- Limits in Logic According to Modern Science
- Views of Logic in Islamic History
- Limits In Logic According to Sufis
- The Sufi Way Forward
Limits in Logic According to Modern Science
As I understand, there were intense discussions among some bright Mathematicians in the first half of the 20th century. There were serious efforts aiming to reach to a solid ground for Mathematics and Logic. But maybe Reality is actually different from what many of us think how "it should be", based on "what appears to us".
Looking at the history of Science, there were many occasions when there were grand and optimistic visions that aimed for something, and not finding it, yet the effort led instead to some fantastic ideas that turned out to be good things benefiting mankind.
It might have been disappointing for some, to find out that man and his knowledge can never be perfect. Yet, it appears that the door to computing and computers was open, as a secondary result of finding out that there are limits in man’s grasp of mathematics. (I think some of Gregory Chaitin’s lectures can be referred to in this regard).
Stephen Hawking wrote an article in 2004 titled “Godel and the end of Physics”. He explains that he used to be among the group that would be disappointed if a final view in Physics is not reached. But, he ended the article by expressing his satisfaction because research and developments in Physics will not stop, just like developments in Mathematics will not end either (because neither will reach a status that can be described as perfect or final or exact). He mentioned that it might be because man and his models are part of the universe man tries to describe, so there is always the self-reference factor in the models, resulting in incomplete and inconsistent models, which – as he noted - is what physicists have at the moment.
Among all the fields of modern science, Physics appears to be the most admired, especially when the achievements on the ground are witnessed. At the same time, it is the most tightly coupled with Mathematics (some major contributions to mathematics were the result of an effort to have suitable mathematical tools to deal with physical phenomena). If neither can be perfect, the situation is very likely to be further away from perfection, in other scientific fields.
As I understand, the problem at the bottom is as follows:
When one needs to build a house, one brings a "solid", "self-evident", "self-explaining" "brick" and put it next to another one to build a wall.
In Mathematics, at the bottom, it appears that there are some missing self-evident, self-explaining rock-solid blocks to base the whole body of mathematics on. To cover the gaps, assumptions are used. It seems that there is a need for a viewer’s arbitrary assumptions to get what a viewer would feel is an acceptable and consistent picture of "what appears out there".
I guess the same can be said for every single field of modern science. Even in Physics, where at the bottom, there is still no such thing as “a solid self-evident, self-explaining brick”. At the subatomic particles’ level, there are no notions of next, before, up, down, left, right, etc. It makes me wonder if ‘concreteness’ has or will ever have any meaning at all, based on what I have understood about views of modern logic and modern physics.
Ok, that's what I understand about the modern scientific view. Let's shift now to what I think I understand about the religious view, and start with a simple idea that Existence is one and the same for all, regardless of the angle anyone might select to view it from. So, what are the traditional Islamic views of Logic? And, are there any specific points to compare with the modern view ?
Views of Logic in Islamic History
The first opinion was that of a group of scholars who tried to distance the public from Logic. When Greek writings were translated into Arabic, writings on logic were linked with other subjects of Greek origin including the metaphysics, which was considered incompatible with the teachings of Islam. So, there was a reprehensive attitude from some scholars towards anything that had ‘any link’ to Greek metaphysics. This group expressed it's view that logic was unnecessary and actually “it is useless.”
What I feel is very interesting is that among this group there were some scholars who detected some shortcomings in the basic forms of the syllogism. However, they used their discovery to show the lack of perfection in Logic, and to support their position regarding Logic by showing that ‘it should not be blindly trusted’.
The second opinion, which, as I understand, was the most prevalent in Islamic history, was that of Kalam scholars. They were quick to distinguish between Greek metaphysics, which they also criticized, and Logic as an abstract instrument that can be used in many useful ways. Kalam scholars described Logic as being ‘a mechanism that prevents the intellect from committing a mistake.’ What I understand is that they viewed Logic as something perfect.
