Empirical evaluations and judgments concerning the observable world (e.g. whether or not I'm eating a watermelon right now) are evidently verifiable; you can confirm that I am indeed eating a watermelon at the moment, and my friends might be able to tell me if I am or not, too.

But how can I be sure of logical or metaphysical truths? How would I go about verifying them without something I can observe?


If one is remarkably confident that one can, indeed, observe things, then this is a dilemma. To such a person, this word, "observe," has a very clear crisp meaning that could not possibly ever be challenged.

They can use that confidence to be sure of logical or metaphysical truths.

Of course, those observations are never deceiving:

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Actually, if you study empiricism, you find that it is a subcategory of epistemology, the study of what we can "know." Empiricists believe that all knowledge stems from "sensory observations," though what those are is a heavily debated topic. Another branch of epistomology, rationalism, believes that all knowledge stems from the use of reason independent from the senses. In rationalism, it is logical or metaphysical truths that one can be certain of, and the "observable" world outside is the part which is treated with suspicion.

  • Your answer would be great, if you added Kant and a few references or links. – Alexander S King Mar 19 '16 at 1:16

You can't be sure about our observations of the world. Sometimes our senses are deceiving us, too.

Now, as there are ways to corroborate our observations, there are ways to corroborate the results of our thinking.

  1. Formal proofs can be checked carefully many times, by many different experts — because we all agree on the rules.

  2. We can try to give another very different proof for a proposition.

  3. Sometimes formal proofs in logic and mathematics can even be checked by a computer.

  4. Results in logic and mathematics can in many cases be applied to the real world. If an application fails, it should make us suspicious of our reasoning.

  5. In some cases we can make trillions of sample checks of a proposition with brute force. A computer can check a theorem in number theory for a huge range of numbers.

  6. Sometimes it is possible to grasp the truth of mathematical theorem in a more direct way, for example visually.

You see that most of the time these methods (especially powerful are 1., 4. and 5.) aren't available in metaphysics (and philosophy in general). That's why consensus in philosophy is so rare.

  • It seems as if these solutions are just affirming our formulations with formulations of the same kind. I'm not sure if this is really verifying anything; it's more like checking to see if we calculated 1+1 correctly with the axioms of math. This doesn't indicate that the proposition is factually true; it only means that according to us and our rules of thought, it does. – Apodictic Apple Juice Mar 19 '16 at 4:22
  • @ApodicticAppleJuice: The problem is how you phrased your question. Maybe mathematical truth isn't more than formal correctness and consistency? What else should it be? I think, you should have rather asked: "How is synthetic a priori knowledge possible?", which is "How can we sometimes acquire knowledge about the world just by reasoning alone?" (that's a very famous question, discussed many times on philosophy.SE). – wolf-revo-cats Mar 19 '16 at 17:06
  • Now, I understand. I guess I'll have to reopen my copy of The Critique. – Apodictic Apple Juice Mar 19 '16 at 20:38

1) The unobservable can be verified in case of mathematics or logic by proof: You have a set of axioms and you derive a proposition by a logical syllogism from the axioms. But in case you do not accept the axioms, e.g.; 2-valued logic, the proof ahs no value for you. The restriction is that the axioms of formal sciences like logic and mathematics are posed neither proved nor derived from any previous truth.

2) In natural sciences one cannot prove general theories. But one can check wether the predictions of the theory conform to the observation. In that case the observation confirms the theory, but it does not prove it. On the opposite, if the observations mostly contradict the predictions the observations refute the theory.

3) Propositions from metaphysics, e.g., nothing happens without a sufficient reason or conservation of the substance, can neither be proved nor compared by experiment with observation. Neither the concepts of metaphysics have precise definitions, nor do the argumentations convince all metaphysicians.

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