And the next U.K. Prime Minister will be?

[steve_bank]

I see Ebs priblem a little more clearly.

To ne the logic of mathematical logic does not mean naything.

Boolean Algebra is consitent, there are no possible anbiguities or false conclusions. The logic mat not properly represnt a problem, but as wrteen Boolean expressions aleys work properly. This contrasts with sylogistic verbal arguments.

One needs to develop a proof. It is unknown if a ptoof exists and there is no clear path to a proof. One starts with an assumption and trues a path. If the all proofs were logical obvious then all proofs would be obvious are all creative human activities of which logic is a part but not sufficient for creative work. It is about the way our neural net is wired.

See the thread on logical positivism. An attempt to reduce scientific reasoning to a set of riles and definitions. An attempt to reduce creative math and science to a a set of philosophical principles. Not possible.

You will not understand unless you try to do a proof. Logic is often applie with non logical reasoning.


How do you apply logic to even syart the proof? There is no mechistic logical process as to how ro apply logic.

Geberal reasoning is logical. If, and, or and so on.

What logic did Aristotle use to create his logic? The proverbiall chicken and egg problem.

Mathematical ogic is an axiomatic system, like arithmetic and geomerty and algebra. There is no absolute proof of anyting, only consistincy.

Aristotle’s logic itself is based on definitions. Prove the basis of the development of Aristotelian logic.

 

[fast]

In EBs syllogism conclusion does not follow from premise, there is no connection between premise and conclusion. It is invalid

If sally is awake, then Sally is at the grocery store.
If sally is awake, then Sally is at home
Sally is awake
Conclusion, Sally is at home

Speakpigeon will see the problem, and so will academics, and both the academics and Speakpigeon will readily conclude the argument to be unsound, but while Speakpigeon claims the argument is invalid, the academics will not.

You’re gonna see the problem too, and I would suppose you too will find the argument unsound, but if you find the argument invalid, is it merely because of the inconsistency? What is it about the inconsistency that captures our attention? We realize one must be false, but ah ha!, that isn’t an issue with form but rather truth. Forget the truth value of the premise in your judgement.

Look at the conclusion. Sally is at home. Is there enough in the argument to get us there? Yes! And that makes it valid. Set what you need in stone and lock it in the safe. The falsities and inconsistencies are distractions.

 

[DBT]

If the argument is unsound, how can it possibly be valid?

 

[fast]

If the argument is unsound, how can it possibly be valid?

A sound argument is both valid and has true premises.

If an argument is valid but has false premises, it’s unsound.
If an argument is invalid and has true premises, it’s unsound.
If an argument is invalid and has false premises, it’s unsound.

Both conditions must be met for an argument to be sound.

 

[fast]

If a cat meows, wolves will howl
A cat meows
Wolves, therefore, will howl

That’s valid, but not all premises are true, so although the argument is unsound, it’s nevertheless a valid argument. The form is not deficient. That’s what’s important.

 

[DBT]

If the argument is unsound, how can it possibly be valid?

A sound argument is both valid and has true premises.

If an argument is valid but has false premises, it’s unsound.
If an argument is invalid and has true premises, it’s unsound.
If an argument is invalid and has false premises, it’s unsound.

Both conditions must be met for an argument to be sound.

Isn't it the point of an argument to provide a set of premises that support a given conclusion?

 

[steve_bank]

In EBs syllogism conclusion does not follow from premise, there is no connection between premise and conclusion. It is invalid

If sally is awake, then Sally is at the grocery store.
If sally is awake, then Sally is at home
Sally is awake
Conclusion, Sally is at home

Speakpigeon will see the problem, and so will academics, and both the academics and Speakpigeon will readily conclude the argument to be unsound, but while Speakpigeon claims the argument is invalid, the academics will not.

You’re gonna see the problem too, and I would suppose you too will find the argument unsound, but if you find the argument invalid, is it merely because of the inconsistency? What is it about the inconsistency that captures our attention? We realize one must be false, but ah ha!, that isn’t an issue with form but rather truth. Forget the truth value of the premise in your judgement.

