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Math, Assumptions, and the Supernatural

beenherebeforeagain

Rogue Animist
Premium Member
Last I heard, there is some evidence that counting (arithmetic) is to some extent not only genetic-based behavior in humans, but also genetic-based behavior in some other animals. For instance, eagles can apparently count as high as three.
and iirc, crows and ravens can count higher than that...and it's been demonstrated, I believe, in a wide variety of species--including bees--can distinguish more than and less than, and I think last year it was shown that bees have a functional concept of zero...or at least none...
 

Polymath257

Think & Care
Staff member
Premium Member
What ought to be taught is that you have consistent assumptions given correct notation. However, if you were to explain to a teacher that Order of Operations doesn't actually work, and that math ought to clearly show a difference between division and fractions, you'd get a C or worse for your efforts.

And the math does make such a distinction.

In 84+59+82/3. the last number is a fraction. And if you put it into a calculator that is intelligently designed, you will get a fraction out. If what you want is an average, you need to put in (84+59+82)/3. In other words, add up all the numbers and *then* divide.

In general, I tell my students, 'when in doubt, add parentheses'.

What is required is a higher standard for teachers, to actually make sure that they know the how and why of math, not just blindly accept proofs that are unproven.

I agree. They need to know much more than just what they are teaching.

When a teacher gives their students a math problem 2+rt9*sq7/5 they have failed them already. They are expecting them, without any advice on how to associate, to solve a complex problem where the order is assumed but not known. Is it 2+((rt9*sq7)/5) or 2+ (the fraction of (3*49)/5)? Is it (2+3)*(49/5)? Or is it ((2+3)*49)/5?

A teacher must show clearly to their students what is right and what is wrong by narrowing any possible assumptions.

Polymath, yes there are times when that is what you want.

But at all times, you should avoid sloppy math.
I agree. To be less sloppy, learn to use parentheses properly.

Just as I don't write a sentence and go on and on without any commas without any breaks of any sort while I list almonds raspberries and pears just as I use commas to separate paired items like peanut butter and jelly from the rest of a list which is why the last of a list should always be comma and just as this sentence sux without any commas math with no parentheses makes it difficult or impossible to reliably perform the problem. This is what a math problem like that would look like as a sentence. It's ****. And Order of Operations uses a procedure that is not common to either basic elementary school math or actual experience using real objects, (in the apple example, the grocer would know something is funny about that math) to get answers that don't apply.

If the teacher doesn't teach order of operations and the use of parentheses, then I agree that there is a problem. If they *do*, then I see no problem. The calculation of the average *does* require parentheses.

It's not about using the calculator correctly. The solar calculator comes to the correct assumption because it DOESN'T USE Order of Operations. The graphing calculator does, and fails a simple math problem. And no, the correct answer is NOT four. The grocer would have gotten 6 apples by the end of his buy period, and sold exactly half of those six. He would be able to look at those three apples left, and without any math besides counting, tell you there are three apples.

But the problem you wrote down is NOT the problem that the grocer should be putting into the calculator. So it *is not* a correct use of the calculator to write 4+2/2 when you want (4+2)/2.

BTW, the solar power calculator that gave you the 'correct' calculation (as you see it) is a fine example of a calculator that has NOT been programmed correctly. Even a slightly better (even cheap solar) calculator will require parentheses (or pushing equality) for the calculation of the average.

In the grocer example, yes if they halved the ones bought from the other guy, then it would be 2+(4/2). But this is why we HAVE parentheses. So we can use them to tell how the math problem should go. When we don't, it should ignore everything and proceed left to right.

And I strongly disagree for the reasons I gave. If you want (4+2)/2, then put in (4+2)/2. If you put in 4+2/2, you *should* get 3 because that is the correct answer for what you put in. if your calculator does NOT give 3, it is poorly programmed.
 

mikkel_the_dane

My own religion
...
Bummer. Well, sort of.

Now, I have been pondering. We all make assumptions about the 'real world'. Among those
is that we are not the only conscious being, that there is an external world that our
senses can perceive, however imperfectly, that our memories are reliable to at least
some extent, etc.

We use these assumptions to move around in the world, learn how that world works, etc.
We develop science and technology, etc. We make art, music, and love others.

Then comes the issue of religion.

People have many different views of what things are true in their religions. There are
multitudes of different religions (especially through time) with huge variations on what
was believed, thought important, etc.

What if the existence of a supernatural is simply inconsistent?

