What should religion do for us today?

EricH

Once you say "transcendental", you are already outside the system itself. What does "transcendental" even mean within a formal system? — alcontali

I am trying to express myself - as much as possible - within your framework. Here is what you said a while back:

Religion also proclaims the transcendental origin of this system of rules, necessarily from outside its formal system of rules. — alcontali

I take this to mean that there are axioms outside the formal system of Islamic Law upon which the laws are based - and that these axioms come from Allah. Am I getting this correct - or am I at least close?

BTW - in your response it's not necessary to cite any scripture - I'm a plain language person - I trust that your explanations are correct. :smile:

Gregory

↪alcontali

Maybe Allah doesn't want us to look for signs, since he doesn't a priori let us know what signs to look for. A great civilization might look great, but as with the "who is smart" question you bring up, intelligence has much to do with how happy you make yourself and others. There is a lot of factors that go into smartness. Just because Islam has the track record of generation after generation keeping the Koran pure, that doesn't mean it's the right religion. Rome so far hasn't proven it doesn't have infallible authority all these years, which could happen by dogmatic contradictions. If you were one who is open to actual miracle claims as proof of divine favor, Christianity has a pretty good case, and Catholicism too after you become a general Christian

alcontali

I take this to mean that there are axioms outside the formal system of Islamic Law upon which the laws are based - and that these axioms come from Allah. Am I getting this correct - or am I at least close? — EricH

Yes, I guess that this is probably quite correct.

It is a bit a similar situation to what you see in mathematics.

There is no justification whatsoever for the axioms of number theory or set theory from within these theories. However, you will still find serious attempts at justification from within the philosophy of mathematics for its ontology.

These ontological considerations are never considered part of mathematics proper. They are not even considered part of metamathematics (which intriguingly, is part of mathematics proper).

The relationship between religious law (formal system) and the transcendental areas in religion (informal views) is the same as between mathematics (formal system) and the ontological philosophy of mathematics (informal views).

It rejoins the general case that at the highest level of understanding there are no formal systems and there are no formal justifications.

According to Islamic theology, human beings are born with an innate inclination of tawhid (Oneness). — Fitrah in the ontology of Islam

mathematics is an exercise of the human intuition, not a game played with meaningless symbols. — Intuitionism in the ontology of mathematics

Still, "the origins of X" debate can easily confuse the matter. That is why I try to avoid it. There is not one, single opinion at that level of understanding.

I simply prefer to work with the formal systems themselves. I am particularly attracted to the mechanical verification of theorems within these formal systems by using the Coq proof assistant.

Athena

↪Michael Lee

What should religion do for us today? Mythology is essential for transmitting cultural knowledge and transitioning youth to adulthood.

The problem with mythology comes with interpreting it concretely instead of abstractly.

Athena

↪alcontali

Wow I am very impressed by your explanation! Comparing religious thoughts and arguments with mathematical thoughts and arguments is consciousness expanding. That is beautiful.

Michael Lee

↪Athena

Dear child of Zeus, mathematics is the greatest knowledge we have.

Athena

↪Michael Lee

I agree about the importance of math. Unfortunately, the video is blocked where I live because of copyright issues. However, I have several videos on math and a few books. Not that my brain can do higher math, but the explanations of math get my attention.

Michael Lee

↪Athena

Pythagoras thought number is the primary substance and I do not agree with him. Being, as described by Parmenides, is the primary substance. My father would always scold me because he thought I wasn't understanding basic arithmetic when I was only four years old and couldn't do so at that age because my mind wasn't prepared for it.

EricH

mathematics is an exercise of the human intuition, not a game played with meaningless symbols. — Intuitionism in the ontology of mathematics

According to Islamic theology, human beings are born with an innate inclination of tawhid (Oneness). — Fitrah in the ontology of Islam — alcontali

Belated response here. I think I'm following this - Fitrah is an axiom.

So next question. How do we go from this axiom all the way to the numerous laws that regulate our behavior to one another? I understand how this works in math. How does it work in Islam? E.g., how does Islam derive the laws governing marital relations from Fitrah? Are there extra axioms and/or steps involved?

alcontali

Fitrah is an axiom. — EricH

No, it is a philosophical explanation for why we adopt axioms. It is not an axiom itself.