Look at the conclusion. Sally is at home. Is there enough in the argument to get us there? Yes! And that makes it valid. Set what you need in stone and lock it in the safe. The falsities and inconsistencies are distractions.

At first I thought it invalid, but it is valid. Conclusion follows from premise. But it is shaky IMO. The premises are confusing without a 4th premise, Sally lives at the store.

If sally is awake, then Sally is at the grocery store.
If sally is awake, then Sally is at home
Sally is awake
Conclusion, Sally lives at the grocery store...

That would be my conclusion based on the premises.

 

[A Toy Windmill]

Here is a "U.K. current affairs" argument.

P1 - Jeremy Corbyn is not Boris Johnson;
P2 - Boris Johnson is not Jeremy Hunt;
P3 - Jeremy Hunt is not Jeremy Corbyn;
P4 - The next U.K. Prime Minister will be either Boris Johnson or Jeremy Hunt;
P5 - The next U.K. Prime Minister will be Jeremy Corbyn;
C - Therefore, the next U.K. Prime Minister will be Boris Johnson.

Thank you to say whether you consider this argument valid or not. P1-P3 are irrelevant. C in no way follows from P4 P5.

Thank you to abstain from commenting before you voted.
EB

It is non squitter. The conclusion does not follow from the premises. The syllogism is not valid, conclusion does not follow from premise.

P1-P3 are irrelevant to C. C does not follow from P4 P5.

The argument can be formalized:

P1) JC != BJ
P2) BJ != JH
P3) JH != JC
P4) PM = BJ || PM = JH
P5) PM = JC

From P4 and P5, we have

C1) PM = BJ || JH = JC

From P3 and P4, we then have

C2) PM = BJ

 

[A Toy Windmill]

If the argument is unsound, how can it possibly be valid?

A sound argument is both valid and has true premises.

If an argument is valid but has false premises, it’s unsound.
If an argument is invalid and has true premises, it’s unsound.
If an argument is invalid and has false premises, it’s unsound.

Both conditions must be met for an argument to be sound.

Ironically, mathematical logicians often use the terms "valid" and "sound" differently to philosophers. I suggest it's another hang-up from syllogistic logic, which was a classification system for 256 argument forms into the valid ones and the fallacious ones. Mathematical logics aren't classifications of arguments. They are "calculii" of statements.

Mathematicians have little interest in how calculii are misapplied, which is to say they have little interest in "miscalculation". And so they have very little interest in the misapplication of logical calculii, which is to say "invalidity." A miscalculation isn't a calculation at all. And an invalid proof isn't a proof at all. So they might say.

Instead, the word "valid" gets co-opted for something else. Instead of calling arguments valid or invalid, mathematical logicians call statements valid or invalid depending on whether they are always logically true. So "P or not-P" is valid statement. But "P or Q" is invalid.

A logical calculus is then a system for deriving all the valid statements. In my post "doing everything without assumptions", I gave such a calculus for deriving all the valid statements of classical propositional logic.

"Sound" is then used sparingly. It's sometimes used for logical calculii themselves, where it just means "consistent." An unsound logic is just an inconsistent one, meaning one whose rules are so broken that they declare way too many statements to be "valid" (usually "way too many" is "all").

Another usage of "sound" comes up in the formal treatment of the logic of counting numbers. Here, the statements that one can or cannot prove have a very clear interpretation in the calculus itself, and statements which agree with this interpretation can be called "sound". This classification is useful when discussing Gödel's theorems. These theorems show that there are statements in the formal logics for counting numbers which are neither provable nor refutable. This, it turns out, means that one can assert the statements or refute the statements as you like, without running into an inconsistency. However, only one way, asserting or refuting, is "sound".

Specifically, one statement that cannot be proved nor refuted in the logic of counting numbers is "the logic of counting numbers is consistent." You can therefore assert "the logic of counting numbers is inconsistent" without running into an inconsistency. Doing so, however, means that your later conclusions may be unsound, because "the logic of counting numbers is inconsistent" is not a sound statement.

 

[fast]

If the argument is unsound, how can it possibly be valid?

