/sci/ - Science & Math

A mathematical entity is the class of all (real or imaginery or other) entities that fulfill its axiomatic properties.

>>5869762
What does that mean ontologically?

>>5869759
I suspect the very notion of "ontological status" is bogus.

>>5870683

existent
non-existent

>>5870771
Exists in what set?

In mathematics one typically talks about existence in terms of sets (i.e., there does not exist a greatest real number), so, if you don't mind, please use that convention here. Otherwise, I'd just be guessing at what you mean.

>>5870894
The existential quantifier is not restricted to sets. It may point at any type.

>>5871397
Ok, sure, but it remains that something still needs to be specified for the question to be meaningful.

By the way, is model theory at all useful or is it just a lot of mental masturbation?

>>5871397
What is the ontological status of an existential quantifier? Can you assert its existence without self-referentially assuming it?

What is the mathematical definition of ontological?

I'm serious.

>>5871881
>I'm serious.

>>5871881

The existential quantifier.

>>5870894

Kripke, possible worlds, etc.

>>5871971
Does the existential quantifier exist in the real world? How can you express its existence without using an existential quantifier?

To assert the existence of quantifiers you'll need meta-quantifiers. Ad infinitum

>>5871512
It is very useful.

>>5871881
You should rather ask what is the ontological view on mathematics.

>>5871849
>Can you assert its existence without self-referentially assuming it?
You can.

>>5876198
How so? Can you write it down in formal logic?

>>5876198
I'd be genuinely interested in seeing you do that.

What is ontology and why do we need it?

>>5878859
It is as simple as propositionally truncating the dependent sum.

>>5875390
You can't talk about ontological without a proper mathematical definition.

>>5880692
But that would imply reversing the hierarchy of ontology and mathematics.

>>5882098
Well yea, it makes much more sense that way.

>>5882620
Why? What happens?

>>5869759
Define 'ontological status'. No? /thread

>>5882754
Philosophy becomes applied math.

>>5871397
Then obviously mathematical objects exist... What's the point of this question? For example 1 exists in the integers. Pi exists in the reals, (1,3,4,5.7,1) exists in R^5....

Metaphysics is the study of ontology - what exists. OP is asking if numbers exist. Nobody can actually know that. Its probably the most controversial issue in metaphysics.

>>5882877
Clearly numbers exist. Could you please explain how it could be otherwise?

>>5882883
The argument against the existence of numbers is a reductionist argument - it says numbers reduce to something. 'Relations' are usually what numbers are said to reduce to.

I agree with you though. The more common consensus is that sets certainly exist, and by extension numbers do too.

Numbers exist in the ethereal plane. By faith and will they are brought into corporeal reality.

>>5882890
>it says numbers reduce to something

They reduce to decimal representations.

>>5882788
That is idiotic. Philosophy and mathematics are the same thing.

>>5871973
>Kripke, possible worlds, etc.

Interesting. I heard of Kripke. What did he say on the topic?

>>5869759
sets

everything is a set of sets

>>5884843
Philosophy uses only logic axiomatizations.
Mathematics uses tons of axiomatizations, though it is common to model them in logic it isn't inherent.

Phil is a small subset of math.

>>5882870
Wrong in all points.

>>5887078
>Philosophy uses only logic axiomatizations.

Most of philosophy rejects logic.

Someone has been keeping at least 35 threads alive
by bumping them twice a day. Compare the post times of
>>5870671 >>5871397 >>5873205 >>5873780 >>5875390 >>5876198
>>5877652 >>5878859 >>5880674 >>5882098 >>5884201 >>5884843
>>5886287 >>5888768
to the post times in other threads.
It's clear most of these are the same person.
The threads being bumped:
>>5858447 >>5861383 >>5862983 >>5863249 >>5865823 >>5866853
>>5867452 >>5867640 >>5868097 >>5868460 >>5868538 >>5869504
>>5869595 >>5869759 >>5869946 >>5872951 >>5873166 >>5873829
>>5874378 >>5874727 >>5875025 >>5876410 >>5876819 >>5878449
>>5878607 >>5878684 >>5878722 >>5880041 >>5880453 >>5880775
>>5881738 >>5883998 >>5884116 >>5884625 >>5885545
Write to moot@4chan.org if you want it to stop.

