Justification of the mathematical definition of logical validity?

[Angra Mainyu]

I’m catching on to what’s being done. There just seems to be a mismatch between what’s being done and what’s being said.

You had to utilize the conclusion in my argument and incorporate it as a premise before turning around to arrive at the conclusion, which means a premise was added in order to show validity. Strangly enough, it doesn’t matter what my conclusion is, as you can see beforehand that ultimately the OLD argument CAN BE shown to be valid —BUT ONLY IF you razzle dazzle my argument with premises never given; that’s why you can’t tell me specifically what the unstated conclusion is to an argument with an undisclosed conclusion.

However, that it’s a two-step process isn’t a major concern for me. No wonder you refused to accept the hidden “or Q” in the argument:

P: P
C: P or Q

I’m a rat
Or, something else
Therefore, I’m a rat or something else

I’m not a rat
Therefore, I’m something else

That’s apparently how it’s going down.

Cool!

No, I did not add a premise. I used a conclusion from the previous premises, and the previous premises. Normally, I would not have done that, since it is clear to me it follows. The only reason I did that was to try to persuade it (it is, of course, also correct reasoning), so I used what you had already accepted.

That aside, I do not understand what you mean by "No wonder you refused to accept the hidden “or Q” in the argument:". I don't remember any exchanges like that. Could you clarify, please?

 

[fast]

I’m catching on to what’s being done. There just seems to be a mismatch between what’s being done and what’s being said.

You had to utilize the conclusion in my argument and incorporate it as a premise before turning around to arrive at the conclusion, which means a premise was added in order to show validity. Strangly enough, it doesn’t matter what my conclusion is, as you can see beforehand that ultimately the OLD argument CAN BE shown to be valid —BUT ONLY IF you razzle dazzle my argument with premises never given; that’s why you can’t tell me specifically what the unstated conclusion is to an argument with an undisclosed conclusion.

However, that it’s a two-step process isn’t a major concern for me. No wonder you refused to accept the hidden “or Q” in the argument:

P: P
C: P or Q

I’m a rat
Or, something else
Therefore, I’m a rat or something else

I’m not a rat
Therefore, I’m something else

That’s apparently how it’s going down.

Cool!

No, I did not add a premise. I used a conclusion from the previous premises, and the previous premises. Normally, I would not have done that, since it is clear to me it follows. The only reason I did that was to try to persuade it (it is, of course, also correct reasoning), so I used what you had already accepted.

That aside, I do not understand what you mean by "No wonder you refused to accept the hidden “or Q” in the argument:". I don't remember any exchanges like that. Could you clarify, please?

You can’t just go from P to P or Q without some underlying logical basis for it. I’m not denying there is a logical basis for it. I’m saying it’s just not being disclosed.

Also, and there is a little thing that keeps scratching at my thoughts. It’s about Q. I never comprehend when it’s equivalent to not ~P and when it’s not.

 

[Angra Mainyu]

Isn't that the material conditional? (https://en.wikipedia.org/wiki/Wason_selection_task)

The Wason selection task can be explained with the classical material conditional, but that doesn't mean it requires it. I think wiki is being sloppy here.

There are good reasons that people get it wrong.

Mostly, because they usually right but then the researchers themselves don't understand that they do.
EB

From the link in the quotation above:

A psychologist, not very well disposed toward logic, once confessed to me that despite all problems in short-term inferences like the Wason Card Task, there was also the undeniable fact that he had never met an experimental subject who did not understand the logical solution when it was explained to him, and then agreed that it was correct.[10]

It seems nearly all people get it wrong, but when the correct solution is explained to them, everyone (well, nearly everyone, because not you, of course) get it.

 

[steve_bank]

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
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.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

Thanks for your answers.
EB

On what basis do you think your net reference is valid pertaining to mathematical logic?

As in the thread Aristotle vs modern logic, mathematical logic is a set of axiomized logical systems with axioms and a grammar , such as Boolean Algebra. Mathematical logic is not Aristotelians logic.

Mathematical logic is based on variables which are ether true or false. The variables are inputs to a logical stamen and the results evaluate to true or false.

Given three logic variables a,b,c I write a Boolean expression a&b -> c. When a and b are both true c is true. If either a or b is false c is false. AND or & is a definition or axiom in the Boolean logic system.

The question of validity as you put it is irrelevant.

In plane geometry the shortest distance between two points is a straight line. That is nether valid nor invalid. Geometry is constant, proper use of the rules and axioms will always lead to the same result. That is the difference between Aristotelian and mathematical logic. There can be no fallacies.

If you try and convert 'all Greeks are liars and George says he is Greek' to Boolean it can not be done. If it were so mathematical logic would be useless.

 

[Speakpigeon]

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:

Validity
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.
Internet Encyclopedia of Philosophy - https://www.iep.utm.edu/val-snd/

Thanks for your answers.
EB

On what basis do you think your net reference is valid pertaining to mathematical logic?

As in the thread Aristotle vs modern logic, mathematical logic is a set of axiomized logical systems with axioms and a grammar , such as Boolean Algebra. Mathematical logic is not Aristotelians logic.

