It was a fantastic read, but the underlying theme that I feel is relevant to this discussion is this:
Socratic philosophy treats logical axioms as “self-evident truths” (i.e. I think, therefore I am).
Mathematics treats logical axioms as “propositions”, and uses logic to see where those propositions lead (i.e. if you have a line and a point, the number/amount of lines that you can draw through the point that’s parallel to the original line determines what type of geometry you are working with (multidimensional, spherical, or flat-plane geometry)).
Scientists treat logical axioms as “hypotheses”, and logical “conclusions” as testable statements that can determine whether those axioms are true or not (i.e. if this weird system known as “quantum mechanics” were true, then we would see an interference pattern when shooting electrons through a screen with 2 slits).
So I guess the point that we should be making is this: which philosophical approach towards logic should we take to study ethics? I believe Wei_Lai would say that the first approach, treating ethical axioms as “self-evident truths” is problematic due to the fact that a lot of hypothetical situations (like my example before) can create a lot of contradictions between various ethical axioms (i.e. choosing between telling a lie and letting terrorists blow up the planet).
Socratic philosophy treats logical axioms as “self-evident truths” (i.e. I think, therefore I am).
I read the article. It’s interesting (I liked the thing about pegs and strings), but I don’t think the guy’s (nor you) read a lot of actual Greek philosophy. I don’t mean that as an attack (why would you want to, after all?), but it makes some of his, and your claims a little strange.
Socrates, in the Platonic dialogues, is unwilling to take the law of non-contradiction as an axiom. There just aren’t any axioms in Socratic philosophy, just discussions. No proofs, just conversations. Plato (and certainly not Socrates) doesn’t have doctrines, and Plato is totally and intentionally merciless with people who try to find Platonic doctrines.
Also, Plato and Socrates predate, for most purposes, logic.
Mathematics treats logical axioms as “propositions”, and uses logic to see where those propositions lead
Right, Aristotle largely invented (or discovered) that trick. Aristotle’s logic is consistant and strongly complete (i.e. it’s not axiomatic, and relies on no external logical concepts). Euclid picked up on it, and produced a complete and consistant mathematics. So (some) Greek philosophy certainly shares this idea with modern mathematics.
Scientists treat logical axioms as “hypotheses”, and logical “conclusions” as testable statements that can determine whether those axioms are true or not
I don’t think scientists treat logical axioms as hypotheses. Logical axioms aren’t empirical claims, and aren’t really subject to testing. But Aristotle’s work on biology, meteorology, etc. forwards plenty of empirical hypotheses, along with empirical evidence for them. Textual evidence suggests Aristotle performed lots of experiments, mostly in the form of vivisection of animals. He was wrong about pretty much everything, but his method was empirical.
This is to say nothing of contemporary philosophy, which certainly doesn’t take very much as ‘self-evident truth’. I can assure you, no one gets anywhere with that phrase anymore, in any study.
I believe Wei_Lai would say that the first approach, treating ethical axioms as “self-evident truths” is problematic due to the fact that a lot of hypothetical situations (like my example before) can create a lot of contradictions between various ethical axioms (i.e. choosing between telling a lie and letting terrorists blow up the planet).
Not if those ethical axioms actually are self-evident truths. Then hypothetical situations (no matter how uncomfortable they make us) can’t disrupt them. But we might, on the basis of these situations, conclude that we don’t have any self-evident moral axioms. But, as you neatly argue, we don’t have any self-evident mathematical axioms either.
Thanks for taking the time to read and respond to the article, and for the critique; you are correct in that I am not well-versed in Greek philosophy. With that being said, allow me to try to expand my framework to explain what I’m trying to get at:
Scientists, unlike mathematicians, don’t always frame their arguments in terms of pure logic (i.e. If A and B, then C). However, I believe that the work that comes from them can be treated as logical statements.
Example: “I think that heat is transferred between two objects via some sort of matter that I will call ‘phlogiston’. If my hypothesis is true, than an object will lose mass as it cools down.” 10 days later: “I have weighed an object when it was hot, and I weighed it when it was cold. The object did not lose any mass. Therefore, my hypothesis is wrong”.
In logical terms: Let’s call the Theory of Phlogiston “A”, and let’s call the act of measuring a loss of mass with a loss of heat “C”.
If A, then C.
Physical evidence is obtained
If Not C, then Not A.
Essentially, the scientific method involves the creation of a hypothesis “A”, and a logical consequence of that hypothesis, “If A then C”. Then physical evidence is presented in favor of, or against “C”. If C is disproven, then A is disproven.
