On Sunday, October 24, 2021 at 1:17:12 AM UTC-4, olcott wrote:
On 10/24/2021 12:06 AM, Dan Christensen wrote:
On Saturday, October 23, 2021 at 11:21:12 PM UTC-4, olcott wrote:Logical implication
If natural language conditionals were understood in the same way, that >>>> would mean that the sentence "If the Nazis won World War Two, everybody >>>> would be happy" is true.
https://en.wikipedia.org/wiki/Paradoxes_of_material_implication
An educated person might point out that such a statement is pure speculation. And that it is an opinion, and not a verifiable fact. As such it is not a logical analysis of the current state of the world.
Dan
Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
p q p ⇒ q
T T T
T F F
F T T
F F T
When we apply semantics to the variables material implication asserts
that the is a relationship between unrelated things. This is an error.
The last two rows of the truth table are mistaken.
You really need to be able to formally prove that A & B => B & A. Your system is DOA otherwise.
Dan
Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
On 2021-10-23 23:09, olcott wrote:
On 10/23/2021 10:14 PM, André G. Isaak wrote:
On 2021-10-23 21:01, olcott wrote:
On 10/23/2021 9:32 PM, André G. Isaak wrote:
On 2021-10-23 19:03, olcott wrote:
On 10/23/2021 6:10 PM, Dan Christensen wrote:
On Saturday, October 23, 2021 at 6:15:15 PM UTC-4, olcott wrote: >>>>>>>> On 10/23/2021 4:58 PM, Dan Christensen wrote:
On Saturday, October 23, 2021 at 3:31:36 PM UTC-4, olcott wrote: >>>>>>>>>> On 10/23/2021 1:44 PM, Dan Christensen wrote:The => implication operator is tossed out on its ass, thus
On Saturday, October 23, 2021 at 12:42:41 PM UTC-4, olcott >>>>>>>>>>> wrote:
If we want to have actual correct reasoning then we get rid >>>>>>>>>>>> of the
Material conditional
p q p → q
T T T
T F F
F T T
F F T
and replace it with if-then
if P then q
p q if p then q
T T T
T F F
F T undefined
F F undefined
Here is a formal proof of ~A => [A =>B], the basis for the >>>>>>>>>>> last two lines of the truth table for A => B. To prevent this >>>>>>>>>>> derivation, somehow you will also have to ban or restrict the >>>>>>>>>>> application of one more of the rules of inference used here. >>>>>>>>>>> Which will it be?
I am saying for symbolic logic is defined incorrectly when >>>>>>>>>> symbolic
logic is required to be the basis for correct reasoning.
You haven't answered the question. Which line(s) in the above >>>>>>>>> proof would be invalid in your proposed alternative system of >>>>>>>>> logic? Somehow, you want to make it impossible to derive
B].
unavailable
for any proof.
Let's start with something REAL easy. How would you prove A & B
B & A?
I reject material implication and the principle of explosion.
You do realize that even if you "eliminate" material implication
and replace it with your version (whatever that might be), you'd
still be able to prove anything from (A & ¬A). The principle of
explosion is usually illustrated using implication but it isn't
actually tied to implication.
André
I reject material implication and the principle of explosion
separately.
Unless you plan on rejecting ∧, ∨ and ¬, you're not going to be able >>> to get rid of the principle of explosion since it is a direct
consequence of the logical definitions of these operators.
We simply forbid any syntactic entailment that is contradicted by
semantic entailment. We put the semantic relevance back into logic
that was removed from Aristotle's syllogism.
How exactly do you 'forbid' something which follows directly from the
rules of the system without ending up with an inconsistent system?
And unless you can provide some actual *rules* which allows us to decide whether or not something is contradicted by 'semantic entailment', the
above is worthless. Note that giving examples of things which you think
do or do not involve 'semantic entailment' is not the same thing as
providing actual explicit rules. So far, any time I've asked you about
your notion of 'semantic relatedness' or other things you've responded
by giving one or two examples of things you consider related or
unrelated, but no actual rule which would allow us to decide whether two arbitary things count as related.
I am not sure how to best express the set of changes that are required. >>>>
A good heuristic might be that when semantic values are assigned to
propositional variables and then when rules of logic are applied to
these variables derive semantic nonsense then this is a rule that
must be discarded.
There are only two semantic values that can be assigned to
propositional variables: true and false. I have no idea what you can
derive from these two values that could possibly objectively count as
'semantic nonsense'.
André
That is not exactly true. Truth conditional semantics is anchored in
true and false yet has a whole additional supporting infrastructure.
That 'supporting architecture', if I understand what you are claiming is *not* part of logic.
It is true that an X is a Y is the propositional level.
When we plug semantics in the we get truth conditional semantics.
It is true that a dog is an animal.
What your referring to here isn't 'semantics'. The only semantic values available to logic are 'true' and 'false'. What you are referring to is 'content'.
The entire point of formal logic is that it looks exclusively at the
form which an argument takes while ignoring the content altogether.
Formal logic has no knowledge whatsoever about dogs or animals, nor
should it.
André
On 10/24/2021 9:59 AM, Dan Christensen wrote:
On Sunday, October 24, 2021 at 1:17:12 AM UTC-4, olcott wrote:
On 10/24/2021 12:06 AM, Dan Christensen wrote:
On Saturday, October 23, 2021 at 11:21:12 PM UTC-4, olcott wrote:Logical implication
If natural language conditionals were understood in the same way, that >>>>> would mean that the sentence "If the Nazis won World War Two,
everybody
would be happy" is true.
https://en.wikipedia.org/wiki/Paradoxes_of_material_implication
An educated person might point out that such a statement is pure
speculation. And that it is an opinion, and not a verifiable fact.
As such it is not a logical analysis of the current state of the world. >>>>
Dan
Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
p q p ⇒ q
T T T
T F F
F T T
F F T
When we apply semantics to the variables material implication asserts
that the is a relationship between unrelated things. This is an error.
The last two rows of the truth table are mistaken.
You really need to be able to formally prove that A & B => B & A. Your
system is DOA otherwise.
A = dogs are animals
B = dogs are not animals
A & B => not one damn thing
A = it is raining outside
B = you go outside unprotected from the rain
C = you get wet
A & B ⊨ C
Dan
Download my DC Proof 2.0 freeware at http://www.dcproof.com
Visit my Math Blog at http://www.dcproof.wordpress.com
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