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

[steve_bank]

An argument can be valid and unsound. Semantics again, what is unsound?

Given evidence different people can make different conclusions from the evidence. Each argument may be valid in from. It happens all the time in group situations.

Given the same evidence one argument could be called more sound than another. Unsound is a subjective term.

In form a syllogism is either true or false, valid or invalid. No fallacies or contradictions or errors in form and the argument is valid.

Sound or unsound refers to choice of premise. Given evidence different people may come up with different premises. Logic in syllogism may mot violate rules, but be unsound. A valid syllogism in no way proves the conclusion in reality.

Which comes down to the fact that syllogisms while called logic are subjective. Application of valid logic may lead to unsound results. Reasoning based on logic does not guarentee the conclusion pans out in reality.

 

[fast]

I’m using “sound” in its technical sense. It’s impossible for a deductive argument to be sound if any of the following conditions exist: 1) the argument is invalid 2) any premise is false. In fact, if the argument is valid and if all premises are true, the conclusion must be true.

 

[fast]

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.

Although I was cognizantly aware of the possibility that her home could also be the store, I had hoped for a little charity as I came up with the example hurriedly. Still, I take blame on that one.

In the missy example, if you focus only on the last two premises, are they sufficient to arrive at the conclusion?

 

[steve_bank]

fast

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

You can not have logical contradictions in the premises.

a = big
!a = not big
(a & !a) is always false logically. Where & is AND in Boolean and you probably call it conjunction.

P1, p2, P3 implies (P1 & P2 & p3)

This is why formal logic and mathematical trumps syllogism.

If you do not grasp that you need a review in logic. Look at the logical fallacy list link.

 

[Angra Mainyu]

fast

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

You can not have logical contradictions in the premises.

a = big
!a = not big
(a & !a) is always false logically. Where & is AND in Boolean and you probably call it conjunction.

P1, p2, P3 implies (P1 & P2 & p3)

This is why formal logic and mathematical trumps syllogism.

If you do not grasp that you need a review in logic. Look at the logical fallacy list link.

Sure you can have logical contradictions in the premises.

 

[DBT]

Is there a reason to deliberately include logical contradictions in the premises?

 

[fast]

Is there a reason to deliberately include logical contradictions in the premises?

Validity is misunderstood. There are a variety of things that sway the unwary into thinking arguments are invalid when technically they are not.

P1: My hat is black
C: My hat is black

That premise alone leads us to the conclusion. Tie a rope around them and remember the connection. Place one end around P1 and one end around C and remember the link that ties them together.

Now, weaken the argument by saying:

P1: my hat is black
P2: Diesel engines usually last longer than gas engines.
C: my hat is black

The rope of validity remains intact...the argument is valid

Now, crank it up a notch:
P1: my hat is black
P2: Diesel engines usually last longer than gas engines.
P3: it is not the case that Diesel engines usually last longer than gas engines
C: my hat is black

We now have a contradiction, but it doesn’t have the relevancy to conflict with P1 and C. The argument is still valid.

Now, let’s really throw a monkey wrench into things:

P1: my hat is black
P2: Diesel engines usually last longer than gas engines.
P3: it is not the case that Diesel engines usually last longer than gas engines
P4: it’s not the case that my hat is black
C: my hat is blacK

Now we have a relevant conflict that might sway our thinking, but technically, the very thing that originally made the argument valid is still intact (recall the rope). The argument is valid for at least that reason.

Now here’s the kicker, burn the rope and drop P1. The damn thing is still valid but for a completely different reason. And I’m not making this up, nor am I confused, as those in the know completely agree with me, well except Speakpigeon, but even he would agree that those that pride themselves of being in the know would agree with me.

I’m not making logical mistakes. Sometimes I do, but this isn’t an instance where I am—or at the very least, what I’m saying accords with academic teachings.

 

[Angra Mainyu]

Is there a reason to deliberately include logical contradictions in the premises?

At the risk of another disagreement like in a previous thread, I would mentioned proofs by contradiction, though maybe ' premise ' is not the right word, in which case I would still say that from some statements, a contradiction is derived, so the statements in question are by definition inconsistent (definition: a set of statements is inconsistent if and only if a contradiction can be derived from them ).

Still, even if there were no good reason to use premises that contradict each other, it would remain the case that some conclusions (all, actually) follow from premises that contradict each other.