A sound argument is both valid and has true premises.

If an argument is valid but has false premises, it’s unsound.
If an argument is invalid and has true premises, it’s unsound.
If an argument is invalid and has false premises, it’s unsound.

Both conditions must be met for an argument to be sound.

Isn't it the point of an argument to provide a set of premises that support a given conclusion?

You’re now asking about the point of an argument. Like tools, an argument can be used as ordinarily intended, but even a TV can be used as a door prop.

I cannot speak on mathematical logic, and apparently I cannot even speak well regarding the words “valid” and “sound” as to how they apply to mathematical logic, but thats not the logic that’s been discussed around these parts for the past 15 years.

When it comes to the deductive/propositional logic, the terms “valid” and “sound” do not apply to the premises. They apply to the argument. Ideally, we should be able to trust that the conclusion to a deductive argument is true if the argument is sound. A deductive argument is not sound unless the two conditions are met.

If someone truthfully tells you that an argument is valid, you have not been given enough information to trust that the argument is sound—even if you trust what’s been told to you. An argument can have a false premise and still be a valid argument, but no deductive argument is sound unless: 1) the form is without flaw and 2) the premises are without falsity.

 

[fast]

In EBs syllogism conclusion does not follow from premise, there is no connection between premise and conclusion. It is invalid

If sally is awake, then Sally is at the grocery store.
If sally is awake, then Sally is at home
Sally is awake
Conclusion, Sally is at home

Speakpigeon will see the problem, and so will academics, and both the academics and Speakpigeon will readily conclude the argument to be unsound, but while Speakpigeon claims the argument is invalid, the academics will not.

You’re gonna see the problem too, and I would suppose you too will find the argument unsound, but if you find the argument invalid, is it merely because of the inconsistency? What is it about the inconsistency that captures our attention? We realize one must be false, but ah ha!, that isn’t an issue with form but rather truth. Forget the truth value of the premise in your judgement.

Look at the conclusion. Sally is at home. Is there enough in the argument to get us there? Yes! And that makes it valid. Set what you need in stone and lock it in the safe. The falsities and inconsistencies are distractions.

At first I thought it invalid, but it is valid. Conclusion follows from premise. But it is shaky IMO. The premises are confusing without a 4th premise, Sally lives at the store.

If sally is awake, then Sally is at the grocery store.
If sally is awake, then Sally is at home
Sally is awake
Conclusion, Sally lives at the grocery store...

That would be my conclusion based on the premises.

Let’s try again

If missy is in her car, her car is in Florida
Missy is in her car
Therefore, her car is in Florida

That’s clearly valid. Now, let’s add some premises:

If missy is in her car, her car is in South Carolina
If missy is in her car, her car is in Georgia
If missy is in her car, her car is in Alabama
If missy is in her car, her car is in North Carolina

Now, let’s put it all together:

If missy is in her car, her car is in South Carolina
If missy is in her car, her car is in Georgia
If missy is in her car, her car is in Alabama
If missy is in her car, her car is in North Carolina
If missy is in her car, her car is in Florida
Missy is in her car
Therefore, her car is in Florida

The argument is valid. The reason it’s valid is for the same reason. The two premises taken together that get us to the conclusion are present.

I could have added this premise:
If missy is in her car, her car is not in Florida. The other premise that helped get us to the conclusion not going away means the premise needed can still be used.

I could have even added, missy’s car is not in Florida. Wouldn’t matter. So long as there is a path to the conclusion, it’s valid.

I’m tall
I’m not tall
Therefore I’m fat

Nothing is in the premises to get us to “I’m fat.”

I’m big
I’m not big
Therefore I’m big

Valid

I’m big
I’m not big
Therefore I’m not big
Just as valid

 

[Speakpigeon]

If the argument is unsound, how can it possibly be valid?

If it has false premises.

Drunk men are fish;
All fish live in a bottle of alcohol;
Therefore, drunk men live in a bottle of alcohol.

Valid, unsound.

