experchange > comp.theory

peteolcott (08-27-19, 06:24 PM)
When-so-ever symbolic logic diverges from the deductive logical inference
symbolic logic errs. The Principle of Explosion is one place where symbolic
logic diverges from the deductive logical inference, thus the Principle of
Explosion is erroneous.


The non-sequitur error occurs in every logical inference where the truth
of the conclusion does not depend upon the truth ALL of the premises.


The principle of explosion (Latin: ex falso (sequitur) quodlibet (EFQ),
"from falsehood, anything (follows)", or ex contradictione (sequitur)
quodlibet (ECQ), "from contradiction, anything (follows)"), or the
principle of Pseudo-Scotus, is the law of classical logic, intuitionistic
logic and similar logical systems, according to which any statement
can be proven from a contradiction.
peteolcott (08-27-19, 06:34 PM)
On 8/27/2019 11:24 AM, peteolcott wrote:
[..]
> principle of Pseudo-Scotus, is the law of classical logic, intuitionistic
> logic and similar logical systems, according to which any statement
> can be proven from a contradiction.


Below is a formal proof of the principle using symbolic logic
Step Proposition Derivation
1 P Assumption
2 ~P Assumption
3 P V Q Disjunction introduction (1)
4 Q Disjunctive syllogism (2,3)

The error is at step 4 we are falsely assuming that P & ~P derives ~P
where in actuality P & ~P derives FALSE.
peteolcott (08-27-19, 08:24 PM)
On 8/27/2019 11:24 AM, peteolcott wrote:
> When-so-ever symbolic logic diverges from the deductive logical inference
> symbolic logic errs. The Principle of Explosion is one place where symbolic
> logic diverges from the deductive logical inference, thus the Principle of
> Explosion is erroneous.
>
> The non-sequitur error occurs in every logical inference where the truth
> of the conclusion does not depend upon the truth ALL of the premises.



A non sequitur is a fallacy in which a conclusion does not
follow logically from what preceded it. Also known as irrelevant
reason and fallacy of the consequent.
[..]
peteolcott (08-27-19, 09:26 PM)
On 8/27/2019 2:21 PM, peteolcott wrote:
> On 8/27/2019 2:12 PM, Fred wrote:
> Symbolic logic begins its screw up by redefining the meanings of the terms [sound] and [valid]
> WHICH IS THE NON SEQUITUR ERROR.


A deductive argument is VALID if the truth of its conclusion depends upon the truth of ALL of its premises.
A deductive argument is SOUND if it is VALID and ALL of its premises are TRUE.
[..]
peteolcott (08-27-19, 10:00 PM)
On 8/27/2019 1:54 PM, Simply Curious wrote:
> On Tuesday, August 27, 2019 at 12:24:45 PM UTC-4, peteolcott wrote:
> Nope.
> That is not what the article says at all.


I had to correct that article, here is one that has wording closer to mine:


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. Otherwise, a deductive argument is said to be invalid.

Let's see if it works in reverse:
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
FALSE and the conclusion nevertheless to be TRUE.

(a) X is a cat
(b) All cats are animals
(c) Therefore X is an animal

(a) Y is (a dog ) not a cat
(b) All cats are animals
(c) Therefore it cannot be concluded that Y is an animal on the basis
of the premises so any conclusion that Y is a dog would be invalid.

I have just shown that my definition of valid is better than the
referenced definitions of valid and non sequitur because my definition
handles the reverse case and the reverse case is proven to be correct.

CORRECTED DEFINITION OF LOGICAL VALIDITY.
CORRECTED DEFINITION OF LOGICAL VALIDITY.
CORRECTED DEFINITION OF LOGICAL VALIDITY.

A deductive argument is VALID if the truth of its conclusion depends
upon the truth of ALL of its premises.
peteolcott (08-27-19, 10:10 PM)
On 8/27/2019 3:00 PM, peteolcott wrote:
[..]
> CORRECTED DEFINITION OF LOGICAL VALIDITY.
> CORRECTED DEFINITION OF LOGICAL VALIDITY.
> CORRECTED DEFINITION OF LOGICAL VALIDITY.