For example, suppose you have the following premises:

P1. It is not the case that the Earth is flat.
P2. The Earth is flat.

Then from P2, we obtain:

C1: Either the Earth is flat, or the Moon is made of cheese. [C1 follows from P2 because (P or Q) follows from P.]

Then from C1 and P1 we obtain

C2: The Moon is made of cheese. [C2 follows from C1 and P1 because Q follows from (P or Q) and ¬P.]

So, in two steps, from P1 and P2 we obtain the conclusion that the Moon is made of cheese. This conclusion follows logically from P1 and P2, as only proper logic rules have been used to derive it. Of course, some people claim that those rules are not proper rules. And some of them claim so in an intelligent manner, whereas others - like Speakpigeon's example in this forum - just incur contradiction themselves.

 

[A Toy Windmill]

Is there a reason to deliberately include logical contradictions in the premises?

Blatant contradictions where one premise is just the denial of another? Perhaps there is no good reason. Perhaps all such arguments are stupid. Perhaps we should be so eager to discard them that we will declare them illegal from the outset. It wouldn't bring the house down to do so.

I come at this from the other direction: until I see a good reason to disallow contradictory premises, they should be permitted. Arguments with contradictory premises may be stupid, but then, there may just be lots of stupid arguments. I know that if you enumerate all the valid statements of propositional logic, most of them will be utterly worthless. But they're still permitted because my distaste isn't compelling enough to disallow them.

 

[DBT]

Is there a reason to deliberately include logical contradictions in the premises?

Blatant contradictions where one premise is just the denial of another? Perhaps there is no good reason. Perhaps all such arguments are stupid. Perhaps we should be so eager to discard them that we will declare them illegal from the outset. It wouldn't bring the house down to do so.

I come at this from the other direction: until I see a good reason to disallow contradictory premises, they should be permitted. Arguments with contradictory premises may be stupid, but then, there may just be lots of stupid arguments. I know that if you enumerate all the valid statements of propositional logic, most of them will be utterly worthless. But they're still permitted because my distaste isn't compelling enough to disallow them.

Nice answer. Perhaps like crossword puzzles, they serve to stimulate mind and thought, and that is sufficient reason.

 

[fast]

Is there a reason to deliberately include logical contradictions in the premises?

Blatant contradictions where one premise is just the denial of another? Perhaps there is no good reason. Perhaps all such arguments are stupid. Perhaps we should be so eager to discard them that we will declare them illegal from the outset. It wouldn't bring the house down to do so.

I come at this from the other direction: until I see a good reason to disallow contradictory premises, they should be permitted. Arguments with contradictory premises may be stupid, but then, there may just be lots of stupid arguments. I know that if you enumerate all the valid statements of propositional logic, most of them will be utterly worthless. But they're still permitted because my distaste isn't compelling enough to disallow them.

I’m probably gonna butcher this, but what would a good reason look like?

Logical possibilities are so broad in scope that it competes with the saying “with God, all things are possible.” Hence, with logic, all things are possible. Well, not all; apparently there was one thing which was good enough to serve as an exception.

I can jump two feet up in the air. That’s a physical possibility. Jumping 300 feet (unaided by some technology or extraordinary condition) is not a physical possibility, but not even physical impossibilities prevent such things from being logically possible. That’s probably a good thing, whether some find that displeasing or not—and some do.

But, the one exception currently allowed was apparently good enough to bar from even the almighty list of potentially enumerated logical possibilities: contradictions. They allow contraries, no problem, but let a contradiction approach the pearly brown gates of logic and it’ll be announced right quick-like that contradictions have been forever banished from entry.

We know from the beginning that whososhallever sprinkles a deductive argument with the evil potion of contradiction will never spawn an accepted yearling...never will ever such a tainted argument become accepted as sound. Yet, we have no good reason? We have no good reason to deny the honorary status of validity?

Told ya i’d probably butcher this, but I feel the antics is helpful, weirdly, and here is why. I can’t just ask “what would a good reason look like” and let it go at that. While I don’t want to allow our subjective preferences be a deciding factor, I don’t want legitimate good reasons be kicked down the road like a can all because one can point out that it’s not necessary to “declare them illegal.”

There’s room for good reason and unnecessary actions to co-exist.

