what is meant by “bank.”

An old man comes back from crabbing and says, “I have crabs.” The young teens chuckle and giggle.

Words are ambiguous, and although your usage is not an incorrect one, using it now is like bringing a soccer ball to a football game. Wrong ball...wrong game...wrong word usage

I still don't see it.

If ''valid'' means that something can be proven to be correct, it can be shown to be correct. The information is available in the premises, so to be correct, the conclusion must follow from the given set of premises.

If there is no relationship between barking dark/silent dogs and the conclusion of spaghetti monster in your bathroom, for example, the conclusion simply does not follow from the premises, hence the conclusion cannot be validated by the information present in the premises.

That the conclusion cannot be validated by the given premises makes the conclusion invalid.

Semantics? Sure. But not in the sense of ambiguous word meanings such as the fisherman who 'has crabs' which depends on context, which sometimes provides a double entendre.
 
steve bank said:
You are proffering debate that can never be resolved in philosophy.
No, I am not.

steve bank said:
This is why as science advanced it split from Natural Philosophy and metaphysics as a means to describe reality.The general stent when reading locic in an intro logic class in philosopy is ' a vaild syllogism or argument must floow from the premise'. That is what valid means in the context of the thread.
No, that is not what it means. The syllogism or argument does not follow from the premises. Rather, the conclusion follows from the premises if the argument is valid.

steve bank said:
Along with that there can be no faults in the prmise.
Sure there can. For example, the premises might be false. Or they might even be contradictory, in which case the argument is valid.

steve bank said:
P1 jack is a dog
P2 Jack is not a dog
C Jack is both a dog and not a dog.

Which looks a kittle like the Liar's Paradox.
It does not. That is a run of the mill argument, and it is valid. But it does not even use that everything follows from a contradiction.

steve bank said:
Resorting to symbolic logic

P1 a
P2 !a not a
C a ^ !a

The AND truth table c = a & b
a b c
F F F
F T F
T F F
T T T

In your syllogism the P1 P2 terns appear as the 2nd and 3rd rows in the truth table. The syllogism conclusion can never be logically true or valid in any context.
The conclusion is not the sort of thing that can be valid or invalid. It is not true, of course. It is false. But it does follow from the premises, and the argument is valid.


steve bank said:
If Jack says he is Greek and all Greeks are liars the conclusion Jack is both Greek and a liar is invalid. In logic a term can only have 2 possible states true or false derived by the rules and definitions in logic. In math and technology we call them Boolean variables.
You are mistaken, though the argument with a premise "Jack says he is Greek", a premise "all Greeks are liars" and a conclusion "Jack is both Greek and a liar" is invalid.
 
Angra is engaging in metaphysisn not logic.

If you apply formal logic properly it does not matter what you call or describe it. The results of the conclusion does not vary.with interpretation.

It is like calculating 1 + 1 = 2 with the rules of arithmetic versus debating what addition 'means' conceptually.

Logic has long passed to math, computer science, and engineering as a discipline..

Arguing context based conclusions and definitions is informal logic. We all use logic all the time. We learn it in part by language immersion growing up and in primary education without formal definitions.

and, or, if then else. not..

A lot of debate on philosophy ends up being about meaning, and some on science. It happens out in the real world, people can't agree on meaning and sometimes it gets hostile. In science one can end debate with a little math. or an experiment.

Whiter a premise is true or false is not the question. The issue is that when are logical faults in the different premises taken together, a valid conclusion is not possible.

A valid logical conclusion in the case of a syllogism is a conclusion that is a binary true or false traceable to the premises using the rules of logic.

P1 Jack is a dog
P2 Jack is not a dog
C Jack is a dog and Jack is not a dog.

Show with formal logic the conclusion follows from the premises.
 
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