Presumably.
EB

 

[Speakpigeon]

In EBs syllogism conclusion does not follow from premise, there is no connection between premise and conclusion. It is invalid

If sally is awake, then Sally is at the grocery store.
If sally is awake, then Sally is at home
Sally is awake
Conclusion, Sally is at home

Speakpigeon will see the problem, and so will academics, and both the academics and Speakpigeon will readily conclude the argument to be unsound, but while Speakpigeon claims the argument is invalid, the academics will not.

It's not formally not valid since it doesn't formally say that x can't be both at home and at the grocery store.

So, as it is, it's formally valid.

You’re gonna see the problem too, and I would suppose you too will find the argument unsound, but if you find the argument invalid, is it merely because of the inconsistency? What is it about the inconsistency that captures our attention? We realize one must be false, but ah ha!, that isn’t an issue with form but rather truth. Forget the truth value of the premise in your judgement.

No, it's form only. A and not A is false whatever A may be. That's what "captures our attention".

Look at the conclusion. Sally is at home. Is there enough in the argument to get us there? Yes! And that makes it valid. Set what you need in stone and lock it in the safe. The falsities and inconsistencies are distractions.

LOL.
EB

 

[Speakpigeon]

It is non squitter. The conclusion does not follow from the premises. The syllogism is not valid, conclusion does not follow from premise.

P1-P3 are irrelevant to C. C does not follow from P4 P5.

The argument can be formalized:

P1) JC != BJ
P2) BJ != JH
P3) JH != JC
P4) PM = BJ || PM = JH
P5) PM = JC

From P4 and P5, we have

C1) PM = BJ || JH = JC

From P3 and P4, we then have

C2) PM = BJ

Junk proof for the junkie kiddie

Kindergarten logic.

Toy logic.

Mathematicians have been playing with toy logic for 165 years and they don't want we put the toy away.

Isn't that sweet?
EB

 

[Speakpigeon]

If the argument is unsound, how can it possibly be valid?

A sound argument is both valid and has true premises.

If an argument is valid but has false premises, it’s unsound.
If an argument is invalid and has true premises, it’s unsound.
If an argument is invalid and has false premises, it’s unsound.

Both conditions must be met for an argument to be sound.

Ironically, mathematical logicians often use the terms "valid" and "sound" differently to philosophers. I suggest it's another hang-up from syllogistic logic, which was a classification system for 256 argument forms into the valid ones and the fallacious ones. Mathematical logics aren't classifications of arguments. They are "calculii" of statements.

Mathematicians have little interest in how calculii are misapplied, which is to say they have little interest in "miscalculation". And so they have very little interest in the misapplication of logical calculii, which is to say "invalidity." A miscalculation isn't a calculation at all. And an invalid proof isn't a proof at all. So they might say.

Instead, the word "valid" gets co-opted for something else. Instead of calling arguments valid or invalid, mathematical logicians call statements valid or invalid depending on whether they are always logically true. So "P or not-P" is valid statement. But "P or Q" is invalid.

A logical calculus is then a system for deriving all the valid statements. In my post "doing everything without assumptions", I gave such a calculus for deriving all the valid statements of classical propositional logic.

"Sound" is then used sparingly. It's sometimes used for logical calculii themselves, where it just means "consistent." An unsound logic is just an inconsistent one, meaning one whose rules are so broken that they declare way too many statements to be "valid" (usually "way too many" is "all").

Another usage of "sound" comes up in the formal treatment of the logic of counting numbers. Here, the statements that one can or cannot prove have a very clear interpretation in the calculus itself, and statements which agree with this interpretation can be called "sound". This classification is useful when discussing Gödel's theorems. These theorems show that there are statements in the formal logics for counting numbers which are neither provable nor refutable. This, it turns out, means that one can assert the statements or refute the statements as you like, without running into an inconsistency. However, only one way, asserting or refuting, is "sound".

Specifically, one statement that cannot be proved nor refuted in the logic of counting numbers is "the logic of counting numbers is consistent." You can therefore assert "the logic of counting numbers is inconsistent" without running into an inconsistency. Doing so, however, means that your later conclusions may be unsound, because "the logic of counting numbers is inconsistent" is not a sound statement.