What if the existence of a supernatural is neither provable nor disprovable from our other
assumptions? What if the question really doesn't have a truth value at all?

Now, if this is the case, what are the advantages and disadvantages of the assumptions either way?

What if all assumptions about the "real world" are inconsistent?
What if no assumptions can prove the "real world"?
What if the question about the "real world" has no real truth value at all.
What are the the advantages and disadvantages of the all different assumptions about the "real world" either way?

You have to do your questions in a general way.
So here it is to the best of the current overall schoolery knowledge:
Cognitive Relativism | Internet Encyclopedia of Philosophy

I am a general skeptic and I can't show this to you, because you can't literally see it. It is cognitive and how you understand it, is in you and nowhere else.
Here is it as in practice:
Strong believer in his/her set of assumptions as true for the real world: I am right and everybody else gets it wrong.
Another strong believer in his/her set of assumptions as true for the real world: No, I am right and everybody else gets it wrong.
Me: None of us including me can do that.
Both to me: You can't be sincere. It makes no sense.
Me: That it makes no sense is cognitive relativism. I just know that is so for all of us. You two can only spot it in everybody else than yourself each individually. I can spot cognitive relativism in everybody including myself. That is it. That is what makes me a general skeptic and you both limited skeptics. You both doubt everybody else's cognition than your own. I have just learned to doubt my own just as I doubt everybody else's.

Welcome to the big league of "playing", what is the "real world" with truth, reason, logic, proof, evidence and what not?
That is a bummer, because it is unknown.
I just get that the joke is on all of us.
How you get the joke, is up to your cognition and thus cognitive relativism.
It is assumptions or rather beliefs and no truth all the way down this rabbit hole of the "real world".
That is so for science, math, religion and philosophy. There is no the truth of the real world:

Regards Mikkel
 

Ponder This

Well-Known Member
Not quite. That would be simply the recognition that some position is independent: that it cannot be known.

Faith would be the further step of adopting one alternative to add to the list of axioms.

With all due respect, it is "quite".

Your additional statements here confirm.

Then again, if you are struggling for a reason to include the "supernatural" as an axiom... then perhaps your problem is merely one of articulation.

If you have a well-defined statement that describes the phenomenon you seek to describe and that is consistent with your other axioms, then, why not include it?
 

Polymath257

Think & Care
Staff member
Premium Member
With all due respect, it is "quite".

Your additional statements here confirm.

Then again, if you are struggling for a reason to include the "supernatural" as an axiom... then perhaps your problem is merely one of articulation.

If you have a well-defined statement that describes the phenomenon you seek to describe and that is consistent with your other axioms, then, why not include it?

Well, in that case, I would consider the phenomenon to be natural (since there is a well-defined statement that describes it) and no assumption about a supernatural is required.

The point here is that *both* directions are equally consistent (in this case, since we are assuming standard axioms, this means consistent with observations and descriptive of those observations): both the assumption and the negation of that assumption. And the question is which to choose to assume: the statement or its negation.
 

mikkel_the_dane

My own religion
Well, in that case, I would consider the phenomenon to be natural (since there is a well-defined statement that describes it) and no assumption about a supernatural is required.

The bold part is an assumption about the "real world" and it is neither true or false. It appears to you to work for you.

The key words are "I would consider". That is a tell-tale sign of 1st person subjective cognition. All it tells us that you are a naturalist. It doesn't tell us if the "real world" is natural, from God or what not.
 

Samantha Rinne

Resident Genderfluid Writer/Artist
And the math does make such a distinction.

In 84+59+82/3. the last number is a fraction. And if you put it into a calculator that is intelligently designed, you will get a fraction out. If what you want is an average, you need to put in (84+59+82)/3. In other words, add up all the numbers and *then* divide.

In general, I tell my students, 'when in doubt, add parentheses'.



I agree. They need to know much more than just what they are teaching.


I agree. To be less sloppy, learn to use parentheses properly.



If the teacher doesn't teach order of operations and the use of parentheses, then I agree that there is a problem. If they *do*, then I see no problem. The calculation of the average *does* require parentheses.



But the problem you wrote down is NOT the problem that the grocer should be putting into the calculator. So it *is not* a correct use of the calculator to write 4+2/2 when you want (4+2)/2.

BTW, the solar power calculator that gave you the 'correct' calculation (as you see it) is a fine example of a calculator that has NOT been programmed correctly. Even a slightly better (even cheap solar) calculator will require parentheses (or pushing equality) for the calculation of the average.