A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for:
(a) The premises to be TRUE and the conclusion nevertheless to be FALSE.
(b) The premises to be FALSE and the conclusion nevertheless to be TRUE.

This is summed up as
--A deductive argument is VALID if the truth of its conclusion depends upon the truth of ALL of its premises.
André G. Isaak (08-28-19, 01:20 AM)
On 2019-08-27 2:10 p.m., peteolcott wrote:
> On 8/27/2019 3:00 PM, peteolcott wrote:
> A deductive argument is said to be valid if and only if it takes a form
> that makes it impossible for:
> (a) The premises to be TRUE and the conclusion nevertheless to be FALSE.
> (b) The premises to be FALSE and the conclusion nevertheless to be TRUE.


So according to you the following argument is not valid:

my pet is a dog
dogs are animals
therefore my pet is an animal.

You reject this on the grounds that one of the premises is false (my pet
is in fact a cat) and yet the conclusion is true which violates part (b)
of your definition. This probably explains why no one ever adopts your
definitions.

André
peteolcott (08-28-19, 01:43 AM)
On 8/27/2019 6:20 PM, André G. Isaak wrote:
> On 2019-08-27 2:10 p.m., peteolcott wrote:
> So according to you the following argument is not valid:
>  my pet is a dog
>  dogs are animals
>  therefore my pet is an animal.
> You reject this on the grounds that one of the premises is false (my pet is in fact a cat) and yet the conclusion is true which violates part (b) of your definition. This probably explains why no one ever adopts your definitions.
> André


No I reanalyzed my position and this is my position:
THE ORIGINAL NOTION OF DEDUCTIVE LOGICAL VALIDITY IS (A)
MY CORRECTION TO THIS ORIGINAL NOTION IS (B)

iep.utm.edu/val-snd/
A deductive argument is said to be valid if and only if it takes a form
that makes it impossible for:
(A) The premises to be TRUE and the conclusion nevertheless to be FALSE.
(B) The premises to be FALSE and the conclusion nevertheless to be TRUE.

SUMMED UP AS THIS:
A deductive argument is VALID if the truth of its conclusion depends
upon the truth of ALL of its premises.
peteolcott (08-28-19, 01:55 AM)
On 8/27/2019 2:18 PM, Simply Curious wrote:
> "Below is a formal proof of the principle using symbolic logic
> Step Proposition Derivation
> 1 P Assumption
> 2 ~P Assumption
> 3 P V Q Disjunction introduction (1)
> 4 Q Disjunctive syllogism (2,3) "
> Aight.
> "The error is at step 4 we are falsely assuming that P & ~P derives ~P where in actuality P & ~P derives FALSE."
> Whaaaaaa...? This is like 5 different levels of wrong. And it is only a sentence long!
> Th-there is no P&~P in that proof...


Line 1 is P
Line 2 is ~P

A deductive argument is VALID if the truth of its conclusion depends
upon the truth of ALL of its premises. WE CAN STOP RIGHT HERE.

> There IS a P though and that is all we use in 1, but we use it on step THREE, not step 4. On step 4, we 'assume' Q derives from ~P,P V Q. Yet again, no P&~P. There may be a valid criticism here, what the whole paraconsistent logic. Yet even intuitionist logic agrees here on the principle of explosion.
> But then we DO know from P&~P that you can derive ~P


THIS IS DEDUCTIVELY INCORRECT.
IF SYMBOLIC LOGIC SAYS THIS THEN SYMBOLIC LOGIC IS WRONG
P & ~P DERIVE FALSE
FALSE & P V Q derive FALSE
André G. Isaak (08-28-19, 01:57 AM)
On 2019-08-27 5:43 p.m., peteolcott wrote:
> On 8/27/2019 6:20 PM, André G. Isaak wrote:
> No I reanalyzed my position and this is my position:
> THE ORIGINAL NOTION OF DEDUCTIVE LOGICAL VALIDITY IS (A)
> MY CORRECTION TO THIS ORIGINAL NOTION IS (B)


And your (B) is what has the effect of making the above argument
'invalid' which is why no sane person is going to adopt your (B).