This is what I mean when I say that hypotheses are “axioms”, and physical experiments are “conclusions”.
In response to this statement:
Socrates, in the Platonic dialogues, is unwilling to take the law of non-contradiction as an axiom. There just aren’t any axioms in Socratic philosophy, just discussions. No proofs, just conversations. Plato (and certainly not Socrates) doesn’t have doctrines, and Plato is totally and intentionally merciless with people who try to find Platonic doctrines.
“No proofs, just conversations”. In the framework that I’m working in, every single statement is either a premise or a conclusion. In addition, every single statement is either a “truth” (that we are to believe immediately), a “proposition” (that we are to entertain the logical implications of), or part of a “hypothesis/implication” pair (that we are suppose to believe with a level of skepticism until an experiment verifies it or disproves it). I believe that every single statement that has ever been made in any field of study falls into one of those 3 categories, and I’m saying that we need to discuss which category we need to place statements that are in the field of ethics.
In the field of philosophy, from my limited knowledge, I think that these discussions lead to conclusions that we need to believe as “truth”, whether or not they are supported by evidence (i.e. John Rawl’s “Original Position”).
This is what I mean when I say that hypotheses are “axioms”, and physical experiments are “conclusions”.
I see. You’re right that philosophers pretty much never do anything like that. Except experimental philosophers, but thus far most of that stuff is just terrible.
“In the framework that I’m working in...”
That’s a good framework with with to approach any philosophical text, including and especially the Platonic dialogues. I just wanted to stress the fact that the dialogues aren’t treatises presented in a funny way. You’re supposed to argue with Socrates, against him, yell at his interlocutors, try to patch up the arguments with premises of your own. It’s very different from, say, Aristotle or Kant or whatever, where its a guy presenting a theory.
In the field of philosophy, from my limited knowledge, I think that these discussions lead to conclusions that we need to believe as “truth”
Would you mind if I go on for a bit? I have thoughts on this, but I don’t quite know how to present them briefly. Anyway:
Students of Physics should go into a Physics class room or book with an open mind. They should be ready to learn new things about the world, often surprising things (relative to their naive impressions) and should often try to check their prejudices at the door. None of us are born knowing physics. It’s something we have to go out and learn.
Philosophy isn’t like that. The right attitude walking into a philosophy classroom is irritation. It is an inherently annoying subject, and its practitioners are even worse. You can’t learn philosophy, and you can’t become an expert at it. You can’t even become good at it. Being a philosopher is no accomplishment whatsoever. You can just do philosophy, and anyone can do it. Intelligence is good, but it can be a hindrance too, same with education.
Doing philosophy means asking questions about things to which you really ought to already know the answers, like the difference between right and wrong, whether or not you’re in control of your actions, what change is, what existing is, etc. Philosophy is about asking questions to which we ought to have the answers, but don’t.
We do philosophy by talking to each other. If that means running an experiment, good. If that means just arguing, fine. There’s no method, no standards, and no body of knowledge, unless you say there is, and then convince someone, and then there is until someone convinces you otherwise.
Scientists and mathematicians don’t hate philosophy. They tend to love philosophers, or at least the older ones do. Young scientists and mathematicians do hate philosophers, and with good reason: part of being a young scientist or mathematician is developing a refined mental self-discipline, and that means turning your back on any froo-froo hand wavy BS and getting down to work. Philosophy is the most hateful thing in the world when you’re trying to be wrong as little as possible. But once that discipline is in place, and people are confident in their ability to sort out good arguments from bad ones, facts from speculation, philosophy starts to look like fun.
In the framework that I’m working in, every single statement is either a premise or a conclusion. In addition, every single statement is either a “truth” (that we are to believe immediately), a “proposition” (that we are to entertain the logical implications of), or part of a “hypothesis/implication” pair (that we are suppose to believe with a level of skepticism until an experiment verifies it or disproves it)
But there is a mini-premise, inference and mini-conclusion inside every “hypothesis-implication pair”.
In the field of philosophy, from my limited knowledge, I think that these discussions lead to conclusions that we need to believe as “truth”, whether or not they are supported by evidence (i.e. John Rawl’s “Original Position”).
I’m curious as to why you referenced Rawl’s work in this context. It’s not apparent to me how Justice as Fairness is relevant here.
I referenced him because I recall that he comes to a very strong conclusion- that a moral society should have agreed-upon laws based on the premise of the “original position”. He was the first philosopher that came to mind when I was trying to think of examples of a hard statement that is neither a “proposition” to be explored, nor the conclusion from an observable fact.