EricH

↪alcontali

OK, fair enough. Can you give me a few axioms - in plain language if possible? :smile:

If there is a more comprehensive list available - again with plain language explanations if available - you can give me a link to check out.

alcontali

Can you give me a few axioms - in plain language if possible? :smile:

If there is a more comprehensive list available - again with plain language explanations if available - you can give me a link to check out. — EricH

In mathematics it is relatively easy to find the basic rules of a theory structured as axioms. The following are the dominant axiomatizations in mathematics:

There are many more. The following is the dominant axiomatization of logic:

Axioms of propositional logic

The axiomatization of logic gives the basic rules for the standard formal language used by the other mathematical axiomatizations (There are other formal languages possible). Hence the quite special status of logic in mathematics and in other axiomatic disciplines. The standard formal language in mathematics is first-order logic.

You can find lots of examples of various axioms in these three standard axiomatizations. Simple example of an axiom:

5 + 3 = 3 + 5

You can swap the order of operands in a sum. Generally:

a + b = b + a, for any a,b being a natural number.

Standard number theory will define what the term "natural number" means, up to final interpretation by an actual natural-number model. A model is also called: an interpretation, a universe, or a world.

The standard model of natural numbers is a regular language such as for example:

$\Bbb{N}$ = 0 | [1-9] [0-9] *

along with the symbols (+, x).

You can pick any number of arbitrary, distinct symbols $(α_0, ..., α_n)$ , two or more, in order to define a collection of strings that represent the natural numbers:

$\Bbb{N}$ = $α_0$ | [ $α_1$ - $α_n$ ] [ $α_1$ - $α_n$ ] *

along with two arbitrary, distinct symbols (⨁,⊗), that will satisfy the standard theory of natural numbers (PA).

If you get used to the terminology, it can be relatively easy to learn to think in terms of axioms. Outside mathematics, axiomatic systems are also possible but have never been seriously formalized. So, their nature may be clearly axiomatic but they do not use symbolic language to express themselves.

EricH

↪alcontali

Sorry - I wasn't clear. What I'm looking for is some axioms of Islam.

alcontali

Sorry - I wasn't clear. What I'm looking for is some axioms of Islam. — EricH

Every verse in the Quran.

(https://quran.com)

EricH

↪alcontali

I may be misunderstanding you (or there may simply be gaps in my knowledge of Islam), but from where I'm sitting there seems to be a contradiction in your writing.

Here's what you said in a response to @Nobeernolife:

You see, Islamic law is a complete formal system with rules concerning morality. — alcontali

However, in your last reply to me, you stated that the Quran - and presumably all the laws therein - consists only of axioms. I think you would agree with me that a list of axioms does not constitute a formal system.

Are there an additional set of laws in Islam that are derived from the Quran? Perhaps analogous to the Talmud?

alcontali

I think you would agree with me that a list of axioms does not constitute a formal system. — EricH

No, it does.

A formal system is a list of axioms.

Such formal system is always augmented with a choice of logic system, which is by default first-order logic.

A formal system is used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system".[1] In 1921, David Hilbert proposed to use such system as the foundation for the knowledge in mathematics.[2] A formal system may represent a well-defined system of abstract thought. — Wikipedia on the term formal system

Since the choice of logic is pretty much always the same, it is often not even mentioned.

In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems.[1] — Wikipedia on axiomatic system

In Islam, the Quran is a set of axioms while religious law ("al fiqh") is the (axiomatic) theory that emerges from the Quran. The Sunnah is considered to be already a set of theorems derived from the Quran and its use is therefore limited to a clarifying role.

