Definition of logical validity

[Speakpigeon]

Here is your chance to re-write logic in its entirety...

An argument is usually said to be logically valid if all cases in which the premises are true, the conclusion is also true.
Or, equivalently, an argument is said to be valid if there is no case in which the premises are true and the conclusion is false.
Do you accept these two definitions?
If not, what definition do you think is the correct one?
EB

[Logik]

an argument is said to be valid if there is no case in which the premises are true and the conclusion is false.

This criterion only applies for deductive arguments.
Inductive argument allows for the premises to be true but for the conclusion to be false.

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

Unlike deductive arguments, inductive reasoning allows for the possibility that the conclusion is false, even if all of the premises are true.[3] Instead of being valid or invalid, inductive arguments are either strong or weak, which describes how probable it is that the conclusion is true.[4] Another crucial difference is that deductive certainty is impossible in non-axiomatic systems, such as reality, leaving inductive reasoning as the primary route to (probabilistic) knowledge of such systems.

Since the context in which you and I exist is reality, and not some artificial axiomatic system then valid deduction is almost impossible in practice.

Deductive validity implies certainty. Certainty is incompatible with falsifiability.

A falsifiable certainty is an oxymoron.

[Speakpigeon]

an argument is said to be valid if there is no case in which the premises are true and the conclusion is false.

This criterion only applies for deductive arguments.

Do you accept this definition for deductive argument, yes or no?

Deductive validity implies certainty. Certainty is incompatible with falsification.

Derail.
Your comment is cryptic.
If you had a point, you would articulate your point.
EB

[Logik]

Do you accept this definition for deductive argument, yes or no?

You are moving the goal posts. Your said "logical validity'.

I accept the criterion for deduction.
I reject the criterion for induction.

Are you doing deduction or are you actually doing induction while mistaking it for deduction?

Derail.
Your comment is cryptic.
If you had a point, you would articulate your point.
EB

My point is that deduction is impossible (maybe I should say improbable, but lets go with some room for error) in practice. You can prove me wrong with a demonstration of a valid AND sound deductive argument.

[FlashDangerpants]

Here is your chance to re-write logic in its entirety...

An argument is usually said to be logically valid if all cases in which the premises are true, the conclusion is also true.
Or, equivalently, an argument is said to be valid if there is no case in which the premises are true and the conclusion is false.
Do you accept these two definitions?
If not, what definition do you think is the correct one?
EB

Technically, sure. But you and I don't seem to agree on what a conclusion actually is. To my mind the conclusion must be a result of and validated by the premises. You seem to be more of the opinion that it can be somewhat coincidental to them, or that it only counts when they are instantiated with correct parameters or something.

[Speakpigeon]

My point is that deduction is impossible (maybe I should say improbable, but lets go with some room for error) in practice.

Go on.

You can prove me wrong with a demonstration of a valid AND sound deductive argument.

I still have not a clue as to what your point may be but as soon as I do I try to oblige.
And you better make it good this time or we will have to leave it at that, i.e. a derail.
If you want to discuss you point, start a thread and we see what happen.
EB

[Logik]

I can articulate my argument from many different perspectives. Let me know which one makes the light bulb in your head come on.
Or let me know which "starting point" is most familiar to you.

The validity criterion in deduction is exceptionally strict.

an argument is said to be valid if there is no case in which the premises are true and the conclusion is false.

Spelled out this requires absolute certainty that the conclusion is true.

Suppose that you have argument A.
The argument is deemed to be Sound (S) and Valid (V)
Lets the conclusion of A be C.

In logical form: S ∧ V ⇒ C

Suppose that we have a conclusion from an argument which we have deemed to be sound and valid.

1 ∧ 1 ⇒ 1

We deduce a conclusion which is True.

Also suppose that empirical evidence contradicts the conclusion of our "sound" and "valid" argument.

"Deduction" says C = True. Empiricism says C = False e.g falsification has taken place

Following the disparity between logic and empiricism:

Would you still say that A is a sound and valid argument?
Would you still say that A is a deductive argument?

If you examine all the evidence a posteriori you should recognise that what happened is that we mistook induction for deduction.

[Speakpigeon]

Technically, sure.

???
Is it a "yes" or is it a "no"?

But you and I don't seem to agree on what a conclusion actually is.

We haven't discussed anything so this just seems to come from left field.

To my mind the conclusion must be a result of and validated by the premises.