I mean, I’m pretty sure his conclusion is a “proposition.” It has premises, and I could construct it logically if you wanted.
In fact, I don’t understand his position to be “that a moral society should have agreed-upon laws” at all, but rather his use of the original position is an attempt to isolate and discover the principles of distributive justice, and that’s really his bottom line.
Interesting piece. I was a bit bemused by this, though:
In fact Plato wrote to Archimedes, scolding him about messing around with real levers and ropes when any gentleman would have stayed in his study or possibly, in Archimedes’ case, his bath.
Problematically for the story, Plato died around 347 BCE, and Archimedes wasn’t born until 287 BCE—sixty years later.
I just stumbled into this discussion after reading an article about why mathematicians and scientists dislike traditional, Socratic philosophy, and my mindset is fresh off that article.
It was a fantastic read, but the underlying theme that I feel is relevant to this discussion is this:
Socratic philosophy treats logical axioms as “self-evident truths” (i.e. I think, therefore I am).
Mathematics treats logical axioms as “propositions”, and uses logic to see where those propositions lead (i.e. if you have a line and a point, the number/amount of lines that you can draw through the point that’s parallel to the original line determines what type of geometry you are working with (multidimensional, spherical, or flat-plane geometry)).
Scientists treat logical axioms as “hypotheses”, and logical “conclusions” as testable statements that can determine whether those axioms are true or not (i.e. if this weird system known as “quantum mechanics” were true, then we would see an interference pattern when shooting electrons through a screen with 2 slits).
So I guess the point that we should be making is this: which philosophical approach towards logic should we take to study ethics? I believe Wei_Lai would say that the first approach, treating ethical axioms as “self-evident truths” is problematic due to the fact that a lot of hypothetical situations (like my example before) can create a lot of contradictions between various ethical axioms (i.e. choosing between telling a lie and letting terrorists blow up the planet).
I read the article. It’s interesting (I liked the thing about pegs and strings), but I don’t think the guy’s (nor you) read a lot of actual Greek philosophy. I don’t mean that as an attack (why would you want to, after all?), but it makes some of his, and your claims a little strange.
Socrates, in the Platonic dialogues, is unwilling to take the law of non-contradiction as an axiom. There just aren’t any axioms in Socratic philosophy, just discussions. No proofs, just conversations. Plato (and certainly not Socrates) doesn’t have doctrines, and Plato is totally and intentionally merciless with people who try to find Platonic doctrines.
Also, Plato and Socrates predate, for most purposes, logic.
Right, Aristotle largely invented (or discovered) that trick. Aristotle’s logic is consistant and strongly complete (i.e. it’s not axiomatic, and relies on no external logical concepts). Euclid picked up on it, and produced a complete and consistant mathematics. So (some) Greek philosophy certainly shares this idea with modern mathematics.
I don’t think scientists treat logical axioms as hypotheses. Logical axioms aren’t empirical claims, and aren’t really subject to testing. But Aristotle’s work on biology, meteorology, etc. forwards plenty of empirical hypotheses, along with empirical evidence for them. Textual evidence suggests Aristotle performed lots of experiments, mostly in the form of vivisection of animals. He was wrong about pretty much everything, but his method was empirical.
This is to say nothing of contemporary philosophy, which certainly doesn’t take very much as ‘self-evident truth’. I can assure you, no one gets anywhere with that phrase anymore, in any study.
Not if those ethical axioms actually are self-evident truths. Then hypothetical situations (no matter how uncomfortable they make us) can’t disrupt them. But we might, on the basis of these situations, conclude that we don’t have any self-evident moral axioms. But, as you neatly argue, we don’t have any self-evident mathematical axioms either.
Thanks for taking the time to read and respond to the article, and for the critique; you are correct in that I am not well-versed in Greek philosophy. With that being said, allow me to try to expand my framework to explain what I’m trying to get at:
Scientists, unlike mathematicians, don’t always frame their arguments in terms of pure logic (i.e. If A and B, then C). However, I believe that the work that comes from them can be treated as logical statements.
Example: “I think that heat is transferred between two objects via some sort of matter that I will call ‘phlogiston’. If my hypothesis is true, than an object will lose mass as it cools down.” 10 days later: “I have weighed an object when it was hot, and I weighed it when it was cold. The object did not lose any mass. Therefore, my hypothesis is wrong”.
In logical terms: Let’s call the Theory of Phlogiston “A”, and let’s call the act of measuring a loss of mass with a loss of heat “C”.
