4 very easy arguments. Are they valid?

[fast]

My spidey-sense keeps nudging me to take caution everytime I hear, “everything follows from a contradiction.” It seems nothing well worth trusting would follow. But then again, I have to remind myself that valid arguments with contradictions guarentee the unsoundness of an argument, so although I cannot trust what validly follows as true, I can trust that if true, it would—and of course then, there would be no contradiction. It all comes together in a nice fit; it just sounds odd to the ear that everything follows.

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

If that’s valid, oh boy!, but what about this:

P1: dogs bark
P2: dogs don’t bark
P3: cucumbers are green
C: snow is blue

Calling the third sentence a premise has no entanglement—it’s not apart of the contradiction and not playing a part in the inference. I guess it’s like calling the people who don’t play players just because they’re on the team—sitting in the dugout and never getting wear on their shoes.

 

[steve_bank]

Beware the Jabberwocky



https://en.wikipedia.org/wiki/Jabberwocky

’Twas brillig, and the slithy toves


Did gyre and gimble in the wabe:


All mimsy were the borogoves,


And the mome raths outgrabe.





“Beware the Jabberwock, my son!


The jaws that bite, the claws that catch!


Beware the Jubjub bird, and shun


The frumious Bandersnatch!”





He took his vorpal sword in hand;


Long time the manxome foe he sought—


So rested he by the Tumtum tree


And stood awhile in thought.





And, as in uffish thought he stood,


The Jabberwock, with eyes of flame,


Came whiffling through the tulgey wood,


And burbled as it came!





One, two! One, two! And through and through


The vorpal blade went snicker-snack!


He left it dead, and with its head


He went galumphing back.





“And hast thou slain the Jabberwock?


Come to my arms, my beamish boy!


O frabjous day! Callooh! Callay!”


He chortled in his joy.





’Twas brillig, and the slithy toves


Did gyre and gimble in the wabe:


All mimsy were the borogoves,


And the mome raths outgrabe.

 

[Angra Mainyu]

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

If that’s valid, oh boy!, but what about this:

P1: dogs bark
P2: dogs don’t bark
P3: cucumbers are green
C: snow is blue

Yes, those are valid.

Calling the third sentence a premise has no entanglement—it’s not apart of the contradiction and not playing a part in the inference. I guess it’s like calling the people who don’t play players just because they’re on the team—sitting in the dugout and never getting wear on their shoes.

It is different because 'player' means that a person play, in the usual sense of the word, but 'premise' does not usually mean that the statement is used in the inference. But for example, there are plenty of times in which we want to know whether a statement follows from a number of other statements (e.g., in mathematics), so we take the latter as premises, without knowing whether we will be able to derive the former, and try to derive it. But often it turns out we can derive the former without using all of the premises. So, we might then say that some of the premises turned out to be unnecessary.

 

[steve_bank]

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

a AND (NOT a) is not valid.
P1 NOT P1 AND
T F F
F T F

P1 AND P2 = C is always false.


C unrelated to P1 or P2, non sequitur. 1 + 1 = 2 therefore the sky is blue.

 

[Angra Mainyu]

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

a AND (NOT a) is not valid.
P1 NOT P1 AND
T F F
F T F

P1 AND P2 = C is always false.


C unrelated to P1 or P2, non sequitur. 1 + 1 = 2 therefore the sky is blue.

You seem to be trying to use some method for checking validity, though I do not understand your notation. In any event, P2 means "it is not the case that dogs bark", so the argument is valid (P2 is the negation of P1).

 

[steve_bank]

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

a AND (NOT a) is not valid.
P1 NOT P1 AND
T F F
F T F

P1 AND P2 = C is always false.


C unrelated to P1 or P2, non sequitur. 1 + 1 = 2 therefore the sky is blue.

You seem to be trying to use some method for checking validity, though I do not understand your notation. In any event, P2 means "it is not the case that dogs bark", so the argument is valid (P2 is the negation of P1).

Symbolic logic. I know it from Boolean Algebra in electronics but I am not an expert.

 

[Angra Mainyu]

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

a AND (NOT a) is not valid.
P1 NOT P1 AND
T F F
F T F

P1 AND P2 = C is always false.


C unrelated to P1 or P2, non sequitur. 1 + 1 = 2 therefore the sky is blue.

You seem to be trying to use some method for checking validity, though I do not understand your notation. In any event, P2 means "it is not the case that dogs bark", so the argument is valid (P2 is the negation of P1).

Symbolic logic. I know it from Boolean Algebra in electronics but I am not an expert.

I understand symbolic logic, though I'm not sure how you're applying it. What does the "=" mean? There should be a "THEN", not an "=", as far as I can tell, unless you mean "THEN" by it.

In any case, "a AND (NOT a)" is not an argument, so it is neither valid nor invalid. It is a contradiction. How about: (a AND (NOT a)) THEN b,
for any b?