Nobeernolife

In Islam, the Quran is a set of axioms — alcontali

A pretty strange axiomic system seeing how many times it contradicts itself (check the difference between Meccanic and Medinaic verses). Go on alcantali!

alcontali

check the difference between Meccanic and Medinaic verses — Nobeernolife

The difference between you and me, is that I know that I have no specialized knowledge in this area, while you are clearly too arrogant to understand your own limitations. I am also not going to try to find and invite a religious scholar to clarify such details and point out what documentation to peruse because you are not polite enough either. It is just going to embarrass everyone involved, except for you, because you could obviously never feel embarrassed.

christian2017

.

christian2017

A pretty strange axiomic system seeing how many times it contradicts itself (check the difference between Meccanic and Medinaic verses). Go on alcantali! — Nobeernolife

I actually see alot of similarities between the way the Koran was written and the book of Mormon. It almost appears they have the same author. However for various reasons i do see most Mormons as actual christians.

EricH

My responses are likely to be slow in coming - real life is taking up most of my time these days. I can maybe squeeze in a half hour here or there.

A formal system is a list of axioms.
Such formal system is always augmented with a choice of logic system, which is by default first-order logic. — alcontali

I could quibble with you over the definition of a formal system. Is a list of axioms by itself without a mechanism to generate theorems a formal system? I'm not qualified to answer that question, but if I had to maker a guess I'd say no.

Meanwhile, I'll continue to attempt to work within your definitional framework. Let me echo back in my own words what I think you are saying:

1) The Quran contains the axioms of Islam. These are transcendental in origin (your words) and not subject to question or dispute.
2) The Sunnah contains the theorems. These theorems are derived from the Quran, but they also rely on the Hadith for supporting evidence.
3) Finally, there is Fiqh which - quoting WIkipedia - "is human understanding of the divine Islamic law as revealed in the Quran and the Sunnah". So this is sort of the day to day interpretation of the Sunnah when the need arises to handle situations that cannot be easily decided by the Quran or the Sunnah.

There are multiple versions of both the Hadith & Sunnah and different denominations of Islam use certain versions and not others. Regarding the Fiqh (and again according the Wikipedia) there are "four prominent schools (madh'hab) of fiqh within Sunni practice, plus two (or three) within Shi'a practice."

I know you are deeply suspicious of organized schools of thought (since they typically become politicized) and consider yourself to be ghair-madhhabi - so no need to re-state that :smile: .

At this point in the conversation I just need to know if my understanding is reasonably close for an outside observer.

alcontali

I could quibble with you over the definition of a formal system. Is a list of axioms by itself without a mechanism to generate theorems a formal system? I'm not qualified to answer that question, but if I had to maker a guess I'd say no. — EricH

The mechanism to generate theorems from axioms is the system of logic:

assert Syllogism {
  all Socrates: univ, Man, Mortal: set univ |
      -- every man is mortal
      Man in Mortal
      -- Socrates is a man
      and (Socrates in Man)
      -- implies Socrates is mortal
      implies Socrates in Mortal
  }
check Syllogism

These theorems are derived from the Quran, but they also rely on the Hadith for supporting evidence. — EricH

Hadith and Sunnah are often used as synonyms for each other.

I have looked it up in Quora, but apparently that view is considered not to be completely correct.

Hadith are testimonies about the prophet's life in which he applies the Quran. So, the Hadith are mostly theorems. The Sunnah, however, are practices transmitted from Mosaic Judaism mentioned in the Hadith. Therefore, part of the Sunnah are also considered to be axioms.

Hence, there is some justification to accept the view that the Hadith is often the 'vehicle' which conveys information about the 'Sunna'. ... There is a fundamental difference between the Hadith and Sunna and though often used synonymously, should be kept distinct. ... — Difference between Hadith and Sunna

But then again, the Quran mentions all axioms already, even when they were transmitted from Mosaic Judaism:

It is clear that the Quran does not support any type of 'Sunna' that does not find sanction from the Quran. — Difference between Hadith and Sunna

That is how we arrive at the simplifying view that the Quran are the axioms while (some of) the Hadith are clarifying, derived rules as applied to practical situations, i.e. theorems.

EricH

↪alcontali

OK. We are saying that in some sense Islamic law is a formal system. However, I think you would agree that it is not a formal system in the same sense as in math. I did a quick search and pulled out this from a different thread:

Mathematics is pure symbol manipulation, i.e. language expressions. It does not take any sensory input. Therefore, it is pure reason. — alcontali

This seems accurate to me. So when we say that Islamic law is a formal system it seems to me that we are making an analogy: Islamic law mirrors some /many of the attributes/behavior/qualities of a formal system. Your thoughts?

