Then in practice we realize the ideas of numbers in objective reality.
On Sat, Mar 8, 2014 at 1:32 AM, Arthur Maisel <arthurmaisel at gmail.com> wrote:
> It seems to me that the lengths people have to go to to deny the reality of
> numbers is the best proof that they are real. The disagreements over
> whether they "exist" always hinge on differing definitions of what that
> word means. Numbers are real for *us*---who else are we talking about?
>
> To posit a perception that is a pure and simple physical response to the
> stimulus of sense data is one example of going to lengths. I see a cat on
> the table because photons bouncing off the mammal on the eating surface
> enter my eyes and stimulate neurons in my brain, QED. Begs rather a lot of
> questions, no? Note how the cat on the table, supposedly the end product of
> this purely material process, is snuck in as the "mammal on the eating
> surface." (W. C. Fields, one imagines, might have been a logical
> positivist---if only he hadn't taken up juggling, alas.)
>
> Or how about this one: because of varying densities of the molecules in the
> air impinging on my ear drums over time, which variations are converted
> into analogous electrochemical impulses in various neural pathways, I hear
> a windy philosophical argument?
>
>
> On Fri, Mar 7, 2014 at 11:06 AM, Charles Brown <cb31450 at gmail.com> wrote:
>
>>
>> http://en.wikipedia.org/wiki/Philosophy_of_mathematics#Indispensability_argument_for_realism
>>
>> Indispensability argument for realism
>>
>> This argument, associated with Willard Quine and Hilary Putnam, is
>> considered by Stephen Yablo to be one of the most challenging
>> arguments in favor of the acceptance of the existence of abstract
>> mathematical entities, such as numbers and sets.[20] The form of the
>> argument is as follows.
>>
>> One must have ontological commitments to all entities that are
>> indispensable to the best scientific theories, and to those entities
>> only (commonly referred to as "all and only").
>> Mathematical entities are indispensable to the best scientific
>> theories. Therefore,
>> One must have ontological commitments to mathematical entities.[21]
>>
>> The justification for the first premise is the most controversial.
>> Both Putnam and Quine invoke naturalism to justify the exclusion of
>> all non-scientific entities, and hence to defend the "only" part of
>> "all and only". The assertion that "all" entities postulated in
>> scientific theories, including numbers, should be accepted as real is
>> justified by confirmation holism. Since theories are not confirmed in
>> a piecemeal fashion, but as a whole, there is no justification for
>> excluding any of the entities referred to in well-confirmed theories.
>> This puts the nominalist who wishes to exclude the existence of sets
>> and non-Euclidean geometry, but to include the existence of quarks and
>> other undetectable entities of physics, for example, in a difficult
>> position.[21]
>>
>> Epistemic argument against realism
>>
>> The anti-realist "epistemic argument" against Platonism has been made
>> by Paul Benacerraf and Hartry Field. Platonism posits that
>> mathematical objects are abstract entities. By general agreement,
>> abstract entities cannot interact causally with concrete, physical
>> entities. ("the truth-values of our mathematical assertions depend on
>> facts involving Platonic entities that reside in a realm outside of
>> space-time"[22]) Whilst our knowledge of concrete, physical objects is
>> based on our ability to perceive them, and therefore to causally
>> interact with them, there is no parallel account of how mathematicians
>> come to have knowledge of abstract objects.[23][24][25] ("An account
>> of mathematical truth ... must be consistent with the possibility of
>> mathematical knowledge."[26]) Another way of making the point is that
>> if the Platonic world were to disappear, it would make no difference
>> to the ability of mathematicians to generate proofs, etc., which is
>> already fully accountable in terms of physical processes in their
>> brains.
>>
>> Field developed his views into fictionalism. Benacerraf also developed
>> the philosophy of mathematical structuralism, according to which there
>> are no mathematical objects. Nonetheless, some versions of
>> structuralism are compatible with some versions of realism.
>>
>> The argument hinges on the idea that a satisfactory naturalistic
>> account of thought processes in terms of brain processes can be given
>> for mathematical reasoning along with everything else. One line of
>> defense is to maintain that this is false, so that mathematical
>> reasoning uses some special intuition that involves contact with the
>> Platonic realm. A modern form of this argument is given by Sir Roger
>> Penrose.[27]
>>
>> Another line of defense is to maintain that abstract objects are
>> relevant to mathematical reasoning in a way that is non-causal, and
>> not analogous to perception. This argument is developed by Jerrold
>> Katz in his book Realistic Rationalism.
>>
>> A more radical defense is denial of physical reality, i.e. the
>> mathematical universe hypothesis. In that case, a mathematician's
>> knowledge of mathematics is one mathematical object making contact
>> with another.
>>
>> On Thu, Mar 6, 2014 at 10:01 AM, Shane Mage <shmage at pipeline.com> wrote:
>> >
>> > On Mar 6, 2014, at 9:11 AM, Charles Brown wrote:
>> >
>> >> "There is nothing but matter and, its mode of existence is motion. " -
>> >>
>> > Nonsense. Matter in motion is ORDERED by mathematical laws.
>> Mathematical
>> > objects (numbers and shapes) ARE and there is nothing MATERIAL about
>> them.
>> >
>> >
>> >
>> > Shane Mage
>> >
>> >
>> > This cosmos did none of gods or men make, but it
>> > always was and is and shall be: an everlasting fire,
>> > kindling in measures and going out in measures.
>> >
>> > Herakleitos of Ephesos
>> >
>> >
>> >
>> >
>> >
>> > ___________________________________
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