The pillars of Islam start with bearing witness that there is no god but Allah (SWT) and that Prophet Muhammad (PBUH) is Allah’s Messenger. This is the subject of the ‘first root of religion’ which is establishing the elements of faith. The rest of the pillars, which are daily Prayers, Fasting, Haj, Zakat, are covered within the ‘second root of religion’ which is Islamic Jurisprudence or Fiqh or Shariah, which is based on formal methods called ‘Usool Al-Fiqh’, which utilises Logic. From the beginning of Islam the pillars were understood, but what came as something new, starting from the second Islamic century, was the ‘presentation’ of the roots using a formal logical framework. This effort gradually gained wide acceptance. The first group of scholars, mentioned above, stayed clear of such efforts, but it appears that later generations of scholars from that group found themselves benefitting from efforts in the second root, based on Usool Al-Fiqh. As for Kalam proper (logical efforts regarding the first root), it was rejected by the first group.
The third opinion, representing the Sufi view, was as far as I understand, not one that can be described as a strictly black-or-white. It might be best presented noting the position of a major scholar like Imam Abu Hamid Al-Ghazali. He was an expert in Kalam and Usool Al-Fiqh. His book, Al-Mustasfa (which was one of the last books he wrote), is a classic in that field and widely accepted, even today. In the introduction of the book he clearly mentions that “anyone who is not competent in Logic, his knowledge cannot be trusted.” Yet, Abu Hamid was a Sufi too, and in his books like Al-Ehya and Al-Munkidh, he did not hide his dislike regarding rational approaches when used in dealing with deep religious concepts. In page 99 of Al-Ehya, he said:
"It might be thought that its [Kalam] benefit is in revealing truths and knowing [things] as they are, but it is not so... Listen to someone [himself] who has known Kalam and examined it thoroughly as far as Kalam can take one, then [probably after seeing limits of Kalam] considered similar/related [rational] fields of knowledge [most likely Greek philosophy], and became certain that the road to truths of knowledge, from that direction [rational thinking] is blocked."
Then in page 101, he continued:
"To reveal truths and know things as they are, and to realize the secrets behind the outer meanings of the words of this Aqeedah [his list of elements of faith], there is no other key [to open the door] than working hard, curbing cravings, and totally directing one's attention towards God, Most High, and keeping one's mind pure from stains of arguments [logical discourse]."
It might seem contradictory to see the same person having two different opinions about Logic. However, it should be noted that there were actually two different contexts.
In any legal system there are basic principles based on which different sets of rules and guidelines are presented, and there is an organized method of how to go from the basics to particular cases and how to deal with unprecedented cases and how to reach new rules that are consistent with the principles and well-connected with the whole system. It is basically a huge ‘organized intellectual effort’ that spans generations. Such an effort can obviously benefit from using Logic. That is true for any legal system and it is true for Islamic Shari’ah. Imam Al-Ghazali mentioned his opinion in the introduction of a sort of a textbook about the methods used in Islamic Law, and he simply was saying to students: “You need to have a good grip on Logic to be successful in this field.” This field happens to be within what is traditionally known as the second root of Religion.
The second Sufi opinion about Logic was not with regards to an introductory level but ‘an advanced level’ of dealing with subjects within the first root of Religion: Belief in God and His Messenger. At the introductory level in this particular area, there is still a ‘need to present’ basic information in an accessible manner to a vast number of people from various backgrounds. Logic can still be useful here. However, the subject matter here is more subtle and delicate and requires more care in phrasing. Imam Al-Ghazali wrote books on Logic and Kalam (the rational approach to deal with deep religious concepts.) Even in his latest works on Sufism he did not totally dismiss using rational approaches in religion. But he certainly gave hints that an intellectual effort is not enough in this field, even at the basic level, as it is clear in the list of elements of faith (please see “Imam Al-Ghazali’s Aqeedah”, Comment No. 2, for details), aimed at the general public. At higher levels of considering such concepts he was specific and clearly laid out his view, and that’s the context within which his second opinion on Logic is mentioned.