Don’t get me wrong; i’m still content on giving all due benefits of the doubts—and will continue to, as I’m not equipped with nearly the knowledge to have an opinion worth listening to (as I’m nowhere near the vacinity of being an expert in the field), but the notion of “no good reason” not being present makes me go hmmm.

 

[A Toy Windmill]

I’m probably gonna butcher this, but what would a good reason look like?

It's a good question.

We know from the beginning that whososhallever sprinkles a deductive argument with the evil potion of contradiction will never spawn an accepted yearling...never will ever such a tainted argument become accepted as sound. Yet, we have no good reason? We have no good reason to deny the honorary status of validity?

But is the status of validity something which tells of the likelihood, or even the possibility, that something will be accepted as sound? It seems that it's often the opposite. I know that you can often take a crappy and invalid argument, where the premises aren't strong enough to reach the conclusion, and simply patch it up by throwing in enough extra justifying premises. But throwing in extra premises is weakening. It makes it such that the argument's premises are less likely to be jointly true. So validity can be gained at the cost of soundness being less likely.

Contradictory premises always being valid are just the extreme of this. Any argument can be made valid by throwing in enough premises to expose a contradiction, weakening it so badly that the premises are never jointly true. The argument's soundness is made less likely, because it's been made impossible for it to be sound!

If we're permitted to take seriously this concept of "weakening", then logic is all about strength: a valid argument is one where the premises are strong enough to reach the conclusion. You can make valid arguments by picking sufficiently strong premises or sufficiently weak conclusions. Strong premises are less often jointly true. Weak conclusions are more often separately true. On this view, a contradiction is near enough the strongest premise one can assert. It is a premise which is never jointly true, and so always makes for a valid argument. This situation has a dual: a tautology is near enough the weakest conclusion one can reach. It is a conclusion which is always true, and so also always makes for a valid argument.

 

[Speakpigeon]

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?”

May not be enough.

There is the mathematical definition of mathematical validity and there is the broader understanding mathematicians (and philosophers etc.) as to what the term is meant to refers to. The thing is, mathematicians, on the whole, believe mathematical validity still refers to logical validity in the usual sense even though its definition is contradictory with Aristotle's idea of validity, idea understood and accepted by nearly all logicians over 2,500 years until mathematicians put their foot on it. The situation is an indescribable mess and with the passing of generations, it's not going to clear up.

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.

For logicians, premises are neither valid, not valid nor invalid.

They are not even all necessarily true or false. Some premises may be contradictory or inconsistent but doesn't make them "not valid", and indeed not even false.

Valid only refers to a deductive inference from premises to conclusion, and by extension to the conclusion itself, which may therefore well be true but not valid.

My point is that logical validity is something like the Moon, it exists whatever you want to say about it. Mathematicians haven't proved that any of the definitions of validity used in mathematical logic would be correct of logical validity. Indeed, they don't even understand the question to begin with or deny its meaningfulness, demonstrating their complete ignorance. They don't even understand Aristotle. He pointed a finger at the logical Moon and the fools look at the finger and make idiotic claims that the finger is chubby.
EB

 

[Speakpigeon]

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."

Whoa.

Grossly fallacious.

Scientists have investigated nature using an empirical method. They actually spend a lot of time, money and brain power to observe nature. Mathematicians didn't and still don't and never will.

Mathematicians started to observe a little bit and got bored with it after five minutes. They made up "axioms", claimed in those times to be "self-evident truths" even though some of them have never been at all self-evident, and they just ran with it.

And very quickly it became too late. Kripke even explicitly wrote it was too late to try and come back to axioms closer to (human) logic because he thought too much had already been "achieved". LOL.

So, too bloody late. There's no discussion possible.

Most people become dogmatic as soon as they realise a contradictory suggestion implies very hard work ahead and most people are just lazy thinkers.

Mathematicians are not paid to think. They are paid to come up with plausible axioms and deduce theorems from the axioms so chosen. A machine with the proper logic will be able to do that deductive task much faster and with less risks of error. The only thinking involved in mathematics is the conceiving of the proof, that's arguably something but nothing like thinking about your most basis assumptions. Only philosophers do that, or mathematicians when they're also philosophers..

Mathematicians are not paid for thinking. Some of them do, of course, but these will be regarded as philosophers, like Frege, Russell, Tarski, Gödel etc. (I'm not sure about Boole).
EB

 

[Speakpigeon]

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.

