On 5/13/2022 4:30 PM, Richard Damon wrote:
> On 5/13/22 4:56 PM, olcott wrote:
>> On 5/13/2022 3:43 PM, Richard Damon wrote:
>>> On 5/13/22 3:43 PM, olcott wrote:
>>>> On 5/13/2022 2:13 PM, Richard Damon wrote:
>>>>> On 5/13/22 2:10 PM, olcott wrote:
>>>>>> On 5/13/2022 12:47 PM, Richard Damon wrote:
>>>>>>> On 5/13/22 1:20 PM, olcott wrote:
>>>>>>>> *Validity and Soundness*
>>>>>>>> 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. https://iep.utm.edu/val-snd/
>>>>>>>>
>>>>>>>> If the Moon is made of green cheese then all dogs are cats is
>>>>>>>> valid and even though premises and conclusion are semantically
>>>>>>>> unrelated.
>>>>>>>>
>>>>>>>> *Here is my correction to that issue*
>>>>>>>> A deductive argument is said to be valid if and only if it takes
>>>>>>>> a form such that its conclusion is a necessary consequence of
>>>>>>>> all of its premises.
>>>>>>>>
>>>>>>>
>>>>>>> And, have you done the basic investigation to find out how much
>>>>>>> of conventional logic you invalidate with that change?
>>>>>>>
>>>>>>
>>>>>> It categorically changes everything that is broken.
>>>>>
>>>>> So, you are saying we need to throw out EVERYTHING we know and
>>>>> start over?
>>>>>
>>>>
>>>> Change everything that diverges from my spec:
>>>> A deductive argument is said to be valid if and only if it takes a
>>>> form such that its conclusion is a necessary consequence of all of
>>>> its premises.
>>>>
>>>>> I think, especially with the comment below, people will decide that
>>>>> your "new" logic systm isn't worth the cost to switch to.
>>>>>
>>>>>>
>>>>>>> Note, that it may be hard to define "necessary consequence" in a
>>>>>>> formal matter.
>>>>>>>
>>>>>>
>>>>>> {A,B} ⊢ C only when truth preserving operations are applied to
>>>>>> {A,B} to derive C.
>>>>>
>>>>> And what do you define truth perserving as?
>>>>>
>>>>
>>>> Semantic relevance is maintained.
>>>>
>>>>> Normally the phrase means that True Premises always generate True
>>>>> Results (which means the statement "If the moon is made of green
>>>>> cheese then ll dogs are cats" IS Truth Preserving, since any time
>>>>> the premise is true (never) the conclusion is true.
>>>>>
>>>>>>
>>>>>>> It should be noted that your example, while considered an vaild
>>>>>>> inference by normal logic, can never be used to actually prove
>>>>>>> its conclusion, so doesn't actually cause problems in normal
>>>>>>> logic (can you show a case where it does?)
>>>>>>>
>>>>>>
>>>>>> With my correction true and unprovable is impossible, unprovable
>>>>>> simply means untrue.
>>>>>>
>>>>>
>>>>> Ok, then you have just stated that your new logic system can't
>>>>> handle mathematics, and thus "Computer SCience" no longer exists as
>>>>> a logical system.
>>>>>
>>>>
>>>> It corrects the divergence of classical and symbolic logic from
>>>> correct reasoning.
>>>>
>>>>> This makes you system not much more than a toy for most people.
>>>>>
>>>>>>> Note, that at least by some meanings of your words, it could be
>>>>>>> construed that you only accept as a correct deductive argument,
>>>>>>> and arguement whose premises can at least some times be true, but
>>>>>>> there are some statements we don't know if they CAN be sometimes
>>>>>>> true, so your logic system would seem to not allow doing logic
>>>>>>> with that sort of statement.
>>>>>>>
>>>>>>
>>>>>> An analytic statement is only known to be true when it is derived
>>>>>> by applying only truth preserving operations to all of its
>>>>>> premises and all of its premises are known to be true, otherwise
>>>>>> its truth value is unknown.
>>>>>>
>>>>>
>>>>> KNOWN to be True, not IS TRUE.
>>>>
>>>> It remains unknown until it is known to be true or false.
>>>> My system only eliminates impossibly true or false.
>>>>
>>>
>>> So, you don't know what is still valid to use?
>>>
>>>
>>>>>
>>>>> Your statement even admits that truth value might be unknow, which
>>>>> might allow it to even be UNKNOWABLE (maybe just in that system) if
>>>>> it can't be proven or refuted.
>>>>>
>>>>
>>>> unprovable in the system means untrue in the system.
>>>
>>> And what does 'untrue' mean?
>>>
>>
>> Untrue means the same thing as Prolog's negation as failure.
>
> Which means... ?
>
> Prolog, as I remember, ASSUMES that anything not provable is FALSE (not
> 'untrue').
>

Unprovable means untrue and does not mean false in Prolog.

>>
>>> We know that there is a number that solves an equation, but we don't
>>> know that number, or how to compute that number.
>>>
>>> Can we say that it is true that such a number exists?
>>>
>>
>> If you defined your terms correctly, then yes because this has been
>> stipulated in your deinitions.
>>
>>> This means that we can define the floor of that number, which will be
>>> an integer (call it N), is it true that this number exists?
>>>
>>> That interger, MUST be either even or odd, so we know that either
>>> iseven(N) is true or isodd(N) is true.
>>>
>>> By your logic, the 'truth value' of both of those must be 'untrue'
>>> since we can not prove which one it is.
>>>
>>> This is the sort of problem you run into with your system.
>>>
>>>>
>>>>> There is NOTHING about an analytic statement that says it can only
>>>>> be true if it is provable. Note, "its truth value is unknown"
>>>>> doesn't mean it doesn't have a truth value, just that we don't know
>>>>> what that value is.
>>>>>
>>>>
>>>> Within any formal system unprovable in the system means untrue in
>>>> the system.
>>>>
>>>> The entire body of analytic truth is constructed only on the basis
>>>> of semantic connections between expressions of language, or
>>>> expressions that are stipulated to have the semantic property of
>>>> Boolean true. Lacking both of these and the expression is untrue.
>>>>
>>>> Since axioms are provable on the basis that they are axioms then
>>>> both of these factors that make an expression true also make it
>>>> provable.
>>>>
>>>
>>> You clearly are just stating words by rote and not actually
>>> understanding them.
>>>
>>
>> There are only two possible ways that any analytical expression of
>> language can possibly be true:
>> (1) It is stipulated to be true.
>> (2) It is derived by applying only truth preserving operations to (1)
>> or the consequences of (2).
>
> So there exists an integer number N is neither Even or Odd? (it is
> untrue for both tests)
>
> I don't think you actually understand what that means.
>
>>
>>> Analytic Truth is truth that is provable, that is correct, but it
>>> accepts that there is OTHER things that happen to be true but are not
>>> provable.
>>>
>>
>> Analytic truth includes every expression of language that can be
>> completely verified as totally true entirely on the basis of its
>> meaning without requiring any sense data from the sense organs.
>>
>> Empirical expressions of language also require sense data from the
>> sense organs to verify their truth.
>
> You still don't understand, do you.
>
> You still confuse Truth with Knowledge.
There are only two possible ways that any analytical expression of
language can possibly be true:
(1) It is stipulated to be true.
(2) It is derived by applying only truth preserving operations to (1)
or the consequences of (2).

Try and provide an example of a possible truth that does not require one
of those two.

--
Copyright 2022 Pete Olcott

"Talent hits a target no one else can hit;
Genius hits a target no one else can see."
Arthur Schopenhauer