André
[..]
peteolcott (08-28-19, 02:35 AM)
On 8/27/2019 6:57 PM, André G. Isaak wrote:
> On 2019-08-27 5:43 p.m., peteolcott wrote:
> And your (B) is what has the effect of making the above argument 'invalid' which is why no sane person is going to adopt your (B).
> André


It would NOT make your example invalid.
It would make every example of the principle of explosion invalid.

I am pretty sure that the correction that I made to valid deduction
is already incorporated in the conventional meaning of the non sequitur
logical error:

a conclusion does not follow logically from what preceded it.
This by itself already includes relevance as confirmed below:


A non sequitur is a fallacy in which a conclusion does not follow
logically from what preceded it. Also known as irrelevant reason
and fallacy of the consequent.

The Principle of Explosion
A & ~A entails anything

Is not how logical entailment actually works. Logical entailment
Logical entailment in the natural language of Aristotle's
syllogism ALREADY requires relevance without any need of a
separate relevance logic.

All men are mortal.
Socrates eats potato chips
Therefore, Socrates is mortal.
[..]
André G. Isaak (08-28-19, 03:23 AM)
On 2019-08-27 6:35 p.m., peteolcott wrote:
> On 8/27/2019 6:57 PM, André G. Isaak wrote:
> It would NOT make your example invalid.


The example I gave includes a false premise and a true conclusion.
According to your (b) it should therefore be invalid. (If your intent
was that *all* of the premises be false, then the above would still be
invalid according to you since, were it to suddenly be discovered that
all dogs were in fact robots it would have no bearing on the fact that
my cat is an animal).

Apparently you are not capable of applying your own 'rule'.

> It would make every example of the principle of explosion invalid.
> I am pretty sure that the correction that I made to valid deduction
> is already incorporated in the conventional meaning of the non sequitur
> logical error:


You seem to be under the misguided impression that 'non sequitur' refers
to a specific logical error. It does not. It is simply a generic term
for any logical fallacy. You really need to stop latching on to terms
that you don't know.

[..]
> Logical entailment in the natural language of Aristotle's
> syllogism ALREADY requires relevance without any need of a
> separate relevance logic.

I've never brought up relevance logic. Do you even know what relevance
logic is?

> All men are mortal.
> Socrates eats potato chips
> Therefore, Socrates is mortal.


There is no need to invoke any notion of relevance to rule out the
above. It is not an Aristotelian syllogism. It is invalid, plain and simple.

>>> iep.utm.edu/val-snd/


You need to stop attributing your definitions to legitimate sources. The
definition below does not come from IEP. It comes from your own imagination.

André
[..]
peteolcott (08-28-19, 03:46 AM)
On 8/27/2019 8:23 PM, André G. Isaak wrote:
[..]
André G. Isaak (08-28-19, 04:04 AM)
On 2019-08-27 7:46 p.m., peteolcott wrote:
> On 8/27/2019 8:23 PM, André G. Isaak wrote:


Did you have a point? If so, you failed to make it. (And why are you
putting quote marks before your added text?)

André
peteolcott (08-28-19, 04:06 AM)
On 8/27/2019 11:24 AM, peteolcott wrote:
> When-so-ever symbolic logic diverges from the deductive logical inference
> symbolic logic errs. The Principle of Explosion is one place where symbolic
> logic diverges from the deductive logical inference, thus the Principle of
> Explosion is erroneous.
>
> The non-sequitur error occurs in every logical inference where the truth
> of the conclusion does not depend upon the truth ALL of the premises.


CORRECTION OF VALIDITY(2)
An argument is deductively valid if the truth of the conclusion depends
upon the truth of ALL of the premises.

Recent Part(B) was incorrect.
[..]

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