Limits In Logic According to Sufis
Is Logic about some ‘laws’ that are absolute, totally perfect, and transcend time and space? Or is Logic part of man’s perception of existence, a perception that is never perfect or absolutely objective, a perception that can evolve and improve introducing improvements in many aspects of man’s knowledge, including Logic?
Logic used to be, basically about certain fixed syllogistic forms, it is now evolved into full languages with great benefits to mankind. So, it does not seem to be something fixed and final. It still may evolve and improve even more.
Hawking used an interesting and simple language when he talked about how man and his models are part of the universe man tries to describe, so there is always the self-reference factor in the models. And if man’s models include models about logic too, then such models can never be perfect, because of the inherent self-reference problem.
Kalam scholars assert that time and space were created with the universe. Modern physicists seem to agree, and add that laws of physics came into existence with time and space, and they talk about a point where there were no laws of physics. Such laws are of course abstract and immaterial, similar perhaps to how one would view logical formulations: abstract and immaterial ? But, I am not aware of any modern view of Logic in particular that is similar to how laws of physics are viewed.
As for Sufis, Ibn Ata-Ellah says in his prayer (addressing God): “How can your existence be proven using something that needs you for its very existence?”. His comment appears to have been about Logic and logical proofs of God’s existence. It appears that he was talking about Logic as something 'created' / 'within creation'.
So, Logic appears to be prone to change and evolvement just like any field of human intellectual endeavor, and as such, it might be considered part of man’s models (suffering from the self-referencing problem), and part of creation (that was nothing then came into existence). If this background of Logic is accepted, then maybe it is difficult to describe Logic as perfect or that it can ever be perfect.
Is that a bad thing? For many who were so sure of a solid bottom on which Logic stands, it might have been disappointing to realize that there is no solid bottom. But, maybe understanding reality better, or "as it is", is never a bad thing.
As for Sufis, it is interesting to note how they distinguish between levels of awareness man can experience (Details about the Sufi view of awareness levels: Hekam #67). The level of being aware of logical means and being adept at using them is acknowledged, but it is not seen as the highest that man can reach. Logic is important and it is a valuable asset, but for certain uses.
Imam Al-Ghazali, as knowledgeable as he was, in his time, regarding rational approaches, described in Al-Munkidh a stage of awareness about which it is not possible to express oneself without making a clear and unavoidable error (in expressed words.) Ibn Arabi talked about a level of awareness that is reached, only ‘when Logic breaks’. (Further notes regarding the Sufi view about limits of Logic: Hekam #42 also #46 on the same page.)
The Sufi Way Forward
Logic is a valuable achievement, and it is immensely useful. There is no doubt about that. But, that does not have to mean that it is perfect.
Most people probably might never see or care about the limits of logic, but there are those who see it. Among those few, some might select to view such limits as something to acknowledge, and then just continue with normal life. As for Sufis, reaching that stage seems like just a beginning of a new level of awareness. It is not a wall to stop at and return back. It is an entrance to go through, and continue forward.
Knowing that logic has limits does not have to mean that there are no guidelines further ahead. It is just that there are different approaches and different preparations and different guidelines more suitable for each stage.
When one is young, usually sensuous issues are dominant in ‘one’s mind’ and they might even make rational guidelines seem less attractive. Then, one eventually grows up and realizes that it is beneficial to keep sensuous issues within appropriate limits. That’s when rational guidelines are visible and maybe even dominant in ‘one’s mind’. But is there a stage one can reach when even rational guidelines would be subject to further considerations about ‘appropriate use’? As I understand, Sufis say yes. Hence, even with their mastership of Logic as normally known, there are many consistent notes about the limits of logic, and warnings about using Logical rules at levels of awareness that Logic just was not designed to cope with. It is first-hand experience, or taste (Dhauq) as Sufis call it, that is there instead. It is pure pristine ‘sight’, that fills ‘one’s mind’, untainted by mental thoughts, and leaving no room for such thoughts in the mind, that is the means of acquiring knowledge at levels when language and logic do not appear to be of much help. Plenty of notes in this regard in Sufi literature.