Athena

↪Nobeernolife

All truths can be found in the Bible. That means it also contradicts itself. The biggest contradiction is God is jealous, revengeful, fearsome and punishing, to God is loving and forgiving. Maybe He is bipolar? :lol:

Athena

↪alcontali
OK. We are saying that in some sense Islamic law is a formal system. However, I think you would agree that it is not a formal system in the same sense as in math. I did a quick search and pulled out this from a different thread:
Mathematics is pure symbol manipulation, i.e. language expressions. It does not take any sensory input. Therefore, it is pure reason.
— alcontali
This seems accurate to me. So when we say that Islamic law is a formal system it seems to me that we are making an analogy: Islamic law mirrors some /many of the attributes/behavior/qualities of a formal system. Your thoughts? — EricH

Wow, are we in favor of robots ruling because they would be pure reason without sensory input? If we are judging religions, I think it is very important to value sensory input. Not to do that would so be as cold as the extermination of Jews. Simply a practical decision. "This year bad weather destroyed the crops so we need to kill 5000 people so those who remain will have enough food and stay healthy".

alcontali

Islamic law mirrors some /many of the attributes/behavior/qualities of a formal system. Your thoughts? — EricH

It is possible to verify syllogisms from their premises, i.e. axioms, by using a tool like the Coq proof assistant:

assert Syllogism {
  all Socrates: univ, Man, Mortal: set univ |
      -- every man is mortal
      Man in Mortal
      -- Socrates is a man
      and (Socrates in Man)
      -- implies Socrates is mortal
      implies Socrates in Mortal
  }

check Syllogism

This approach requires encoding the Quran, as system-wide premises, in the formal language of Coq. It is an inordinate amount of work, but it should allow to operate a Quranic formal system for the mechanical verification of (a subset of) the existing knowledge database of religious advisories. Curating that enormous knowledge database is another massive task. In fact, for mathematics proper, this curation and encoding work has been completed only very partially. With enough budget, however, I feel that it could also be done for Islamic law and yield very interesting results.

Michael Lee

↪Athena

I am a so-called "bipolar" man, and I possess knowledge.

EricH

↪alcontali

So you would be mapping the text of the Quran into a set of symbols with no semantic content?

alcontali

So you would be mapping the text of the Quran into a set of symbols with no semantic content? — EricH

When you look at logic sentence such as:

Man in Mortal and (Socrates in Man) implies Socrates in Mortal

You can see that the conclusion is a syntactic entailment of its premises. The symbols actually themselves do not matter. It would also work perfectly-well like this:

x in k and (s in x) implies s in k

In the end, the reason why this syllogism entails is entirely structuralist:

Structuralism is a position holding that mathematical theories describe structures, and that mathematical objects are exhaustively defined by their places in such structures, consequently having no intrinsic properties. — Wikipedia on mathematical structuralism

That is because the symbols are "alpha-equivalent":

A basic form of equivalence, definable on lambda terms, is alpha equivalence. It captures the intuition that the particular choice of a bound variable, in an abstraction, does not (usually) matter. For instance, λx.x and λy.y are alpha-equivalent lambda terms, and they both represent the same function (the identity function). — Wikipedia on alpha equivalence (lambda calculus)

So, yes, actual semantic content does not matter in the context of syntactic entailment.

However, a system with large numbers of sentences written in the second, nondescript manner would be much harder to debug. Software is not just written for only the machine to read. It must also be suitable for other people to read, so that it can be troubleshooted and maintained.

Therefore, both a religious script representing a religious advisory as well as the Quranic base library are just like other software. On the one side, they are purely structuralist, but on the other side, they are also meant to communicate to other religious programmers what the otherwise alpha-equivalent symbols are all about.

Athena

↪Athena I am a so-called "bipolar" man, and I possess knowledge. — Michael Lee

Okay. My daughter says I am bipolar and that could be. But a bipolar god? I was joking when I suggested God is bipolar.

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