On Apr 14, 11:22Â pm, Immortalist
yahoo.com> wrote:> On Apr 14, 2:03Â pm, J Jones
aol.com> wrote:
>>> It is difficult to find a useful significance for the logical operators
>> if we take them at face value. Take these instances:
>
>> A and not A
>> Either A or not A
>> Neither A nor not A
>
>> All these are true in a spatiotemporal framework. They are also not true
>> in a spatiotemporal framework, and this without contradiction.
>> To add insult to injury, in the spatiotemporal framework "either A or
>> not A" can ALSO imply "A and not A". ...
>
> Do you mean "some" A or "all" A, if the former there is no problem but
> if the later you commit the existential fallacy;
>
> The quantity of a categorical proposition is determined by whether or
> not it refers to all members of its subject class (i.e., universal or
> particular). The question "How many?" is asking for quantity.
> Indicators of "how much" are called quantity indicators (quantifiers)
> and specifically are "all," "no," and "some."
>
>
http://philosophy.lander.edu/logic/prop.html
>
> Universal Quantifier:
>
> All x
>
> Existential Quantifier:
>
> Some x
>
> Examples:
>
> All philosophers are wise.
>
> Some philosophers are silly.
>
>
http://www.fallacyfiles.org/quanfall.html
>
> Existential Import and Categorical Propositions
>
> Consider the following propositions:
>
> All unicorns have horns.
> No perpetual motion machine has been patented.
>
> Both are true even though there are no unicorns or perpetual motion
> machines. Thus, these statements lack existential import.
>
> Many modern logicians hold that existential import is a function of a
> statement's logical form. According to this view, universal
> categorical statements in general do not have existential import.
>
> Statements that are particular in nature, however, do have existential
> import. To say that some S are P, or that some S are not P, is to
> imply the existence of Ss; if there are no Ss, then both statements
> are false.
>
>
http://www.wwnorton.com/college/phil/logic3/ch8/import.htm
>
> Existential Fallacy
>
> Any argument whose conclusion implies that a class has at least one
> member, but whose premisses do not so imply.
>
> A proposition has existential import if it implies that some class is
> not empty, that is, that there is at least one member of the class.
>
>
http://www.fallacyfiles.org/existent.html
>
>
>
>> ...These observations are based simply
>> on the everyday ontology of spatiotemporal objects.
>
>> In other words, as I would like to point out here, if we insist that the
>> logico-mathematical operators and their objects are Platonically real,
>> then we must define the properties of their ontological framework. For
>> it is clear that if we do not so define that framework then we are drawn
>> into the ambiguities delivered to us by an otherwise default ontology
>> given by the spatiotemporal framework, which I have described above.
>
>> But there is a greater threat to logic than that posed by a default
>> ontology. The choice of an ontology for logic and its objects could not
>> be made on any 'ontological' basis. Accordingly, the claim that Platonic
>> logico-mathematical objects are (ontologically) "real" must remain on
>> the table. Logic cannot find its ground in any ontology. It would be
>> difficult then, to find an operational domain for logic, for any
>> (ontological domain) is quite independent of any mooted ontologically
>> absolute logical principle(s).-
That is unless you are talking about the argument you made recently
about rain
rain = A
it is raining in the same place it is not raining, because there is no
rain drops between drops, or something? I think this is the sorites
fallacy.
Continuum fallacy
Continuum fallacy, also called fallacy of the beard[citation needed],
is a logical fallacy related to the Sorites paradox, or paradox of the
heap. The fallacy appears to demonstrate that two states or conditions
can not be considered distinct (or do not exist at all) because
between them there exists a continuum of states. According to the
fallacy, differences in quality cannot result from differences in
quantity.
The fallacy can be described in the form of a conversation:
Q: Does one grain of wheat form a heap?
A: No.
Q: If we add one, do two grains of wheat form a heap?
A: No.
Q: If we add one, do three grains of wheat form a heap?
A: No.
...
Q: If we add one, do one hundred grains of wheat form a heap?
A: No.
Q: Therefore, no matter how many grains of wheat we add, we will never
have a heap. Therefore, heaps don't exist!
Other uses of this fallacy seem to prove that:
No one can be bald (or everyone is bald) because there are people with
varying quantities of head hair.
No man has a beard, no matter how long it is (or every post-pubescent
male has a beard, no matter how cleanly shaven) because a beard can
have varying lengths.
A room is never either "hot" or "cold", because of the continuum of
temperatures.
Separate languages don't exist, because they are in a dialect
continuum.
One argument against the fallacy is based on simple induction: there
are bald people and people who aren't bald. Another argument is that
for each degree of change in states, the degree of the condition
changes slightly, and these "slightly"s build up to shift the state
from one category to another. For example, perhaps the addition of a
grain of rice causes the total group of rice to be "slightly more" of
a heap, and enough "slightly"s will certify the group's heap status.
In general, any argument against the Sorites paradox can also be used
on the continuum fallacy.
http://en.wikipedia.org/wiki/Continuum_fallacy