Yet your argument here is not valid but not for the reason you give!

It is not valid only because it doesn't include the premises necessary to say that Georgia is not Alabama etc.

Because, from a logical validity point of view, it is possible that Georgia is Alabama unless a premise specifies otherwise.

Thus, there's no premises in your argument precluding the car being in all places at once because they are the same place.

Still, yes, it is no valid. But not for the reason you give.

Even your claim that "a car can not be in two places at once" could not be left implicit. There is nothing in logic that says something cannot be in two places at once.

Still a long way to go, Steve.
EB

 

[Speakpigeon]

Which comes down to the fact that syllogisms while called logic are subjective.

Nonsense.

Application of logic is the application of logic, not logic itself.

Logic is fundamentally the investigation of the validity of arguments (or logical formulas), not the application of logic.

It's entirely irrelevant to logic that the application of logic may lead to a false conclusion just because the premises may be false.

Whatever the argument, or the formula, it is the responsibility of the person who decides to apply the argument to make such the premises are true. Nothing to do with logic whatsoever.

You make all sorts of idiotic claims as if you knew logic through and through and yet you know so very little I feel for you. The world must be a very strange place for your twisted mind.
EB

 

[Speakpigeon]

In fact, if the argument is valid and if all premises are true, the conclusion must be true.

And that's just talking about validity.

Nothing to do with soundness.

You only get to soundness when you go beyond the "if" here and apply logic to the real world. And to do that, you have to assert the premises as "actually" true, not just assume them, i.e. assert them for the purpose of discussing validity.

Not easy, right?

Interestingly, there's an overlap between validity and soundness but mathematical "logicians", a contradiction in terms, are too thick to even notice or understand.

Not easy at all.
EB

 

[Speakpigeon]

P1, p2, P3 implies (P1 & P2 & p3)

This is why formal logic and mathematical trumps syllogism.

And yet another stoopid claim for the ignoramus. You have zero competency on Aristotelian logic and yet you pontificate idiocy after idiocy as if you did.

You know what a syllogism? Well, no, you don't.

If you do not grasp that you need a review in logic. Look at the logical fallacy list link.

Do that yourself, Steve.
EB

 

[Speakpigeon]

P1: My hat is black
C: My hat is black

That premise alone leads us to the conclusion. Tie a rope around them and remember the connection. Place one end around P1 and one end around C and remember the link that ties them together.

Now, weaken the argument by saying:

P1: my hat is black
P2: Diesel engines usually last longer than gas engines.
C: my hat is black

The rope of validity remains intact...the argument is valid

Now, crank it up a notch:
P1: my hat is black
P2: Diesel engines usually last longer than gas engines.
P3: it is not the case that Diesel engines usually last longer than gas engines
C: my hat is black

We now have a contradiction, but it doesn’t have the relevancy to conflict with P1 and C. The argument is still valid.

No reason for that. The rope between premise P1 and the conclusion only works for your first two arguments here.

Your last argument says that the conclusion follows from the premises, not just from premise P1 or from P1 and P2. You can't leave any of premises P2 or P3 out.

But, sure, you can define valoud logic all you like as long as you're not trying to convince DBT of your nonsensical logic.

Not that you'd have any chance succeeding if past experience is any guide.
EB

 

[Speakpigeon]

Is there a reason to deliberately include logical contradictions in the premises?

Blatant contradictions where one premise is just the denial of another? Perhaps there is no good reason. Perhaps all such arguments are stupid. Perhaps we should be so eager to discard them that we will declare them illegal from the outset. It wouldn't bring the house down to do so.

I come at this from the other direction: until I see a good reason to disallow contradictory premises, they should be permitted. Arguments with contradictory premises may be stupid, but then, there may just be lots of stupid arguments. I know that if you enumerate all the valid statements of propositional logic, most of them will be utterly worthless. But they're still permitted because my distaste isn't compelling enough to disallow them.

Hey, you can make sense when you want to.

I started out from the same "premise" and look where I am. The difference between you and me is you ignore what I know, i.e. the "good reason to disallow contradictory premises". And the way mathematicians think, they will never know it. Well, an it's empirically likely they won't. 163 years and they haven't found it. Whoa. Millions of mathematicians haven't found the good reason found by a crackpot dropout. LOL.

But you can stay in your profound ignorance as far as I am concerned.
EB