That should be true if you are applying truth tables properly, which is equivalent to say that any b follows from a and the negation of a.

 

[DBT]

My spidey-sense keeps nudging me to take caution everytime I hear, “everything follows from a contradiction.” It seems nothing well worth trusting would follow. But then again, I have to remind myself that valid arguments with contradictions guarentee the unsoundness of an argument, so although I cannot trust what validly follows as true, I can trust that if true, it would—and of course then, there would be no contradiction. It all comes together in a nice fit; it just sounds odd to the ear that everything follows.

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

If that’s valid, oh boy!, but what about this:

P1: dogs bark
P2: dogs don’t bark
P3: cucumbers are green
C: snow is blue

Calling the third sentence a premise has no entanglement—it’s not apart of the contradiction and not playing a part in the inference. I guess it’s like calling the people who don’t play players just because they’re on the team—sitting in the dugout and never getting wear on their shoes.

Valid statements. Valid premises. They are not arguments.

 

[steve_bank]

Symbolic logic. I know it from Boolean Algebra in electronics but I am not an expert.

I understand symbolic logic, though I'm not sure how you're applying it. What does the "=" mean? There should be a "THEN", not an "=", as far as I can tell, unless you mean "THEN" by it.

In any case, "a AND (NOT a)" is not an argument, so it is neither valid nor invalid. It is a contradiction. How about: (a AND (NOT a)) THEN b,
for any b?

That should be true if you are applying truth tables properly, which is equivalent to say that any b follows from a and the negation of a.

See the new thread.

In logic an augment means a logical term of a larger logical construct.
a & b = c or a AND b = c means

a b c
f f f
f t f
t f f
t t t

If john has testicles and a penis and males have testicles and penusis than john is male. Ignoring other issues for sake of argument.

P1 John has testicles and penis
P2 Males have atesticles and penis'
C John is male

[John has testicles and penis] & [males have penis and testacies= [John is male]
a & b = c

John has tentacles and penis males have tentacles and penis John is male
false false false
false true false
true false false
true true true

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

P1 and P2 are mutually exclusive, a fact can not be both true and false. The logical and of a and b with b = NOT a will always be false.

If( true and false) can never be true in logic. if(true AND false) then c will always be false.

C being unrelated to P! and P@ is non sequitur.

 

[Angra Mainyu]

See the new thread.

Okay, I will do so later or tomorrow, with more time.

In logic an augment means a logical term of a larger logical construct.
a & b = c or a AND b = c means

a b c
f f f
f t f
t f f
t t t

Okay, so that is what you are trying to say (I do understand logic). You got it wrong. When you have "if...then..", you should not use "=" instead of "then".

If john has testicles and a penis and males have testicles and penusis than john is male. Ignoring other issues for sake of argument.

P1 John has testicles and penis
P2 Males have atesticles and penis'
C John is male

No, that is invalid. Here, P2 means:

P2': For all X, if X is a male, then X has testicles and a penis.

(P2' is false because, say, castrated males are still males, but leaving that aside).
It does not follow from that that just because John has testicles and a penis, he is a male (he might be a hermaphrodite, but regardless, the point is that it does not follow from P1 and P2').

[John has testicles and penis] & [males have penis and testacies= [John is male]
a & b = c

That is not the same to the previous argument. Here, you are using "=" which is an "if and only if", instead of an "if...then". But in addition, the equivalence does not follow logically, either.

P1 and P2 are mutually exclusive, a fact can not be both true and false. The logical and of a and b with b = NOT a will always be false.

The first sentence is true. I don't understand the second one.

If( true and false) can never be true in logic.

Nor can it be false, because it is an "if" without a "then", and so not well formed.

if(true AND false) then c will always be false.

Actually, if (true and false) then c is always true.

 

[fast]

My spidey-sense keeps nudging me to take caution everytime I hear, “everything follows from a contradiction.” It seems nothing well worth trusting would follow. But then again, I have to remind myself that valid arguments with contradictions guarentee the unsoundness of an argument, so although I cannot trust what validly follows as true, I can trust that if true, it would—and of course then, there would be no contradiction. It all comes together in a nice fit; it just sounds odd to the ear that everything follows.

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

If that’s valid, oh boy!, but what about this:

P1: dogs bark
P2: dogs don’t bark
P3: cucumbers are green
C: snow is blue

Calling the third sentence a premise has no entanglement—it’s not apart of the contradiction and not playing a part in the inference. I guess it’s like calling the people who don’t play players just because they’re on the team—sitting in the dugout and never getting wear on their shoes.

Valid statements. Valid premises. They are not arguments.

The only thing that can be valid is the argument.