Good to know what's in your mind but what you say here implies that the definition of logical validity given in this thread is not correct.
If you feel that way, then perhaps you need to redact the definition given so that it takes what you say here into account.
Once you're done, you can go worldwide and announce you have a new definition.
And wait for the Nobel Prize.

You seem to be more of the opinion that it can be somewhat coincidental to them, or that it only counts when they are instantiated with correct parameters or something.

No, I am of the opinion that what most people mean with words is explained by the definitions given in dictionaries and that we would better abide by that, so, I take the definition of validity here at face value and that's it. No ifs and buts.
Still, here's your chance to redact this definition for the world to know what validity really means.
EB

[Speakpigeon]

Also suppose that empirical evidence contradicts the conclusion of our "sound" and "valid" argument.
"Deduction" says C = True. Empiricism says C = False e.g falsification has taken place

I clipped the rest because it was unnecessary.
Only these two lines are necessary to making your point.
A point which you could have explained straight away but didn't.

Following the disparity between logic and empiricism:

No.
You haven't justified that there was such a disparity.
Clearly, your example isn't a case of disparity between logic and empiricism.
It's much more trivial than that.
So, no Nobel Prize for you yet.

Would you still say that A is a sound and valid argument?
Would you still say that A is a deductive argument?

A is still logically valid. And still a deductive argument.
And we're not discussing soundness here.

If you examine all the evidence a posteriori you should recognise that what happened is that we mistook induction for deduction.

No.
We're talking about validity in this thread and your explanation here only shows how scientists get to revise their beliefs whenever new facts come to contradict the conclusion of the theory currently accepted as science.
So, assume a valid argument. Assume also premises are accepted as true given scientific facts. So, the argument is sound. And as such, it can be applied to all empirical cases scientist care to look at and can be used to make predictions.
Now, suppose one day predictions turn out to be wrong. Some fact falsifies the expected conclusion. Collective gasp.
Well, no. The argument is still valid. We're discussing logical validity here. Validity doesn't depend on any empirical facts outside the wording of the argument itself and the interpretation we give to the words used in the argument. You could falsify all we think we know about the real world that it still wouldn't make any valid argument invalid.
EB

[FlashDangerpants]

But you and I don't seem to agree on what a conclusion actually is.

We haven't discussed anything so this just seems to come from left field.

I have pointed it out already, you must have missed it.

To my mind the conclusion must be a result of and validated by the premises.

Good to know what's in your mind but what you say here implies that the definition of logical validity given in this thread is not correct.
If you feel that way, then perhaps you need to redact the definition given so that it takes what you say here into account.
Once you're done, you can go worldwide and announce you have a new definition.
And wait for the Nobel Prize.

Alas my eligibility for that price is in doubt given that I am hardly the inventor of this notion.
Here is the top link on a Google search for "definition of deductive argument"

A deductive argument is the presentation of statements that are assumed or known to be true as premises for a conclusion that necessarily follows from those statements. Deductive reasoning relies on what is assumed to be known to infer truths about similarly related conclusions.

You have put too much effort into finding loopholes for validity to notice that you had excluded your output by means of presenting something less than argument. That misdirection is why you are having such a hard time with the validity discussion.

You seem to be more of the opinion that it can be somewhat coincidental to them, or that it only counts when they are instantiated with correct parameters or something.

No, I am of the opinion that what most people mean with words is explained by the definitions given in dictionaries and that we would better abide by that, so, I take the definition of validity here at face value and that's it. No ifs and buts.
Still, here's your chance to redact this definition for the world to know what validity really means.
EB

The dictionary definition of valid? You mean the version of the word that fits into this sentence I got from the Cambridge dictionary? ... "My way of thinking might be different from yours, but it's equally valid"

I saw you dismiss Bahman's use of the word may, so I'm not sure of your commitment to this dictionary thing tbh.

[Speakpigeon]

OK, I think I can ignore you safely.
Have a good trip.
EB

[FlashDangerpants]

For all that we know, the state of object SpunkPigeon may be 'PISSY'
PISSY people are probably grumpy about being caught trying to pull off a bait and switch.
Therefore SpunkPigeon may have been caught pulling off a bait and switch.


You see the problem with this sort of argument is the sloppiness in the misuse of the word 'therefore'
Neither proposition is especially necessary to the conclusion which may or may not be true on its own merits without them.
They are there really to define the existence of some objects and states, not to do anything useful with them.

You can casually use the word 'therefore' as if it the summation of a speech 'therefore I put it to you that this thread is a waste of time' and so on.
But in a philosophical argument, 'therefore' indicates a relationship of necessity between premise and conclusion. If you don't have that, what you have is not an argument.

