On 5/13/2022 5:14 PM, Richard Damon wrote:
> On 5/13/22 5:53 PM, olcott wrote:
>> 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.
>>
>
> The result of applying the operation of replacing N by N/2 if  N is even
> or by 3N+1 if N is odd will eventually get you to the number 1 for all
> Natural numbers N > 0.
>
> This statement MUST be either True or False, by its nature, there is no
> other possible state.
>
> This statement seems to be true, but it has unable to be proven to be true.
>
> Yes, we can not validly USE the idea that this statement is true to
> prove something else, because we know that it is still possible that it
> won't be true. But we CAN use that it will either be true or false to
> show something.
>
> That is an analytical expression that isn't proven to be an analytical
> truth, but it may still be true,

Probably an unconscious strawman error, that does not contradict my
original claim because it is a strawman error.

True(x) iff Stipulated_True(x) or Proven_True(x)
I am referring to <is> true and you are referring to <might be> true,
they are not the same.

--
Copyright 2022 Pete Olcott

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