*Further, Harris's entire argument rests in part upon his ability to articulate an objective nadir, an absolute minimum, in that space – the maximum possible suffering of every sentient creature.*The entire moral landscape can be thus thought of as a partially ordered set of moral positions together with their resultant consequences as measured on hypothetical metric related to well-being and suffering.Our senses tell us that a table, for example, is a solid object; science tells us that the table is mostly empty space.

*Further, Harris's entire argument rests in part upon his ability to articulate an objective nadir, an absolute minimum, in that space – the maximum possible suffering of every sentient creature.*The entire moral landscape can be thus thought of as a partially ordered set of moral positions together with their resultant consequences as measured on hypothetical metric related to well-being and suffering.Our senses tell us that a table, for example, is a solid object; science tells us that the table is mostly empty space.

Of course, mathematics is most clearly applicable to philosophy where it intersects with the mathematically hard sciences, like physics.

Much in physics, for example, depends upon clearly understanding the scope, power, and impact of Noether's (first) theorem, named for Emmy Noether.

To what extent should our actions be guided by our theories in ethics and elsewhere? until we have felt the force of the knowledge, it is not ours” (adapted from Arnold Bennett).

Discuss this vision of the relationship between knowledge and emotion.

Thus maths and science are crucial for good philosophy – for getting things right. As a quirk of our base-ten number system, for example, the number 0.999..., the one that is an infinite concatenation of nines, happens to equal 1. The proofs of this fact are numerous, easy, and accessible to people without a background in mathematics (the easiest being to add one third, 0.333..., to two thirds, 0.666..., and see what you get).

This result isn't intuitive, and – as anyone who has taught it can attest – not everyone is comfortable with it at first blush.But even sciences investigating scales more familiar to us, like biological evolution, are nonintuitive and uncomfortable to the point of being rejected by surprising numbers of people despite overwhelming scientific consensus spanning nearly a century and a half.Thinking philosophically requires the capacity to logically and rigorously engage ideas and then either accept the results or reject our assumptions – no matter how nonintuitive or how uncomfortable those assumptions may be.Her theorem, proved a century ago and published in 1918, was truly revolutionary for physics because it completely changed how we understand conservation laws, revealing that conservation laws follow automatically from certain assumptions of invariance of physical laws (for example, if the laws of physics do not vary with locations in space, conservation of momentum automatically follows).Whether Noether's theorem is best classified as a result in abstract mathematics or theoretical physics isn't important, but that philosophers need to understand it is, at least if they want to work competently on ideas related to that which it pertains.Even philosophical efforts on desperately difficult topics like ethics – the apparently subjective nature of which serves quite reasonably something of a against the intrusion of too much objective empiricism into the provinces of philosophy – benefit from the habits of mathematical thought.For example, take Sam Harris's controversial 2010 contribution to the field in his bestselling book, .If you want to be a good philosopher, don’t rely on intuition or comfort. They’ll allow you access the best methods we have for knowing the world while teaching you to think clearly and analytically.Mathematics is the philosophical language nature prefers, and science is the only truly effective means we have for connecting our philosophy to reality. and 1, are simply two ways to express the same thing.Aeon email newsletters are issued by the not-for-profit, registered charity Aeon Media Group Ltd (Australian Business Number 80 612 076 614).This Email Newsletter Privacy Statement pertains to the personally identifying information you voluntarily submit in the form of your email address to receive our email newsletters More generally, when visiting the Aeon site you should refer to our site Privacy Policy here.

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