In the case of nondeductive arguments, they are neither valid nor invalid. The only thing true to say of nondeductive arguments in terms of validity is to say they are not valid. So, although it’s false to say of nondeductive arguments that they are invalid, it’s true to say of them that they are not valid; hence, there’s a meaningful distinction between “invalid” and “not valid.”

Although “not valid” is a common definition of “invalid,” I have successfully argued that the definition as an explanation of its meaning is inadequate for a thourough understanding of its meaning.

Earlier, I said, “the only thing that can be valid is the argument.” That’s true. When used as a technical term, it’s application is specific to deductive arguments only. However, nothing but the form of the argument is valid or invalid. It is a category error to regard anything else as valid or invalid. That’s why it’s improper to regard either a sentence or a premise as valid or invalid—when employing the technical and stipulative sense in which the word is used.

P1: it is the case that X
P2: it is not the case that X
C: Y

Y can be anything (so I’m told) for the fact the preceding premises contain a contradiction.

So, had I said:
C: snow is blue
Or even:
C: snow is yellow only after alien spacecraft have landed on the them

The form is valid, for like it’s been said, everything follows, even the impossible.

Between the choices of valid and not valid, the argument is valid
Between the choices of valid and invalid, the argument is valid

The form of the argument is valid, so the argument is valid.

What’s not valid (not to be mistaken with invalid) is everything else (for instance the sentences or premises); specifically, it is false to say the sentences are invalid specifically because they are not valid based on the category error.

 

[DBT]

My spidey-sense keeps nudging me to take caution everytime I hear, “everything follows from a contradiction.” It seems nothing well worth trusting would follow. But then again, I have to remind myself that valid arguments with contradictions guarentee the unsoundness of an argument, so although I cannot trust what validly follows as true, I can trust that if true, it would—and of course then, there would be no contradiction. It all comes together in a nice fit; it just sounds odd to the ear that everything follows.

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

If that’s valid, oh boy!, but what about this:

P1: dogs bark
P2: dogs don’t bark
P3: cucumbers are green
C: snow is blue

Calling the third sentence a premise has no entanglement—it’s not apart of the contradiction and not playing a part in the inference. I guess it’s like calling the people who don’t play players just because they’re on the team—sitting in the dugout and never getting wear on their shoes.

Valid statements. Valid premises. They are not arguments.

The only thing that can be valid is the argument.

In the case of nondeductive arguments, they are neither valid nor invalid. The only thing true to say of nondeductive arguments in terms of validity is to say they are not valid. So, although it’s false to say of nondeductive arguments that they are invalid, it’s true to say of them that they are not valid; hence, there’s a meaningful distinction between “invalid” and “not valid.”

Although “not valid” is a common definition of “invalid,” I have successfully argued that the definition as an explanation of its meaning is inadequate for a thourough understanding of its meaning.

Earlier, I said, “the only thing that can be valid is the argument.” That’s true. When used as a technical term, it’s application is specific to deductive arguments only. However, nothing but the form of the argument is valid or invalid. It is a category error to regard anything else as valid or invalid. That’s why it’s improper to regard either a sentence or a premise as valid or invalid—when employing the technical and stipulative sense in which the word is used.

P1: it is the case that X
P2: it is not the case that X
C: Y

Y can be anything (so I’m told) for the fact the preceding premises contain a contradiction.

So, had I said:
C: snow is blue
Or even:
C: snow is yellow only after alien spacecraft have landed on the them

The form is valid, for like it’s been said, everything follows, even the impossible.

Between the choices of valid and not valid, the argument is valid
Between the choices of valid and invalid, the argument is valid

The form of the argument is valid, so the argument is valid.

What’s not valid (not to be mistaken with invalid) is everything else (for instance the sentences or premises); specifically, it is false to say the sentences are invalid specifically because they are not valid based on the category error.

I don't see an argument, just a list of premises. I see no relationship in terms of an argument - premises leading to a conclusion - between ''snow is blue'' and whether dogs bark or do not bark. Barking dogs have nothing to do with the colour of snow. Silent dogs have nothing to do with the colour of snow.

Now, I am aware that I may be missing some deep philosophical connection in this line of reasoning, but it's probably too subtle for my poor brain to grasp.

 

[ruby sparks]

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

If that’s valid, oh boy!, but what about this:

P1: dogs bark
P2: dogs don’t bark
P3: cucumbers are green
C: snow is blue

Yes, those are valid.

Calling the third sentence a premise has no entanglement—it’s not apart of the contradiction and not playing a part in the inference. I guess it’s like calling the people who don’t play players just because they’re on the team—sitting in the dugout and never getting wear on their shoes.

It is different because 'player' means that a person play, in the usual sense of the word, but 'premise' does not usually mean that the statement is used in the inference. But for example, there are plenty of times in which we want to know whether a statement follows from a number of other statements (e.g., in mathematics), so we take the latter as premises, without knowing whether we will be able to derive the former, and try to derive it. But often it turns out we can derive the former without using all of the premises. So, we might then say that some of the premises turned out to be unnecessary.