And I strongly disagree for the reasons I gave. If you want (4+2)/2, then put in (4+2)/2. If you put in 4+2/2, you *should* get 3 because that is the correct answer for what you put in. if your calculator does NOT give 3, it is poorly programmed.

The last number is not a fraction.

A fraction is actually (1/2) not 1 / 2. This is because when you don't specify otherwise, all addition and subtraction is put on the numerator line.

1+2+3 / 2 in elementary school up until you are taught otherwise by "learned" people using order of operations just gets turned into one big fraction, unless it is somehow clear that the last one is a fraction. As in, early math ignores order of operations, and just focuses on order period.

1+2+3
--------
2

Now

3 + 1 + 2
--
2

Is a different story. That's why they teach little kids about fractions, to show them that some math is self-contained. And some is not. Fractions are self-contained division, meaning (x/y). Other division is not self-contained, which why a schoolteacher will immediately see something wrong with typing three numbers into a calculator and then typing a division of the total by three and getting an answer over 100.

In fact, many calculators, pre-total which is to say
2+4+5/3
is done 2+4=6+5=11/3
(2+4+5)/3
Same result
Consistency in math means you're doing something right.
Inconsistency, means assumptions are faulty.

Order of Operations is a theory based on assuming that the last number is a fraction. But as my math teacher put it, assume makes an *** out of u and me. When you actually check the common use of math problems, 80% of the time you should be doing

(2+4+5)/3

not 2+4+(5/3)

Order of Operations is like an annoying search engine that when you ask for a Japanese term, corrects your spelling as well as suggesting that
Shiro no Megami direct to all searches relating to the Shire of Meghan (Harry's wife's town where they live).

If you wanted a fraction, wouldn't you have made a fraction?
 

Polymath257

Think & Care
Staff member
Premium Member
The bold part is an assumption about the "real world" and it is neither true or false. It appears to you to work for you.

The key words are "I would consider". That is a tell-tale sign of 1st person subjective cognition. All it tells us that you are a naturalist. It doesn't tell us if the "real world" is natural, from God or what not.


Well, it is sort of a definition of the term 'natural', now isn't it. If we can get a description that works and is testable, then we are doing science and the phenomenon is natural.

This is one of the reasons I consider the whole notion of 'supernatural' to be self-contradictory: if we can detect and describe the phenomenon, then it is natural. If we cannot, then it is meaningless to say it exists.
 

Polymath257

Think & Care
Staff member
Premium Member
The last number is not a fraction.

A fraction is actually (1/2) not 1 / 2. This is because when you don't specify otherwise, all addition and subtraction is put on the numerator line.

1+2+3 / 2 in elementary school up until you are taught otherwise by "learned" people using order of operations just gets turned into one big fraction, unless it is somehow clear that the last one is a fraction. As in, early math ignores order of operations, and just focuses on order period.

1+2+3
--------
2

Now

3 + 1 + 2
--
2

Is a different story. That's why they teach little kids about fractions, to show them that some math is self-contained. And some is not. Fractions are self-contained division, meaning (x/y). Other division is not self-contained, which why a schoolteacher will immediately see something wrong with typing three numbers into a calculator and then typing a division of the total by three and getting an answer over 100.

In fact, many calculators, pre-total which is to say
2+4+5/3
is done 2+4=6+5=11/3
(2+4+5)/3
Same result
Consistency in math means you're doing something right.
Inconsistency, means assumptions are faulty.

Order of Operations is a theory based on assuming that the last number is a fraction. But as my math teacher put it, assume makes an *** out of u and me. When you actually check the common use of math problems, 80% of the time you should be doing

(2+4+5)/3

not 2+4+(5/3)

Order of Operations is like an annoying search engine that when you ask for a Japanese term, corrects your spelling as well as suggesting that
Shiro no Megami direct to all searches relating to the Shire of Meghan (Harry's wife's town where they live).

If you wanted a fraction, wouldn't you have made a fraction?


And if you use the notation *correctly* there is no ambiguity. And, that notation that you dislike makes things a LOT easier at more advanced levels. Which is why it is used.
 

mikkel_the_dane

My own religion
Well, it is sort of a definition of the term 'natural', now isn't it. If we can get a description that works and is testable, then we are doing science and the phenomenon is natural.