It might have been disappointing for some, to find out that man and his knowledge can never be perfect. Yet, it appears that the door to computing and computers was open, as a secondary result of finding out that there are limits in man’s grasp of mathematics. (I think some of Gregory Chaitin’s lectures can be referred to in this regard).
Stephen Hawking wrote an article in 2004 titled “Godel and the end of Physics”. He explains that he used to be among the group that would be disappointed if a final view in Physics is not reached. But, he ended the article by expressing his satisfaction because research and developments in Physics will not stop, just like developments in Mathematics will not end either (because neither will reach a status that can be described as perfect or final or exact). He mentioned that it might be because man and his models are part of the universe man tries to describe, so there is always the self-reference factor in the models, resulting in incomplete and inconsistent models, which – as he noted - is what physicists have at the moment.
Among all the fields of modern science, Physics appears to be the most admired, especially when the achievements on the ground are witnessed. At the same time, it is the most tightly coupled with Mathematics (some major contributions to mathematics were the result of an effort to have suitable mathematical tools to deal with physical phenomena). If neither can be perfect, the situation is very likely to be further away from perfection, in other scientific fields.
As I understand, the problem at the bottom is as follows:
When one needs to build a house, one brings a "solid", "self-evident", "self-explaining" "brick" and put it next to another one to build a wall.
In Mathematics, at the bottom, it appears that there are some missing self-evident, self-explaining rock-solid blocks to base the whole body of mathematics on. To cover the gaps, assumptions are used. It seems that there is a need for a viewer’s arbitrary assumptions to get what a viewer would feel is an acceptable and consistent picture of "what appears out there".
I guess the same can be said for every single field of modern science. Even in Physics, where at the bottom, there is still no such thing as “a solid self-evident, self-explaining brick”. At the subatomic particles’ level, there are no notions of next, before, up, down, left, right, etc. It makes me wonder if ‘concreteness’ has or will ever have any meaning at all, based on what I have understood about views of modern logic and modern physics.
It's not uncommon to have a strong feeling about exactness and perfection. But sometimes, it seems that no matter how much one tries, a goal may appear to be just a mirage; the harder the attempts to reach it, the more it is realized to be unattainable. Sometimes I get the feeling that the goal of making science exact will remain just a dream about a perfect ideal world. But I think it is healthy to have such dreams. And perhaps it is worth noting why do we have such an affinity for perfection, or rather, why do we always sense the existence of perfection, even if we can not find a way to touch it or have a firm grip on it.
Ok, that's what I understand about the modern scientific view. Let's shift now to what I think I understand about the religious view, and start with a simple idea that Existence is one and the same for all, regardless of the angle anyone might select to view it from. So, what are the traditional Islamic views of Logic? And, are there any specific points to compare with the modern view ?
Views of Logic in Islamic History
The first opinion was that of a group of scholars who tried to distance the public from Logic. When Greek writings were translated into Arabic, writings on logic were linked with other subjects of Greek origin including the metaphysics, which was considered incompatible with the teachings of Islam. So, there was a reprehensive attitude from some scholars towards anything that had ‘any link’ to Greek metaphysics. This group expressed it's view that logic was unnecessary and actually “it is useless.”
What I feel is very interesting is that among this group there were some scholars who detected some shortcomings in the basic forms of the syllogism. However, they used their discovery to show the lack of perfection in Logic, and to support their position regarding Logic by showing that ‘it should not be blindly trusted’.
The second opinion, which, as I understand, was the most prevalent in Islamic history, was that of Kalam scholars. They were quick to distinguish between Greek metaphysics, which they also criticized, and Logic as an abstract instrument that can be used in many useful ways. Kalam scholars described Logic as being ‘a mechanism that prevents the intellect from committing a mistake.’ What I understand is that they viewed Logic as something perfect.
