Thanks for the comment! My inspiration for that objection was primary W.V.O. Quine and C.S. Peirce, both of whom (as I understand them) adopt the position that we can't be absolutely certain about anything and actually shouldn't try; but that we can nonetheless have better and worse reasons for what we believe. I don't think it's an absurd position, though of course it might ultimately be incorrect or more problematic than it's worth.
@@owlofminerva1503 my main objection with their objection is that it disdains progress. Having no foundation makes everything float without proper justification. All of mathematics' foundation lies on Set Theory, specifically Zermelo-Frankel Choice or ZFC if I remember correctly. Though Godel prove that there can be no consistent and useful mathematical system, the foundation is still important. A foundation is a common language that everyone can agree on thus making it easier to build from the "shoulders of giants". In contrast, a floating web of ideas is prone to contradictions that we just keep in this web. A web is much harder if not impossible to teach once it matures enough compared to a tower with basic axiomatic foundations. I think their objection is contrary to what progress needs. It is stagnation.
@@jakeaustria5445 I think I understand the anxieties about not having a foundation. That would imply that whatever we "discover" is still not perfectly certain, and therefore we can never be certain that we've made progress either. However, I don't think there's any contradiction between the idea that our beliefs and theories are not certain and not grounded in any foundation, and the idea that we are (at least possibly) making progress in our beliefs and theories. I also think there are versions of the idea of progress that are consistent with the web-of-belief idea (for instance: progress according to the available evidence and under the assumption of one or another adopted standard or metric, such as consistency with experimental results or ability to predict behaviors of a system, etc.). And many of your examples, such as the "foundations" of mathematics (whether in set theory or group theory or something else is, as I understand it, still a contested matter among mathematicians), and Goedel's as-yet unrefuted proof that a consistent and complete axiomatic foundation for arithmetic is not possible, seem to suggest that the non-foundational model is truer, at least for the domain of math. So: I neither think that non-foundationalism is incompatible with the idea of progress, nor do I think that the fear of this incompatibility should dissuade us from accepting non-foundationalism in any area where strong arguments seem to suggest that it is true.
![a chance encounter [You are remembering how to walk the unknown path]](http://i.ytimg.com/vi/mqVkMiICWpY/mqdefault.jpg)
Lovin this series, using some of these ideas for my studies...
I appreciate highlighting the text in green. Makes it easy to skip to a specific part.
Thanks for the feedback!
Subscribed. Nice work !!
Please notice me! Can you answer what is the controverisies met the Rene Descartes evolution?
Hi Jhon, Sorry, I don't understand the question. Can you say a bit more about what you're asking?
Thank You. Although the first objection to the method of doubt is bullshit.
Thanks for the comment! My inspiration for that objection was primary W.V.O. Quine and C.S. Peirce, both of whom (as I understand them) adopt the position that we can't be absolutely certain about anything and actually shouldn't try; but that we can nonetheless have better and worse reasons for what we believe. I don't think it's an absurd position, though of course it might ultimately be incorrect or more problematic than it's worth.
@@owlofminerva1503 my main objection with their objection is that it disdains progress. Having no foundation makes everything float without proper justification. All of mathematics' foundation lies on Set Theory, specifically Zermelo-Frankel Choice or ZFC if I remember correctly. Though Godel prove that there can be no consistent and useful mathematical system, the foundation is still important. A foundation is a common language that everyone can agree on thus making it easier to build from the "shoulders of giants". In contrast, a floating web of ideas is prone to contradictions that we just keep in this web. A web is much harder if not impossible to teach once it matures enough compared to a tower with basic axiomatic foundations. I think their objection is contrary to what progress needs. It is stagnation.
@@jakeaustria5445 I think I understand the anxieties about not having a foundation. That would imply that whatever we "discover" is still not perfectly certain, and therefore we can never be certain that we've made progress either. However, I don't think there's any contradiction between the idea that our beliefs and theories are not certain and not grounded in any foundation, and the idea that we are (at least possibly) making progress in our beliefs and theories. I also think there are versions of the idea of progress that are consistent with the web-of-belief idea (for instance: progress according to the available evidence and under the assumption of one or another adopted standard or metric, such as consistency with experimental results or ability to predict behaviors of a system, etc.). And many of your examples, such as the "foundations" of mathematics (whether in set theory or group theory or something else is, as I understand it, still a contested matter among mathematicians), and Goedel's as-yet unrefuted proof that a consistent and complete axiomatic foundation for arithmetic is not possible, seem to suggest that the non-foundational model is truer, at least for the domain of math. So: I neither think that non-foundationalism is incompatible with the idea of progress, nor do I think that the fear of this incompatibility should dissuade us from accepting non-foundationalism in any area where strong arguments seem to suggest that it is true.