If A, then C.
Physical evidence is obtained
If Not C, then Not A.
Essentially, the scientific method involves the creation of a hypothesis “A”, and a logical consequence of that hypothesis, “If A then C”. Then physical evidence is presented in favor of, or against “C”. If C is disproven, then A is disproven.
This is what I mean when I say that hypotheses are “axioms”, and physical experiments are “conclusions”.
In response to this statement:
“No proofs, just conversations”. In the framework that I’m working in, every single statement is either a premise or a conclusion. In addition, every single statement is either a “truth” (that we are to believe immediately), a “proposition” (that we are to entertain the logical implications of), or part of a “hypothesis/implication” pair (that we are suppose to believe with a level of skepticism until an experiment verifies it or disproves it). I believe that every single statement that has ever been made in any field of study falls into one of those 3 categories, and I’m saying that we need to discuss which category we need to place statements that are in the field of ethics.
In the field of philosophy, from my limited knowledge, I think that these discussions lead to conclusions that we need to believe as “truth”, whether or not they are supported by evidence (i.e. John Rawl’s “Original Position”).
I see. You’re right that philosophers pretty much never do anything like that. Except experimental philosophers, but thus far most of that stuff is just terrible.
“In the framework that I’m working in...”
That’s a good framework with with to approach any philosophical text, including and especially the Platonic dialogues. I just wanted to stress the fact that the dialogues aren’t treatises presented in a funny way. You’re supposed to argue with Socrates, against him, yell at his interlocutors, try to patch up the arguments with premises of your own. It’s very different from, say, Aristotle or Kant or whatever, where its a guy presenting a theory.
Would you mind if I go on for a bit? I have thoughts on this, but I don’t quite know how to present them briefly. Anyway:
Students of Physics should go into a Physics class room or book with an open mind. They should be ready to learn new things about the world, often surprising things (relative to their naive impressions) and should often try to check their prejudices at the door. None of us are born knowing physics. It’s something we have to go out and learn.
Philosophy isn’t like that. The right attitude walking into a philosophy classroom is irritation. It is an inherently annoying subject, and its practitioners are even worse. You can’t learn philosophy, and you can’t become an expert at it. You can’t even become good at it. Being a philosopher is no accomplishment whatsoever. You can just do philosophy, and anyone can do it. Intelligence is good, but it can be a hindrance too, same with education.
Doing philosophy means asking questions about things to which you really ought to already know the answers, like the difference between right and wrong, whether or not you’re in control of your actions, what change is, what existing is, etc. Philosophy is about asking questions to which we ought to have the answers, but don’t.
We do philosophy by talking to each other. If that means running an experiment, good. If that means just arguing, fine. There’s no method, no standards, and no body of knowledge, unless you say there is, and then convince someone, and then there is until someone convinces you otherwise.
Scientists and mathematicians don’t hate philosophy. They tend to love philosophers, or at least the older ones do. Young scientists and mathematicians do hate philosophers, and with good reason: part of being a young scientist or mathematician is developing a refined mental self-discipline, and that means turning your back on any froo-froo hand wavy BS and getting down to work. Philosophy is the most hateful thing in the world when you’re trying to be wrong as little as possible. But once that discipline is in place, and people are confident in their ability to sort out good arguments from bad ones, facts from speculation, philosophy starts to look like fun.
The second part of your post is terrific. :)
But there is a mini-premise, inference and mini-conclusion inside every “hypothesis-implication pair”.
I’m curious as to why you referenced Rawl’s work in this context. It’s not apparent to me how Justice as Fairness is relevant here.
I referenced him because I recall that he comes to a very strong conclusion- that a moral society should have agreed-upon laws based on the premise of the “original position”. He was the first philosopher that came to mind when I was trying to think of examples of a hard statement that is neither a “proposition” to be explored, nor the conclusion from an observable fact.
I mean, I’m pretty sure his conclusion is a “proposition.” It has premises, and I could construct it logically if you wanted.
In fact, I don’t understand his position to be “that a moral society should have agreed-upon laws” at all, but rather his use of the original position is an attempt to isolate and discover the principles of distributive justice, and that’s really his bottom line.
Interesting piece. I was a bit bemused by this, though:
Problematically for the story, Plato died around 347 BCE, and Archimedes wasn’t born until 287 BCE—sixty years later.
Thank you for an awesome read. :)
science uses logical rules of inference. Does science take them as self-evident? Or does it test them? And can it test them without assuming them?