What is the relation between metaphysics and observational science? I believe that, in answering this, we can also provide a robust theory which can produce models of confirmation beyond mere lack of succumbing to falsification á la Popper.

Here is an example of which the principle lends itself to explaining what could be done in all other areas of scientific inquiry.

Suppose we know it is the case that there is a triangle. Now there are certain things we know of a triangle due to our metaphysical knowledge (i.e. what a triangle is) which tells us what that triangle must be like in certain conditions. For example, we know that in Euclidean space the interior angles of the triangle will add up to 180. This means we can express the relationship in this way;

∆ –> 180 (interior angles)

There are properties of triangles that must follow in certain instances which we can determine merely from our metaphysical knowledge of triangles (i.e. our knowledge of triangles that is not inducted). For instance, if you have a Euclidean triangle, for which one of the angles is 90 degrees, it follows that the length of the sides can be expressed by a certain formula. The principle of knowledge and deduction from our inducted knowledge in this case holds for all other scientific endeavors.

Consider that, if it is the case that we can make a triangle in which the interior angles do not add up to 180 degrees, then we know that space is not Euclidean, at least not everywhere.

Example of the experiment: Put three objects in space that can aim lasers at each other very precisely over very long distances, like at least several lightminutes. Create a laser-triangle. Add up the interior angles. If the interior angles are not 180 degrees, then we have confirmed that space can bend.

Of course there are certain assumptions that build into the experiment; the assumption that light travels in a straight line and would follow the contours of space, that it might not be bent by other forces within the universe, and so on. Granting these assumptions, we could postulate that, void anything unknown, space is (at least sometimes) non-Euclidean.

While this isn’t as entirely “confirmational” as we might like, this sort of experiment, in line with our metaphysical knowledge of triangles, produces some definite knowledge of what must be the case provided some other systems are in place. This also highlights where our metaphysical knowledge meets empirical knowledge, of which more will be said in the next part.

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