The pillars of Islam start with bearing witness that there is no god but Allah (SWT) and that Prophet Muhammad (PBUH) is Allah’s Messenger. This is the subject of the ‘first root of religion’ which is establishing the elements of faith. The rest of the pillars, which are daily Prayers, Fasting, Haj, Zakat, are covered within the ‘second root of religion’ which is Islamic Jurisprudence or Fiqh or Shariah, which is based on formal methods called ‘Usool Al-Fiqh’, which utilises Logic. From the beginning of Islam the pillars were understood, but what came as something new, starting from the second Islamic century, was the ‘presentation’ of the roots using a formal logical framework. This effort gradually gained wide acceptance. The first group of scholars, mentioned above, stayed clear of such efforts, but it appears that later generations of scholars from that group found themselves benefitting from efforts in the second root, based on Usool Al-Fiqh. As for Kalam proper (logical efforts regarding the first root), it was rejected by the first group.
The third opinion, representing the Sufi view, was as far as I understand, not one that can be described as a strictly black-or-white. It might be best presented noting the position of a major scholar like Imam Abu Hamid Al-Ghazali. He was an expert in Kalam and Usool Al-Fiqh. His book, Al-Mustasfa (which was one of the last books he wrote), is a classic in that field and widely accepted, even today. In the introduction of the book he clearly mentions that “anyone who is not competent in Logic, his knowledge cannot be trusted.” Yet, Abu Hamid was a Sufi too, and in his books like Al-Ehya and Al-Munkidh, he did not hide his dislike regarding rational approaches when used in dealing with deep religious concepts. In page 99 of Al-Ehya, he said:
"It might be thought that its [Kalam] benefit is in revealing truths and knowing [things] as they are, but it is not so... Listen to someone [himself] who has known Kalam and examined it thoroughly as far as Kalam can take one, then [probably after seeing limits of Kalam] considered similar/related [rational] fields of knowledge [most likely Greek philosophy], and became certain that the road to truths of knowledge, from that direction [rational thinking] is blocked."
Then in page 101, he continued:
"To reveal truths and know things as they are, and to realize the secrets behind the outer meanings of the words of this Aqeedah [his list of elements of faith], there is no other key [to open the door] than working hard, curbing cravings, and totally directing one's attention towards God, Most High, and keeping one's mind pure from stains of arguments [logical discourse]."
It might seem contradictory to see the same person having two different opinions about Logic. However, it should be noted that there were actually two different contexts.
In any legal system there are basic principles based on which different sets of rules and guidelines are presented, and there is an organized method of how to go from the basics to particular cases and how to deal with unprecedented cases and how to reach new rules that are consistent with the principles and well-connected with the whole system. It is basically a huge ‘organized intellectual effort’ that spans generations. Such an effort can obviously benefit from using Logic. That is true for any legal system and it is true for Islamic Shari’ah. Imam Al-Ghazali mentioned his opinion in the introduction of a sort of a textbook about the methods used in Islamic Law, and he simply was saying to students: “You need to have a good grip on Logic to be successful in this field.” This field happens to be within what is traditionally known as the second root of Religion.
The second Sufi opinion about Logic was not with regards to an introductory level but ‘an advanced level’ of dealing with subjects within the first root of Religion: Belief in God and His Messenger. At the introductory level in this particular area, there is still a ‘need to present’ basic information in an accessible manner to a vast number of people from various backgrounds. Logic can still be useful here. However, the subject matter here is more subtle and delicate and requires more care in phrasing. Imam Al-Ghazali wrote books on Logic and Kalam (the rational approach to deal with deep religious concepts.) Even in his latest works on Sufism he did not totally dismiss using rational approaches in religion. But he certainly gave hints that an intellectual effort is not enough in this field, even at the basic level, as it is clear in the list of elements of faith (please see “Imam Al-Ghazali’s Aqeedah”, Comment No. 2, for details), aimed at the general public. At higher levels of considering such concepts he was specific and clearly laid out his view, and that’s the context within which his second opinion on Logic is mentioned.
