Ti valuing types are sometimes criticized for ignoring empirical data if it is not consistent with their views. The argument, so it goes, is that empirical data is real or factual, and views can be changed, therefore the empirical data takes precedence over any prior belief that one may have concerning it.
While this is true, it can be misleading if taken too far, and in fact seriously impeded the progress of science on different occasions in history. One is the discovery by Galileo (ILE) that all objects in free fall will fall at the same rate. Typically if you drop a feather and a bowling ball they will not fall at the same rate. But as we now know, this is due to special conditions that exist on the Earth's surface (air resistance) and in no way contradicts the more basic and fundamental truth. Galileo presented an argument to this effect, but it is said that he did arrive at this fact empirically, by cleverly choosing an experiment in which air resistance wouldn't be a factor. The whole idea of doing controlled experiments in fact does mean "ignoring facts" or rather assuming a certain model of the world, in which the other factors are thought not to matter. (An assumption which may not be valid depending on how the experiment is set up.)
Another example is the Copernican model of the solar system (or rather the universe as it was known at that time). In fact the Copernican model was not much more accurate than the Ptolemaic model, although it did require fewer epicycles. The backlash it suffered is not unlike the reactions faced by proponents of speculative or revolutionary theories today, even if the one was supposedly based on religious dogma and the others on hard-nosed skepticism.
What this suggests is that reasoning from facts (Te) is not enough. One may also reason based on ideas or pure logic (Ti, with intuition). The most extreme example of this in the history of science is the theory of general relativity by Einstein (also ILE). Unlike quantum mechanics, which was cobbled together from various different observations, and whose interpretation and principles are still in dispute, Einstein started out with a clear physical principle: the laws of physics should be invariant under smooth changes of coordinates. Since there are many different ways of describing the same situation with different coordinates, it should not matter which ones we use. To this he added some empirical requirements, like reproducing Newton's laws in the limit — but in fact, he too was misled by this! He became stuck, trying to reconcile the idea with the "empirical" data. It was not until he realized that in fact coordinate invariance was the primary requirement (and the so-called facts required subtle modification) that he finally completed the theory. Empirical evidence for general relativity actually remained somewhat scant for many years. Another point to note here is that it is easy to confuse an interpretation of the facts (like a "proven" past model) for the facts themselves. All observations except the most basic are tied up in some way with interpretation.
So, as one might expect, the approach I (LII) use to develop socionics uses a great deal of a priori reasoning (while of course making use of both). It's like you have two masses, one consisting of knowledge that is known to be true by reasoning, and one consisting of all observations of the world. You can then bring them together by moving either point towards the other, or both, until they meet in the true model. In fact, a priori truths may seem disconnected or cover different domains (like general relativity and quantum mechanics), and themselves require unification. Our basic physical understanding of the universe has been stuck for decades, and what we need to move forward is a thorough re-examination of the concepts underlying the theories, starting with what is absolutely clear and building on top of that until everything has been "digested" into an indisputable form, or else cast aside as remnants of past confusion. This is a huge task, but it can, and will, be done.