Mathematical logic is based on variables which are ether true or false. The variables are inputs to a logical stamen and the results evaluate to true or false.

Given three logic variables a,b,c I write a Boolean expression a&b -> c. When a and b are both true c is true. If either a or b is false c is false. AND or & is a definition or axiom in the Boolean logic system.

The question of validity as you put it is irrelevant.

The definition I provided is the mainstream view in mathematical logic. This is the definition I also find in all the textbooks I have looked at. But it doesn't matter, provide a justification for ANY definition. Fair enough?

So, here is the question again, properly amended to suit your tastes:

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that ANY of the definitions of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?

And of course, if one definition is the correct one, any other will be ipso facto implied as incorrect. So, not all mathematicians can be right in this respect.
EB

 

[Speakpigeon]

There are good reasons that people get it wrong.

Mostly, because they usually right but then the researchers themselves don't understand that they do.
EB

From the link in the quotation above:

A psychologist, not very well disposed toward logic, once confessed to me that despite all problems in short-term inferences like the Wason Card Task, there was also the undeniable fact that he had never met an experimental subject who did not understand the logical solution when it was explained to him, and then agreed that it was correct.[10]

It seems nearly all people get it wrong, but when the correct solution is explained to them, everyone (well, nearly everyone, because not you, of course) get it.

LOL
EB

 

[Speakpigeon]

I think there's something quite aberrant about deducing (P or Q) from P. You have P, why water things down by throwing in a random Q? It's an utterly absurd
thing to do, and not even those lying idiot mathematicians would engage in such behaviour.

But what if your friend Alice says: roll up! Roll up! If you have either a P or a Q, I have a million quid for you!

Now you're there with a P. And you say, hang on, I have P, which means I can fulfill Alice's requirements and get me my million quid. Those requirements say I need either a P or a Q, and indeed, I have a P.

I have P. Therefore, I have either P or Q. And so I'm destined to be a millionaire.

The lesson here is that the rules of logic are often less about the conclusions you can make, and more about the requirements you can fulfill. Always check which side of the turnstile you're standing.

Me, don't have any problem with A implies A or B.

If it's true that it rains, then it's true that my cat is a bird or that it rains.

That's true because the consequent cannot be false whenever the antecedent is true.

Yet, some "specialists of mathematical logic" don't even understand that.

Right. Says it all.
EB

 

[Speakpigeon]

what bothers me is that the reasoning feels hidden

It feels like that because it is.

Aristotle explained what logic is, not how it works. Since then, logicians have tried to make the "how does that work exactly" explicit. They really tried. For 2,500 years now they have tried. Yet, no one has been able to produce anything like an algorithmic solution to the question of validity. No one knows today how to compute validity. So, yeah, it's hidden. This is why I say logic is a capacity of the brain, not a capacity of the mind. All we can do is ask our own brain if this or that implication is valid. It's called logical intuition. We all have a brain with a logical capacity, as near perfect as any sensory perception. This is conclusively demonstrated by our ability to infer meaning beyond what is actually said when we have conversations. But it's also true that most people don't seem to know how to use their logical intuition to produce valid formal arguments. So, yes, it's essentially hidden. We can get to know the answer, if we know how to ask our intuition, but we never get to know how the answer is produced exactly. 2,500 years that Aristotle pointed at the existence of this capacity we have. For 2,500 years already, thinkers have tried to explained how it could work exactly. How they have been able to do was to glose on Aristotle's work. This is in effect the oldest unsolved (rational) question. Both Quantum Mechanic and Relativity were solved in only a few decades after people realised there was a problem to begin with. Yet, logic is still a complete mystery. But, you gave the explanation for that. The process is hidden. It is hidden because our brain does it and we don't really need to know how it does it. We function 100% good without knowing. Aristotle played a trick on us.

Good point, though.
EB

 

[steve_bank]

On what basis do you think your net reference is valid pertaining to mathematical logic?

As in the thread Aristotle vs modern logic, mathematical logic is a set of axiomized logical systems with axioms and a grammar , such as Boolean Algebra. Mathematical logic is not Aristotelians logic.

Mathematical logic is based on variables which are ether true or false. The variables are inputs to a logical stamen and the results evaluate to true or false.

Given three logic variables a,b,c I write a Boolean expression a&b -> c. When a and b are both true c is true. If either a or b is false c is false. AND or & is a definition or axiom in the Boolean logic system.

The question of validity as you put it is irrelevant.

The definition I provided is the mainstream view in mathematical logic. This is the definition I also find in all the textbooks I have looked at. But it doesn't matter, provide a justification for ANY definition. Fair enough?

So, here is the question again, properly amended to suit your tastes:

Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that ANY of the definitions of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?

And of course, if one definition is the correct one, any other will be ipso facto implied as incorrect. So, not all mathematicians can be right in this respect.
EB

You read but do not comprehend and understand. The terms you use are philosophical and are not precise definitions.

In your own words what is the difference between classical or Aristotelian logic and what you refer to as mathematical logic. No jargon, explain it to me.


Since your quote references deductive arguments, what is the difference between inductive and deductive, again in your own words with no jargon from the net.

