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To me, this is a great illustration that there's no other coherent place to start any form of discussion, reasoning, or belief than with axioms (or assumptions)

To me, this is a great illustration that there's no other coherent place to start any form of discussion, reasoning, or belief than with axioms (or assumptions). Regressive and circular arguments only shift the problem. I believe that if one is looking for truth in a big-picture sense (religious or philosophical), the best approach is to evaluate various existing systems of axioms/assumptions and apply a twofold test to each: (1) correspondence to reality and (2) internal consistency. It's a given that applying the first test requires stepping into the subjective, since one must honestly apply it to personal experience.

tunesmith 9y ago
Combine it with Hume's Guillotine and you realize that all "should" conclusions really just start with moral "value" axioms. So then you can make a distinction between people that reason correctly from values that are different than yours, and people that reason badly from their axioms. And you can also make a distinction between philosophies that are based off of unprovable beliefs (which is fine), and philosophies that are anti-factual (which isn't). I like to define the former as religion and the latter as ignorance, but unfortunately there are a lot of the latter that claim it's religion.
romwell 9y ago
I heavily disagree; axioms are never a good place to start, nor, historically, they ever were a starting place. Working mathematicians do a lot of mathematics and constructions before stopping to look and say: "OK, we can distill this rich theory down to this small set of axioms". Geometry has been quite developed before Euclid's axioms, and number theory took its sweet millenia before Peano's axioms were developed. On a more modern side, a lot of topology has been produced before people decided to write down a list of axioms for homology, which all the different homology constructions satisfied. The point is that understanding almost always precedes formal reasoning, language follows ideas, and rigid systems arise on a fertile soil of messy experiments - mental or physical. If you look at the history of science and mathematics, nothing was ever built up from the formulas and axioms (criminally contrary to the way these subjects are taught). There is an underappreciated beauty in our ability to argue about, reason with, and make use of concepts that we haven't even really defined. Everyone knew Newton's Calculus was full of holes, and people used it for centuries before coming up with solid definitions of limits, derivatives and integrals - the most fundamental concepts of the subject! And on that note, people used real numbers for a long time before having the formal machinery to define them. Zeno didn't have the axioms to resolve his paradox. Didn't stop anyone from using these weird objects in reasoning and practice. ---------------------------------------------------- TL;DR: never start with axioms, end with them.
- TimTheTinker 8y ago
  I'm talking about different sorts of axioms than those that science and math work towards. For example, any discussion between 2 people depends on mutually accepting basic assumptions such as: - I and you are persons. We exist. - The words we speak and hear have meaning. - The words you hear are the words I spoke, and vice versa. We can't even have a meaningful, coherent discussion without assuming things like that. We also can't live a meaningful, coherent life without basic assumptions about origin, meaning, morality, and destiny. Everyone has them, and unless we're careful, they're easy to catch like the cold from folks we hang around. A coherent, truthful worldview is essential. The test for truth (correspondence to reality and internal consistency) does provide us a way of comparing religions and philosophies (and ruling out the obviously false ones). Once we do arrive at a coherent worldview that best corresponds to reality and is internally consistent, we have to assume it and derive our beliefs and practices from it without proof (i.e. faith). (BTW, we all have a worldview, but we haven't all subjected our worldview to the truth test.) Everyone has faith: it's required to accept the axioms of one's worldview.

tunesmith 9y ago

Combine it with Hume's Guillotine and you realize that all "should" conclusions really just start with moral "value" axioms. So then you can make a distinction between people that reason correctly from values that are different than yours, and people that reason badly from their axioms. And you can also make a distinction between philosophies that are based off of unprovable beliefs (which is fine), and philosophies that are anti-factual (which isn't). I like to define the former as religion and the latter as ignorance, but unfortunately there are a lot of the latter that claim it's religion.

romwell 9y ago

I heavily disagree; axioms are never a good place to start, nor, historically, they ever were a starting place. Working mathematicians do a lot of mathematics and constructions before stopping to look and say: "OK, we can distill this rich theory down to this small set of axioms". Geometry has been quite developed before Euclid's axioms, and number theory took its sweet millenia before Peano's axioms were developed. On a more modern side, a lot of topology has been produced before people decided to write down a list of axioms for homology, which all the different homology constructions satisfied. The point is that understanding almost always precedes formal reasoning, language follows ideas, and rigid systems arise on a fertile soil of messy experiments - mental or physical. If you look at the history of science and mathematics, nothing was ever built up from the formulas and axioms (criminally contrary to the way these subjects are taught). There is an underappreciated beauty in our ability to argue about, reason with, and make use of concepts that we haven't even really defined. Everyone knew Newton's Calculus was full of holes, and people used it for centuries before coming up with solid definitions of limits, derivatives and integrals - the most fundamental concepts of the subject! And on that note, people used real numbers for a long time before having the formal machinery to define them. Zeno didn't have the axioms to resolve his paradox. Didn't stop anyone from using these weird objects in reasoning and practice. ---------------------------------------------------- TL;DR: never start with axioms, end with them.

TimTheTinker 8y ago
I'm talking about different sorts of axioms than those that science and math work towards. For example, any discussion between 2 people depends on mutually accepting basic assumptions such as: - I and you are persons. We exist. - The words we speak and hear have meaning. - The words you hear are the words I spoke, and vice versa. We can't even have a meaningful, coherent discussion without assuming things like that. We also can't live a meaningful, coherent life without basic assumptions about origin, meaning, morality, and destiny. Everyone has them, and unless we're careful, they're easy to catch like the cold from folks we hang around. A coherent, truthful worldview is essential. The test for truth (correspondence to reality and internal consistency) does provide us a way of comparing religions and philosophies (and ruling out the obviously false ones). Once we do arrive at a coherent worldview that best corresponds to reality and is internally consistent, we have to assume it and derive our beliefs and practices from it without proof (i.e. faith). (BTW, we all have a worldview, but we haven't all subjected our worldview to the truth test.) Everyone has faith: it's required to accept the axioms of one's worldview.