Once you've redefined all the terminology including what "valid" means, there's no sensible conversation possible.

Mathematicians should abstain from involving themselves in any logical conversation with non-mathematicians.

Which, on the whole, they do.
EB

 

[Speakpigeon]

Isn't it the point of an argument to provide a set of premises that support a given conclusion?

Yes, using an argument to convince people of the conclusion, you better make sure they will agree that the premises are true.

But you also need to make sure you use a valid argument.

All men are mortal;
Trump is either a man or a God;
Therefore, Trump is mortal.

Here we have true premises and a true conclusion (hopefully) but the argument is not valid.

So, true premises are not enough and it is therefore important to be able to tell whether arguments are valid or not, irrespective of whether the premises are true or not.

The only point of the science of logic is to be able to decide whether particular arguments are valid or not.

Given what people understand of the subject, it would seem to be a very useful science.
EB

 

[fast]

Ironically, mathematical logicians often use the terms "valid" and "sound" differently to philosophers. I suggest it's another hang-up from syllogistic logic, which was a classification system for 256 argument forms into the valid ones and the fallacious ones. Mathematical logics aren't classifications of arguments. They are "calculii" of statements.

Mathematicians have little interest in how calculii are misapplied, which is to say they have little interest in "miscalculation". And so they have very little interest in the misapplication of logical calculii, which is to say "invalidity." A miscalculation isn't a calculation at all. And an invalid proof isn't a proof at all. So they might say.

Instead, the word "valid" gets co-opted for something else. Instead of calling arguments valid or invalid, mathematical logicians call statements valid or invalid depending on whether they are always logically true. So "P or not-P" is valid statement. But "P or Q" is invalid.

A logical calculus is then a system for deriving all the valid statements. In my post "doing everything without assumptions", I gave such a calculus for deriving all the valid statements of classical propositional logic.

"Sound" is then used sparingly. It's sometimes used for logical calculii themselves, where it just means "consistent." An unsound logic is just an inconsistent one, meaning one whose rules are so broken that they declare way too many statements to be "valid" (usually "way too many" is "all").

Another usage of "sound" comes up in the formal treatment of the logic of counting numbers. Here, the statements that one can or cannot prove have a very clear interpretation in the calculus itself, and statements which agree with this interpretation can be called "sound". This classification is useful when discussing Gödel's theorems. These theorems show that there are statements in the formal logics for counting numbers which are neither provable nor refutable. This, it turns out, means that one can assert the statements or refute the statements as you like, without running into an inconsistency. However, only one way, asserting or refuting, is "sound".

Specifically, one statement that cannot be proved nor refuted in the logic of counting numbers is "the logic of counting numbers is consistent." You can therefore assert "the logic of counting numbers is inconsistent" without running into an inconsistency. Doing so, however, means that your later conclusions may be unsound, because "the logic of counting numbers is inconsistent" is not a sound statement.

Once you've redefined all the terminology including what "valid" means, there's no sensible conversation possible.

Mathematicians should abstain from involving themselves in any logical conversation with non-mathematicians.

Which, on the whole, they do.
EB

What if they changed the spelling to (oh say) “valoud?”

An argument they call valid wouldn’t be valid but instead valoud. Some arguments would be both valid and valoud while others you bring up though invalid would nevertheless be valoud. Of course, we’d still need another term (oh say) “valent” when referring to premises (which would never be valid nor valoud) since neither ever refer to premises.

 

[A Toy Windmill]

I cannot speak on mathematical logic, and apparently I cannot even speak well regarding the words “valid” and “sound” as to how they apply to mathematical logic, but thats not the logic that’s been discussed around these parts for the past 15 years.

To repeat, I like everything you said about stipulative and lexical definitions.

There are stipulative definitions, such as those in mathematics, which appropriate common terms. Mathematical logic is not peculiar in this appropriation of natural language. Physics has stipulative definitions of many common terms, like "time", "space", "energy" and "particle". Most of us don't get worked up over this. On the contrary, we tend to give physicists the benefit of the doubt that their appropriation of these terms is for the better.