This is one of the reasons I consider the whole notion of 'supernatural' to be self-contradictory: if we can detect and describe the phenomenon, then it is natural. If we cannot, then it is meaningless to say it exists.

You can't see your own assumptions as just that assumptions. You treat them as "true" or "real" and what not. They are none of that. They work for you, but that is not truth and what not. BTW the "we" is also an assumption just as natural is.
You are an expert on math. Not epistemology. Stop taking for granted your own nature(psychology in part) and nurture(culture, condition and so on) hold for the "real world". The "real world" is philosophy.

Start here:
Ancient Greek Skepticism | Internet Encyclopedia of Philosophy
Start with Agrippa's Five Modes.
That applies to all claims of Truth, Knowledge, Evidence, Truth and so on for the "real world".

Your "Well, it is sort of a definition of the term 'natural', now isn't it." is a dogmatic claim, if it is to be taken as the "bedrock" for knowledge, but it is not. It is an unsupported assumption and the point is that applies to all version of "I know as true and what not" for the "real world".

Now decide, are you doing methodological naturalism? If so, then this applies:
Science has limits: A few things that science does not do
Including this:
"Science doesn't draw conclusions about supernatural explanations"

Or are you doing philosophy?
That is a reason for methodological naturalism. And that requires that you can do what amounts to philosophy.
So decide, are we doing science or philosophy?
It appears that you are doing philosophy. If so, stop dragging science into it. Science is silent on the supernatural.
 

mikkel_the_dane

My own religion
Well, it is sort of a definition of the term 'natural', now isn't it. If we can get a description that works and is testable, then we are doing science and the phenomenon is natural.

This is one of the reasons I consider the whole notion of 'supernatural' to be self-contradictory: if we can detect and describe the phenomenon, then it is natural. If we cannot, then it is meaningless to say it exists.

Take 2:
Take a rock. You know, stone from a mountain and so on.
We can use science on a rock. We can see it and test it using different instruments.
Take meaningless. We can't see it, hold it. It is no tangible and we can't it using different instruments. Meaningless doesn't exist.

It doesn't stop there. It is also the case with reason, consider, notion, self-contradictory and exist.
There is whole lot of words, which are not natural according to your standard of existence.
We are now deep down in the limit of empiricism and that problem of the rule of only that, which we can observe, exists.
We can't observe the rule, so the rule doesn't exist.

You really can't see your own first person assumption as that or can you?
Please explain the phenomenon of existence or the property of existence. You can't! It is empty and only works if you believe in it. I don't believe in it.
I know that I experience but not everything I experience are from the senses; i.e. phenomenon.
That is easy to test:
You: All that exists are phenomenons.
Me: No!

You are doing a common feature of thinking.
All/everything/the world and so on can be explain with one methodology, fact, category, property or what not.
All is X.
All is logic.
All is natural.
All is physical.
In all of the cases, I just answer no. Then the "no" is logic, natural and physical, but that is absurd or it doesn't exists. But if
doesn't exist, then how can I answer no? I have done a reductio ad absurdum. You know that one. Well, start applying it to your own thinking.

That are at least 5 kinds of overall questions relevant to the belief in a common world for us all.
How do we explain, what we observe and otherwise do with our bodies and what happens in relationship to that?
How do we think in abstract terms and what can we learn from that?
Ho do we interact with other humans in a human way?
What is the meaning of one's own life?
What is everything independent of the mind?

Well, science can only do the first one. You can do the second as math.
But you can't use math and science on the last 3.
And for the last one, the answer is that it is unknown.
And please don't claim that the unknown doesn't exist, because you can't know that. The unknown neither exists or don't. It is unknown.

I seem to recall that you feel that the problem of the matrix is silly. But that is not based on reason, logic, proof or evidence.
So IFF you are in the matrix, it won't stop you from being in the matrix, just because you feel, it is silly. If you feeling silly stops you from being in the matrix, then that is a case of magical thinking.
Your feelings doesn't decide the metaphysical, ontological and epistemological status of the "real world". That line of feeling is no different than a religious person, who feels it is silly to consider that there is no God.

Polymath257, stop doing philosophy.
 

mikkel_the_dane

My own religion
... The OP ...

Take 3:
It is possible to as consistent internally, with completeness AND(logically consistent) in a strong sense(not tautological) to make a model, that matches the map?
That is testable.
Someone: There is for all of the observations from the map one model and only one as described above, which matches the map.
Me: No!
Someone: That is a contradiction.
Me: No! It is an over-reduction, which don't take into account the classical second law of thought as for the world and not just abstract logic. The non-contradiction law for the world is that something can't for the same time, place and property/sense have another property, which is different as opposite to the first property, but that doesn't rule out that something else at another time and place can have a different as opposite property.

