On 5/13/2022 6:14 PM, Richard Damon wrote:
> On 5/13/22 6:23 PM, olcott wrote:
>> 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.
>>
>
> Then why dod you say "Possible truth", if you meant an ACTUAL truth.
>

My system rejects expressions of language that are impossibly true such
as expressions that are true and unprovable.

> How about;
>
> x: there exist a number N that the 3N+1 / N/2 pattern never gets to 1
>
> True(x | ~x) is KNOWN to be true, but isn't a Stipulated Truth or a
> Proven Truth by your rules.
>

--
Copyright 2022 Pete Olcott

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