Ipso facto? The short answer is you do not know and are just copying from the net. The reason math and science evolved past philosophy is philosophy is imprecise. Axiomatic mathematical logic is axiomatic with none of the fallacies from syllogisms.

 

[fromderinside]

The following gets to the crux of the relation between statistical and logical validity.  Validity

It is generally accepted that the concept of scientific validity addresses the nature of reality in terms of statistical measures and as such is an epistemological and philosophical issue as well as a question of measurement. The use of the term in logic is narrower, relating to the truth of inferences made from premises. In logic, and therefore as the term is applied to any epistemological claim, validity refers to the consistency of an argument flowing from the premises to the conclusion; as such, the truth of the claim in logic is not only reliant on validity

Now if one can make an argument that establishes the commonality of measurement and philosophical validity then one has created a bridge between the two. I argue that those who have found ways to establish through conjoint measurement a link between measures where operability can be established by low correlations of individual measure dimensions, independence, by methods such as path analysis one can attain consistent and congruent scales for workload.

I worked on one such task back in the eighties. The first was presented at Edwards AFB at a workload conference of academicians and military researchers in 1982 and the second was presented as a report by Boeing and MDC jointly to AF and FAA.

We applied two four level ordinal measures, mental effort, and physical effort, through a conjoint measure process. Within that task we examined correlations between the two scales and a third scale, criticality, and arrived at correlations of less than 0.07 between ME and PE as defined and trained in observers via path analysis.

In the second task we evaluated all workload literature we found, over 1000 articles to analyses of method, measure, reliability, and validity.

Thus satisfied we are confident to take the resultant recombination of ratings as essentially linear interval scale resulting from the combination of two ordinal scales by the conjoint process used in the measures NASA TLX, AF SWAT, and Navy SOMA. This is akin to finding that physical (objective) and mental effort (subjective) are both valid according to demands of measurement and argument.

I think.

 

[Speakpigeon]

Since your quote references deductive arguments, what is the difference between inductive and deductive, again in your own words with no jargon from the net.

There's no inductive logic. I guess that's one big difference. Is that enough do you think?

Ipso facto? The short answer is you do not know and are just copying from the net.

OK. Steve. You are talking bullshit. Please justify immediately what you assert here by providing links to material on the net that I could have "copied".
EB

 

[steve_bank]

EB

There have been threads on inductive vs inductive.

The reality is you do not have one without the other. In reasoning we often go back and forth between inductive and inductive zeroing in on a conclusion by trial and error.

While technically deductive logic is always true or can be proven true, that does not mean deduction always leads to a correct conclusion for a real problem.

One can have the proper form of a deductive argument where c follows from p, but there is no guarantee that that the argument reflects truth in reality.

Holmes is called the great Deductive Detective, yet in the stories he goes back and forth between deduction and induction. I read Doyle's bio. He was an MD who took on cases. He actually rescued someone from the gallows by proving him imminent.

In science and math deriving a truth uses deduction and induction as tools. The final test is always empirical.

There are several definitions. For me the defense between inductive and inductive is the starting point.

Given a true conclusion such as a murder with a body I work back developing premises. Or I see a evidence observationaly and a derive a conclusion. The logic per se is the same, and, or, if then. It is the string point.

A book on math proofs I read called it backwards vs forwards. Give a desired proof which it is not known if it is possible one can start at the conclusion or desired result and work backwards developing steps to support the conclusion, or vice versa. In reality it is a combination.

If II observe I an wet why am I wet? I observe it is raining and conclude if I go out I will get wet. I see my car is wet, and I enumerate the possibilities with probabilities. Did it rain or did my neighbor use his sprinkler?

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

Your problem is lack of experience.

 

[Speakpigeon]

EB

There have been threads on inductive vs inductive.

The reality is you do not have one without the other. In reasoning we often go back and forth between inductive and inductive zeroing in on a conclusion by trial and error.

While technically deductive logic is always true or can be proven true, that does not mean deduction always leads to a correct conclusion for a real problem.

One can have the proper form of a deductive argument where c follows from p, but there is no guarantee that that the argument reflects truth in reality.

Holmes is called the great Deductive Detective, yet in the stories he goes back and forth between deduction and induction. I read Doyle's bio. He was an MD who took on cases. He actually rescued someone from the gallows by proving him imminent.

In science and math deriving a truth uses deduction and induction as tools. The final test is always empirical.

There are several definitions. For me the defense between inductive and inductive is the starting point.

Given a true conclusion such as a murder with a body I work back developing premises. Or I see a evidence observationaly and a derive a conclusion. The logic per se is the same, and, or, if then. It is the string point.

A book on math proofs I read called it backwards vs forwards. Give a desired proof which it is not known if it is possible one can start at the conclusion or desired result and work backwards developing steps to support the conclusion, or vice versa. In reality it is a combination.

If II observe I an wet why am I wet? I observe it is raining and conclude if I go out I will get wet. I see my car is wet, and I enumerate the possibilities with probabilities. Did it rain or did my neighbor use his sprinkler?

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

Your problem is lack of experience.

Your problem is you don't know that and yet you assert it.

And no, there is no inductive logic.
EB