That is it. It is that simple and that is the limit of logic and the world.
You can't make as consistent internally, with completeness AND(logically consistent) in a strong sense (not tautological) a model of all of the world, because I can in effect do it differently.
In philosophy, that is the limit of the coherence theory of truth in the strong sense. That is what you are doing.
You are not the only human, how have considered, what logic is.

So here it is for humans in general as common: There is a limit to human mobility apparently. E.g. no human on earth can fly solely by the use of their individual bodies. That doesn't mean that mobility is impossible. It means that it is limited, but not impossible.
It is the same for human behavior, when it comes to the use of reason, logic/proof, objectivity, evidence, knowledge and so on.

The joke with your natural model, is that we, naked apes, are so fond of our big brains, what we believe, we can make sense of all of the world. But that is not, how biology works. The replication of the fittest gene don't "test" for making sense of all of the world. For us as a sexual reproducing life form, it "tests" for the 4 Fs relative to our biological niche. It doesn't test for and it can't test for making sense of all the world.

Your idea is no different than the idea of God. You can believe in it, but you can't show, that it works for all of the world.
I don't believe in the truth for all of the world, so I am a non-believer, yet I am a believer in God, because that works of me as me. And, yes, I can't show that as for all of the world, but neither can you do that with the truth.
The difference is, that you believe, it works for an universal "we". It doesn't!!! I know that for both of our positions, yet you judge me by a standard, that you yourself can't achieve. That has a name. It is called inconsistent.

Welcome to the big league of the really big words.
I never win nor do I loose. I always make it a draw. We are both humans with warts and all. We just consider that differently, because you believe your warts are "better" than me. They are not nor are they worse. They are different and as long as you "play for a win", I play for a draw. I don't hold Objective Authority with the Truth over other humans. Nor do you and your "we", but as longs as you in effect claim that, I "fight" you to achieve a draw.
We are all equal as being different parts of the world and we share similarities, but we are not the same with logic as above, so as long as you in effect, claim you be able to do something, which you in effect do differently than you claim, I "fight" you.
We are both believers and non-believers. We just do it differently.

In effect, stop claiming logic for all of the world. I just answer "No!".
 

Ponder This

Well-Known Member
Well, in that case, I would consider the phenomenon to be natural (since there is a well-defined statement that describes it) and no assumption about a supernatural is required.

The point here is that *both* directions are equally consistent (in this case, since we are assuming standard axioms, this means consistent with observations and descriptive of those observations): both the assumption and the negation of that assumption. And the question is which to choose to assume: the statement or its negation.

What you mean by the use of the word "supernatural" in this context is unclear. Perhaps you should clarify what you mean.
But more to the point, since you don't have a well-defined statement... how can you add either it or its negation as an axiom? Does it make sense to have an ill-defined axiom? What does your question even mean when you ask about assuming either an ill-defined statement or its negation? What is the negation of an ill-defined statement? How can we make sense of this?
 

Polymath257

Think & Care
Staff member
Premium Member
What you mean by the use of the word "supernatural" in this context is unclear. Perhaps you should clarify what you mean.
But more to the point, since you don't have a well-defined statement... how can you add either it or its negation as an axiom? Does it make sense to have an ill-defined axiom? What does your question even mean when you ask about assuming either an ill-defined statement or its negation? What is the negation of an ill-defined statement? How can we make sense of this?

How about 'something that exists that cannot be detected by the procedures of science'.
 

mikkel_the_dane

My own religion
How about 'something that exists that cannot be detected by the procedures of science'.

That would be your sentence in part 'something that exists that cannot be detected by the procedures of science'. That is a mental construct and can't be detected by science. You can show correlation, but you can't use science on the sentence as such. It is not a case of objective empirical observation.

Science has limits: A few things that science does not do

There seems to be a lot of that around.
Good and bad, useful, beauty and metaphysics in part.

Stop doing philosophy of science. It is not that simple and logical positivism and its variants don't work in practice.
As for existence the jury is still out on that one: Existence (Stanford Encyclopedia of Philosophy)
A related question is if all individuals are material/physical? I just have to answer "No!" and we are inside the mental and not the physical. :) The same in part with the smile. And this one: ;)
 
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