Mathematicians do the same, and they ask that you give them the benefit of the doubt that they've found better uses for "valid" than you get from the dictionary and intuition. If you really can't get on board with this, I have zero problem with you using the word "valoud" instead. But if I allow this, I also have to allow that you want to use "tome" instead of "time", "spoce" instead of "space" and "frenergy" instead of "energy."

I'd still like you to give us the benefit of the doubt that "valoud" is an interesting concept, and potentially far more interesting than the pre-theoretic "valid." If you still refuse, please at least learn mathematical logic before you decide that "valoud" is not interesting, so you've at least seen the concept at work.

Because the fact is, the overwhelming majority of people who study mathematical logic come away thinking that "valoud" is so fecund that it's worth ditching "valid" entirely, and insisting that "valoud" was the natural concept all along.

 

[fast]

I cannot speak on mathematical logic, and apparently I cannot even speak well regarding the words “valid” and “sound” as to how they apply to mathematical logic, but thats not the logic that’s been discussed around these parts for the past 15 years.

To repeat, I like everything you said about stipulative and lexical definitions.

There are stipulative definitions, such as those in mathematics, which appropriate common terms. Mathematical logic is not peculiar in this appropriation of natural language. Physics has stipulative definitions of many common terms, like "time", "space", "energy" and "particle". Most of us don't get worked up over this. On the contrary, we tend to give physicists the benefit of the doubt that their appropriation of these terms is for the better.

Mathematicians do the same, and they ask that you give them the benefit of the doubt that they've found better uses for "valid" than you get from the dictionary and intuition. If you really can't get on board with this, I have zero problem with you using the word "valoud" instead. But if I allow this, I also have to allow that you want to use "tome" instead of "time", "spoce" instead of "space" and "frenergy" instead of "energy."

I'd still like you to give us the benefit of the doubt that "valoud" is an interesting concept, and potentially far more interesting than the pre-theoretic "valid." If you still refuse, please at least learn mathematical logic before you decide that "valoud" is not interesting, so you've at least seen the concept at work.

Because the fact is, the overwhelming majority of people who study mathematical logic come away thinking that "valoud" is so fecund that it's worth ditching "valid" entirely, and insisting that "valoud" was the natural concept all along.

Thank you for your kind response, and I am very receptive to what you said. I would not have spoken to you with the same inquisitive nature had I addressed my recent comments to you. I wasn’t trying to be ugly to him either.

Here’s the thing. I think there’s sometimes a psychological disposition at play because of spelling alone. The baggage carries over when the very same letters are used.

Also, I feel the spirit behind what you’re saying when you say “natural concept all along.” If the deviation between the usages are substantive yet the lexical definition (being a function of common usage) hasn’t changed, although it’s not a misuse of the term, it speaks volumes to our room for intuitive improvement. In other words, there’s an inadequacy within us when it comes to intuition, and the works by those I should give the benefit of the doubt to might very well be justified.

Either way, I have a whole lot more learning to do before I’d feel comfortable speaking ill of those that have blazened the trails to share with us what they’ve learned.

 

[steve_bank]

Fast, I have no ode4a what you are in a tizzy over. Academic or not in your syllogism if Sally id awake she is indeed home, a valid conclusion from the premises.

There are more conclusions

P1 if sally is awake she is at the store
P2 if sally is awake she is home’
P3 sally is awake’
C1 if her home is the store sally is at home
C2 If her home is the store sally is at the store
C3 Sally lives at the store, assuming home is where she lives.

Validity of a syllogism is in form. In your syllogism conclusion follows from premise. There are no fallacies in your syllogism. It does illustrate the problems with sylogisms, they are not absolute and open to interpretation and semantics. What is clear to you may not be clear to others.The contradiction is open to debate.If you had said also sally's home is not the store then it would be invalid.

If missy is in her car, her car is in South Carolina
If missy is in her car, her car is in Georgia
If missy is in her car, her car is in Alabama
If missy is in her car, her car is in North Carolina
If missy is in her car, her car is in Florida
Missy is in her car
Therefore, her car is in Florida

Here the contradiction is clear, a car can not be in two places at once.