Limits In Logic According to Sufis
Is Logic about some ‘laws’ that are absolute, totally perfect, and transcend time and space? Or is Logic part of man’s perception of existence, a perception that is never perfect or absolutely objective, a perception that can evolve and improve introducing improvements in many aspects of man’s knowledge, including Logic?
Logic used to be, basically about certain fixed syllogistic forms, it is now evolved into full languages with great benefits to mankind. So, it does not seem to be something fixed and final. It still may evolve and improve even more.
Hawking used an interesting and simple language when he talked about how man and his models are part of the universe man tries to describe, so there is always the self-reference factor in the models. And if man’s models include models about logic too, then such models can never be perfect, because of the inherent self-reference problem.
Kalam scholars assert that time and space were created with the universe. Modern physicists seem to agree, and add that laws of physics came into existence with time and space, and they talk about a point where there were no laws of physics. Such laws are of course abstract and immaterial, similar perhaps to how one would view logical formulations: abstract and immaterial ? But, I am not aware of any modern view of Logic in particular that is similar to how laws of physics are viewed.
As for Sufis, Ibn Ata-Ellah says in his prayer (addressing God): “How can your existence be proven using something that needs you for its very existence?”. His comment appears to have been about Logic and logical proofs of God’s existence. It appears that he was talking about Logic as something 'created' / 'within creation'.
So, Logic appears to be prone to change and evolvement just like any field of human intellectual endeavor, and as such, it might be considered part of man’s models (suffering from the self-referencing problem), and part of creation (that was nothing then came into existence). If this background of Logic is accepted, then maybe it is difficult to describe Logic as perfect or that it can ever be perfect.
Is that a bad thing? For many who were so sure of a solid bottom on which Logic stands, it might have been disappointing to realize that there is no solid bottom. But, maybe understanding reality better, or "as it is", is never a bad thing.
As for Sufis, it is interesting to note how they distinguish between levels of awareness man can experience (Details about the Sufi view of awareness levels: Hekam #67). The level of being aware of logical means and being adept at using them is acknowledged, but it is not seen as the highest that man can reach. Logic is important and it is a valuable asset, but for certain uses.
Imam Al-Ghazali, as knowledgeable as he was, in his time, regarding rational approaches, described in Al-Munkidh a stage of awareness about which it is not possible to express oneself without making a clear and unavoidable error (in expressed words.) Ibn Arabi talked about a level of awareness that is reached, only ‘when Logic breaks’. (Further notes regarding the Sufi view about limits of Logic: Hekam #42 also #46 on the same page.)
The Sufi Way Forward
Logic is a valuable achievement, and it is immensely useful. There is no doubt about that. But, that does not have to mean that it is perfect.
Most people probably might never see or care about the limits of logic, but there are those who see it. Among those few, some might select to view such limits as something to acknowledge, and then just continue with normal life. As for Sufis, reaching that stage seems like just a beginning of a new level of awareness. It is not a wall to stop at and return back. It is an entrance to go through, and continue forward.
Knowing that logic has limits does not have to mean that there are no guidelines further ahead. It is just that there are different approaches and different preparations and different guidelines more suitable for each stage.
When one is young, usually sensuous issues are dominant in ‘one’s mind’ and they might even make rational guidelines seem less attractive. Then, one eventually grows up and realizes that it is beneficial to keep sensuous issues within appropriate limits. That’s when rational guidelines are visible and maybe even dominant in ‘one’s mind’. But is there a stage one can reach when even rational guidelines would be subject to further considerations about ‘appropriate use’? As I understand, Sufis say yes. Hence, even with their mastership of Logic as normally known, there are many consistent notes about the limits of logic, and warnings about using Logical rules at levels of awareness that Logic just was not designed to cope with. It is first-hand experience, or taste (Dhauq) as Sufis call it, that is there instead. It is pure pristine ‘sight’, that fills ‘one’s mind’, untainted by mental thoughts, and leaving no room for such thoughts in the mind, that is the means of acquiring knowledge at levels when language and logic do not appear to be of much help. Plenty of notes in this regard in Sufi literature.
