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, and is neither stipulated true or
derived from an analytical proof.

Again. you are confusing True, with Proven/Known.

It MAY be True, or its Converse IS True, we know it must be one or the
other.

It is not KNOWN to be True, or Proven.