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Sextus Empiricus
Sextus Empiricus
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Intuitively, when I think about dependence, I think about relations like A=2∗B. In this case, A clearly depends on B (it is always the double of B). However, in this case, the equation doesn't say that the value of B depends on the value of A. Indeed, if that was the case, this would be a circular definition.

You seem to be using the non-symmetric 'causation' in place of 'statistical dependence' or functional relationship.

Say you throw a ball at an angle 45 degrees. Then the distance $x$ in meters and speed $v$ in meters per second could be related by:

$$x = \frac{2}{9.8} v^2$$

There is nothing circular to say that '$x$ depends on $v$' as well as '$v$ depends on $x$'. At least, not in a statistical sense. The dependence here is that you can predict the speed at which a ball has been thrown based on the distance that it travels. And vice versa, you can predict the distance that a ball travels based on the speed at which it has been thrown.

With causation you indeed have non symetric relations. E.g. you have if-then relationships which are depicted by a nonsymmetric arrow. See also https://en.wikipedia.org/wiki/Affirming_the_consequent

If two events are independent, thus neither one influences the probability of the other, then the probability for both events to occur together is P(a,b) = P(a)P(b), the product of the individual proabilities. From that you can deduce P(a|b) = P(a,b)/P(b) = P(a)

Intuitively, when I think about dependence, I think about relations like A=2∗B. In this case, A clearly depends on B (it is always the double of B). However, in this case, the equation doesn't say that the value of B depends on the value of A. Indeed, if that was the case, this would be a circular definition.

You seem to be using the non-symmetric 'causation' in place of 'statistical dependence' or functional relationship.

Say you throw a ball at an angle 45 degrees. Then the distance $x$ in meters and speed $v$ in meters per second could be related by:

$$x = \frac{2}{9.8} v^2$$

There is nothing circular to say that $x$ depends on $v$ as well as $v$ depends on $x$. At least, not in a statistical sense. The dependence here is that you can predict the speed at which a ball has been thrown based on the distance that it travels. And vice versa, you can predict the distance that a ball travels based on the speed at which it has been thrown.

With causation you indeed have non symetric relations. E.g. you have if-then relationships which are depicted by a nonsymmetric arrow. See also https://en.wikipedia.org/wiki/Affirming_the_consequent

If two events are independent, thus neither one influences the probability of the other, then the probability for both events to occur together is P(a,b) = P(a)P(b), the product of the individual proabilities. From that you can deduce P(a|b) = P(a,b)/P(b) = P(a)

Intuitively, when I think about dependence, I think about relations like A=2∗B. In this case, A clearly depends on B (it is always the double of B). However, in this case, the equation doesn't say that the value of B depends on the value of A. Indeed, if that was the case, this would be a circular definition.

You seem to be using the non-symmetric 'causation' in place of 'statistical dependence' or functional relationship.

Say you throw a ball at an angle 45 degrees. Then the distance $x$ in meters and speed $v$ in meters per second could be related by:

$$x = \frac{2}{9.8} v^2$$

There is nothing circular to say that '$x$ depends on $v$' as well as '$v$ depends on $x$'. At least, not in a statistical sense. The dependence here is that you can predict the speed at which a ball has been thrown based on the distance that it travels. And vice versa, you can predict the distance that a ball travels based on the speed at which it has been thrown.

With causation you indeed have non symetric relations. E.g. you have if-then relationships which are depicted by a nonsymmetric arrow. See also https://en.wikipedia.org/wiki/Affirming_the_consequent

If two events are independent, thus neither one influences the probability of the other, then the probability for both events to occur together is P(a,b) = P(a)P(b), the product of the individual proabilities. From that you can deduce P(a|b) = P(a,b)/P(b) = P(a)

Source Link
Sextus Empiricus
Sextus Empiricus
  • 86.5k
  • 6
  • 115
  • 302

Intuitively, when I think about dependence, I think about relations like A=2∗B. In this case, A clearly depends on B (it is always the double of B). However, in this case, the equation doesn't say that the value of B depends on the value of A. Indeed, if that was the case, this would be a circular definition.

You seem to be using the non-symmetric 'causation' in place of 'statistical dependence' or functional relationship.

Say you throw a ball at an angle 45 degrees. Then the distance $x$ in meters and speed $v$ in meters per second could be related by:

$$x = \frac{2}{9.8} v^2$$

There is nothing circular to say that $x$ depends on $v$ as well as $v$ depends on $x$. At least, not in a statistical sense. The dependence here is that you can predict the speed at which a ball has been thrown based on the distance that it travels. And vice versa, you can predict the distance that a ball travels based on the speed at which it has been thrown.

With causation you indeed have non symetric relations. E.g. you have if-then relationships which are depicted by a nonsymmetric arrow. See also https://en.wikipedia.org/wiki/Affirming_the_consequent

If two events are independent, thus neither one influences the probability of the other, then the probability for both events to occur together is P(a,b) = P(a)P(b), the product of the individual proabilities. From that you can deduce P(a|b) = P(a,b)/P(b) = P(a)