Ok now I'm confused.

P1: dogs bark
P2: dogs don’t bark
C: snow is blue

I had thought that 'valid' meant the conclusion must follow from the premises, not just (a) that it could or (b) merely did not contradict them (or whatever the correct word is if it's not contradict).

ETA: I see from this that I apparently had it wrong:

"A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false."
https://www.iep.utm.edu/val-snd/

Is that, in your opinion, a good definition of validity?

If so, gosh. Validity seems to tell us less (give us less information) than I thought before joining this thread, and even less than I thought it did before finding out that contradictions did not make an argument invalid, or not valid (I confess I'm not understanding the distinction).

No hang on.

A few lines later, that source adds:

"In effect, an argument is valid if the truth of the premises logically guarantees the truth of the conclusion."

Which is not the same as what is in blue above? There's nothing about dogs that guarantees anything about snow (unless the dogs pee on it I suppose).

 

[fast]

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

The point (I guess) is that there are different forms of deductive arguments: some are valid while some are not; some are intuitive; others, not so much.

 

[untermensche]

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.

All the second premise and conclusion are is a restatement (with a shift in time frame) of the first premise.

If this is supposed to mean something I have no clue.

 

[ruby sparks]

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.

I get the first one, about smiling.

 

[Angra Mainyu]

I had thought that 'valid' meant the conclusion must follow from the premises, not just (a) that it could or (b) merely did not contradict them (or whatever the correct word is if it's not contradict).

Yes, the conclusion must follow from the premises. It is not the case that the conclusion never contradicts the premises of a valid argument. For example:

P1: Joe is a cat.
P2: Joe is not a cat.
C: Joe is a cat and Joe is not a cat.

The conclusion follows from the premises, and it also contradicts the premises (this can happen because the set of premises is an inconsistent set).

"A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false."
https://www.iep.utm.edu/val-snd/

Is that, in your opinion, a good definition of validity?

Yes, I think it is, because I think everything follows from a contradiction. The vast majority of philosophers, mathematicians and logicians believe so too, but there are people who disagree. Still, that is a matter different from the matter of whether a contradiction can be the conclusion of a valid argument - on that, as far as I know, everyone in those fields agree that it can.

A few lines later, that source adds:

"In effect, an argument is valid if the truth of the premises logically guarantees the truth of the conclusion."

Which is not the same as what is in blue above? There's nothing about dogs that guarantees anything about snow (unless the dogs pee on it I suppose).

It is the same, actually. The dogs in the argument you post are irrelevant. The only thing that matters is the following:


P1
P2: ¬P1.
C: snow is blue

(or, for that matter, C': There is an invisible dragon in my garage.).

The point is that P2 is the negation of P1 (i.e., "dogs don't bark" means "it is not the case that dogs bark"). It does not matter what P1 says. The truth of the premises logically guarantees the truth of the conclusion because it is logically impossible that all of the premises be true but the conclusion false. But this is so because it is logically impossible that all of the premises be true.

 

[fast]

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.

All the second premise and conclusion are is a restatement (with a shift in time frame) of the first premise.

If this is supposed to mean something I have no clue.

P1: If I deposit $10 to my checking account which currently has $50 in it, my new balance will be $1,000,000.
P2: I deposited $10 to my checking account.
Therefore, C: my new balance is what?

If (IF) the premises are true, it must be true that my balance is $1,000,000

 

[untermensche]

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.

All the second premise and conclusion are is a restatement (with a shift in time frame) of the first premise.

If this is supposed to mean something I have no clue.

P1: If I deposit $10 to my checking account which currently has $50 in it, my new balance will be $1,000,000.
P2: I deposited $10 to my checking account.
Therefore, C: my new balance is what?

If (IF) the premises are true, it must be true that my balance is $1,000,000

Considering P1 true is insanity not logic.

 

[fast]

P1: If I deposit $10 to my checking account which currently has $50 in it, my new balance will be $1,000,000.
P2: I deposited $10 to my checking account.
Therefore, C: my new balance is what?

If (IF) the premises are true, it must be true that my balance is $1,000,000

Considering P1 true is insanity not logic.

There can be unstated reasons for why it would be true; but that’s not the point.

All cats are mammals
Tiger is a cat
Therefore, Tiger has teeth

All three statements are true, yet the conclusion doesn’t follow from the premises.

If a big brute tackles the frail old man hard, he will fall
A big brute tackled the frail old man
The second premise doesn’t have to be true to realize what would folllow IF it were true. The first premise doesn’t have to be true either, but if it was, you should readily grasp what would follow. Even if neither were true, what would be guarenteed is the conclusion IF they were true.

If validity speaks only to form (which it does in the context I’m speaking), the truth of premises are irrelevant when it comes to determining validity.