So you can ignore me if you like, but it's not really your smart choice given that you seem to care about what happens to these arguments and I never gave much of a fuck about them.

[Logik]

I clipped the rest because it was unnecessary.
Only these two lines are necessary to making your point.
A point which you could have explained straight away but didn't.

Your comprehension seems to be limited so I would rather be verbose.

No.
You haven't justified that there was such a disparity.
Clearly, your example isn't a case of disparity between logic and empiricism.

You are playing mental gymnastics. The word "impossible" has a pretty unambiguous meaning, wouldn't you say?

an argument is logically valid if it is in principle impossible for the premises to be true and the conclusion false at the same time

This spells out that IF the premises (P) are true and the conclusion (C) is determined true but falsified a posteriori, then this is NOT a deductively valid argument.

A is still logically valid. And still a deductive argument.
And we're not discussing soundness here.

If the premises are valid and the conclusion is not true it is not deduction: P ∧ ¬C ⇒ ¬D

No.
We're talking about validity in this thread and your explanation here only shows how scientists get to revise their beliefs whenever new facts come to contradict the conclusion of the theory currently accepted as science.

Yes. That is exactly what I am doing. Welcome to reality.

Your hypothesis is that you are doing deduction.
My hypothesis is that you SAY you are doing deduction, but you are actually doing induction.

So, assume a valid argument. Assume also premises are accepted as true given scientific facts. So, the argument is sound. And as such, it can be applied to all empirical cases scientist care to look at and can be used to make predictions.

I don't need to make any assumptions! At any given moment I can simply evaluate whether P ∧ ¬C ⇒ ¬D

If P is true, C is true but empiricism disagrees with C, it's NOT deduction.

Now, suppose one day predictions turn out to be wrong. Some fact falsifies the expected conclusion. Collective gasp.

The argument is still valid. We're discussing logical validity here. Validity doesn't depend on any empirical facts outside the wording of the argument

That's shifting the goal posts. If at ANY point in time or in any context P ∧ ¬C ⇒ ¬D

That you want to contrive some idealised textbook scenario is your prerogative.
In reality - I don't care about your tunnel vision and inability to see the full picture.

If you are doing deduction then the argument is valid.
If you are doing induction then the argument is invalid.

Are you doing deduction or induction? Decision problem.

Your WORDS say that you are doing deduction, but the evidence says otherwise.
I am not going to call you a liar, so I will call you ignorant of what goes on in your own mind.

[Speakpigeon]

No.
You haven't justified that there was such a disparity.
Clearly, your example isn't a case of disparity between logic and empiricism.

You are playing mental gymnastics. The word "impossible" has a pretty unambiguous meaning, wouldn't you say?

an argument is logically valid if it is in principle impossible for the premises to be true and the conclusion false at the same time

This spells out that IF the premises (P) are true and the conclusion (C) is determined true but falsified a posteriori, then this is NOT a deductively valid argument.

There is no need to use the word "impossible" to define validity:

An argument is usually said to be logically valid if all cases in which the premises are true, the conclusion is also true.
Or, equivalently, an argument is said to be valid if there is no case in which the premises are true and the conclusion is false.

So, again, the validity of an argument isn't affected by the falsification of its conclusion, for example by empirical observations. It is routine in logic to assume the conclusion of a valid argument false and from there to infer something, but not that the argument is invalid after all. Because validity doesn't depend on that. Read the definition I just provided, you might be able to understand. For now, it is clear that you don't.
EB

[Logik]

There is no need to use the word "impossible" to define validity:

And yet the definition uses it. If you want to change the definition, go ahead.

An argument is usually said to be logically valid if all cases in which the premises are true, the conclusion is also true.
Or, equivalently, an argument is said to be valid if there is NO CASE in which the premises are true and the conclusion is false.

This simple requirement means that ALL probabilities are off-limits.

Even if there is 1 in 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 probability that the premises can be true but the conclusion can be false then that is ONE CASE where the premises can be true, but the conclusion can be false.

Since A CASE is more than NO CASE.
SInce 1 > 0, you have violated the requirements for validity stated in the definition.

So, again, the validity of an argument isn't affected by the falsification of its conclusion, for example by empirical observations. It is routine in logic to assume the conclusion of a valid argument false and from there to infer something, but not that the argument is invalid after all. Because validity doesn't depend on that. Read the definition I just provided, you might be able to understand. For now, it is clear that you don't.

Lets agree to disagree. You can remain in your theoretical/idealised realm, and I'll continue to call you an idiot.