>>5886287
He said that Einstein was actually right all along.

>>5889573
Right with respect to what?

They do not exist

>>5890608
The cosmological constant.

>>5891329
What does this have to do with mathematical logic?

>>5893028
Watch TBBT and find out.

>>5893791
I cannot remember an episode where they talked about mathematical logic.

>>5894909
le 15 hour bump

>>5894916
Why does it annoy you that people are having conversation on a discussion board?

>>5869759
Any collection of self consistent structural relations among axiomatically defined principles has the same status, some mathematical structures are just more useful than others.

The relationship of binary logic to actual reality is really, really tricky to tease out and I'm not comfortable doing so.

>>5882883
psychic artifacts of the human mind, structural relations, pure conceptual features, etc.

>>5895724
But they are physically represented in the brain's neuronal structures.

>>5896893
SPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMPSPAMBUMP

>>5895724
Infinity is a number yet there are no "psychic artifacts of the human mind, structural relations, pure conceptual features, etc." of infinity.

>>5897781
When people think of infinity, certain areas in their brain are activated. Neuroscience can check this in a brain scan.

>>5899224
just like any other number, nice contribution bump spammer

>>5899224
How would someone think of infinity?

>>5899840
By mentally visualizing a Frechet manifold.

>>5901065
How would they do that?

>>5901862
It requires an IQ higher than 180.

>>5903263
It is a good thing I fit into this category.

>>5903978
What are the morphisms in this category?

>>5905477
The identity morphisms.

>>5906276
So this is the reason why geniuses are so narcissistic.

>>5907933
What would happen if they were not?

>>5908613
Their IQ would be lower.

>>5910124
nice job bumpspammer. 18 hour bump

>>5910130
Thank you.

>>5910130

that really rustles your jimmies doesn't it?

maybe it's finally time to get that OCD looked at.

>>5910124
By how many points?

>>5912850
at least 20

>>5911884
How are you able to diagnose mental disorders on an anonymous image board?

>>5914855
Maybe she has studied psychopathology.

Math id invented, not discovered.

>>5916034
I would be interesting in the anonymous image board subdiscipline.

>>5919107
It is currently being researched.

>>5920427
There must be a lot of scientists involved.

>>5921194
Indeed. Just look at the recent publications.

>>5922213
Where am I able to find them?

>>5923134
In a journal.

>>5924099
In what journal?

Mathematical entities exist as much as Luke Skywalker exists. They just happen to be enjoyable and solve a few of our problems.

>>5925473
>Mathematical entities exist as much as Luke Skywalker exists.

He surely does exist. I saw him in tv.

>>5925457
A science journal.

>>5927390
Which science journal?

>What is the ontological status of mathematical entities?

They exist.

>>5929218
The scientific one.

>>5932196
How do I know which one that is?

The noun ontology has 2 senses

1. ontology -- ((computer science) a rigorous and exhaustive organization of some knowledge domain that is usually hierarchical and contains all the relevant entities and their relations)
2. ontology -- (the metaphysical study of the nature of being and existence)

In terms of computer science, known ones are defined.
If you want to know metaphysics, wrong board.

>>5934364
I don't see how the first definition isn't a special case of the second.

>>5934364
We are talking about math, not computer science.

>>5935964

Computer science is a branch of mathematics.

>>5935992
No, it is not.

>>5935992
Building the newest gaming PC has never been a branch of math.

Math literally exists.

>>5940564
In what meaning of "literally"?

How is ontology objectively testable?

>>5944369

with modal logic

>>5944401
Modal logic is just an application of first order logic.

>>5944401
Is modal logic even math? I never see it used outside of philosophy.

>>5947757
Modal logic is usually used as a tool in theology.

>>5949166
So it cannot prove anything at all?

>>5949958
It can, see e.g. Löbs theorem.

>>5950043
>for any formula P, if it is provable that "if P is provable then P is true", then P is provable

What the fuck?