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Does it make sense in science to have theories that make claims that are not empirical? By a non-empirical claim, I mean something that cannot be tested by means of observation or experimentation. I am not able to think of any concrete example.

But let us suppose we have a theory T that combines two theories, A and B, both of which are empirical in nature. But in order to do that, T makes certain claims, postulates existence of certain entities that we will never be able to test. Does T still have any merit? Well, it certainly explains the two theories, it unifies them. So what other criterion should T fulfill apart from being wholly emprical (only certain subsets of it are empirical), to be accepted as a theory in science?

I hope I am not being vague.

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    As a matter of definition, science typically reserves the word 'theory' for models which have been empirically verified. So the answer to your question as such would automatically be no. But that just shifts your question to whether or not models that have not or cannot be empirically tested have any merit. And to that I'd answer probably, perhaps as an intermediate stage towards producing one that can be. – David H Mar 2 '15 at 7:50
  • @DavidH Hmm.. Suppose we have two theories (A and B) that explain the same empirical data. A is more easy to understand, but it also postulates the existence of an entity, which we cannot empirically verify. Does it make sense to choose A over B? – The very fluffy Panda Mar 2 '15 at 8:00
  • Is there anything that is empirically verifiable? – Keelan Mar 2 '15 at 8:23
  • @Keelan I don't understand. Maybe I am being naive. There are kangaroos in Australia is an empirically verifiable statement. – The very fluffy Panda Mar 2 '15 at 8:26
  • Doesn't that depend on your senses functioning correctly? Then you first need to verify that. How would you go about that? :) – Keelan Mar 2 '15 at 8:28
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They are in a sense ubiquitous. Take for example the principle of inertia in newtonian physics which states that an object will keep moving at the same speed if no force is imposed. First, such situation is almost impossible because there are gravitational forces everywhere. But more importantly, you need an inertial frame of reference before measuring a speed (and testing the principle). An inertial frame of reference is a frame attached to an inertial body and that makes the principle a circular principle. Another circularity occurs in the way mass and force are defined relatively to each other.

The lesson is not that newtonian physics cannot be tested empirically. It is that the theory is only tested as a whole (and under suitable idealisations). No fundamental hypothesis is ever tested in isolation. What scientists do is build models from all the fundamental hypothesis taken together and confront them to empirical data.

So one can say that the fundamental principles of the theory are never tested directly. After all the fact that the empirical consequences of the theory are true doesn't mean that the theory itself is true. The principles could well be false, while only the empirical consequences of the theory would be true. The principles would be mere convenient tools for building models and making predictions more easily. This view is entertained by empiricists.

This is also true of more metaphysical or methodological principles underlying the theory (atomism, reductionism, causality...), or for example the conservation of energy, which are never tested directly. And I think this applies well to your example of unifying two different theories (although their combination might yield new empirical consequences). The fundamental principles of a theory look very much like the unifying principles you're refering to: a good theory merely unifies disparate observational regularities.

However all these hypothesis contribute to the models or their application and are tested indirectly. If you were seeking hypothesis which do not contribute whatsoever to any empirical test, you'll probably won't find any because then they are superfluous and should be eliminated.

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You might want to have a stricter definition of non-empirical. For example string theory makes statement that cannot currently verified by any experimental method (and is a prime example of a theory T that combines two theories, A and B, with A being Quantum Mechanics and B being General Relativity). But the consensus among string theorists is that sometime in the future, either the technology available or the theory itself will advance enough for us to be able to test it.

I think this might be an assumption not just in science, but even in some branches of metaphysics, that sometime in the future these theories will have advanced enough and so will technology that we will be able to test them.

Democritus' atomism certainly seemed non-empirical when he first came up with it, but nobody would dispute it's empirical nature now.

So you would have to separate "currently non empirical claims" vs "absolutely non empirical claims". I wonder what would be an example of the second category?

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Yes! Scientific theories include important "non-empirical claims"!

You might want to distinguish between different types of "non-empirical claims" that come up in science:

  • Conventions or stipulative definitions
  • Non-observable entities
  • Idealizations

Many claims about non-observable entities (unobservables) can, and indeed are, empirical. Other answers have already given more examples, so I won't go into more detail.

The nature of "non empirical claims" in science is a thorny matter. It was only in the 19th century that philosophically inclined scientists and mathematicians started to appreciate the role that analytic statements play in science.1

Far from being a collection of synthetic statements (empirical generalizations, etc.), advanced scientific theories contain important analytic statements.

Pierre Duhem, Henri Poincaré and Édouard LeRoy stressed the analytic part of scientific theories, discussed its constitutive role and argued the importance of this part for the very concept of a scientific theory. They are known today as philosophers in the tradition of conventionalism. Many of the examples quen_tin gives in his answer where "discovered" by them.

Yet they disagreed on many aspects, in particular:

  • Is the division between analytic and synthetic statements absolute or not? Can one and the same scientific statement be analytic or synthetic relative to how it is employed? (This was in particular a discussion about the empirical or analytic character of scientific laws, arguably a very important class of statements in a scientific theory.)

  • How are analytic statements justified in scientific theories?

  • How far does the analytic character of scientific theories go?


1 Not in the sense that scientific theories are expressed in the language of mathematics, which is (mostly) thought to be analytic.

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Scientific method assumes the principle of induction by simple enumeration (IBSE); but the principle itself cannot be proved empirically.

IBSE is fallacious, but is simply assumed in science: Any theory that does not contradict observations is valid. Given a finite number observed occurrences, infinite number of theories are valid; with each additional observation, infinite number of theories are invalidated, but at the same time, infinite more become possible. This is why scientific outlook must be tentative, subject to revision based on new evidence.

Among infinite number of theories, it is Occam's razor that helps us select one out of many. But what exactly is called simple is rather vague. In the theoretical community, people are actually making do: Everything is tentative. For a given set of observations and a sufficient theory, neither the theory nor "the entities" implied by it are necessary. The only reason that makes a theory acceptable is that the theory does not contradict observations. And infinite number of theories are acceptable for a given set of observations: this is a feature of inductive reasoning.

Philosophical scrutiny only increases doubt.

In Human Knowledge: its scope and limits, Bertrand Russell scrutinized IBSE and traced a priori assumptions further back. He suggested that "the postulates required to validate scientific method may be reduced to five." They are:

a. The postulate of quasi-permanence.

b. The postulate of separable causal lines.

c. The postulate of spatio-temporal continuity in causal lines.

d. The postulate of the common causal origin of similar structures ranged about a center, or, more simply, the structural postulate.

e. The postulate of analogy.

Source: Russell, Bertrand. Human Knowledge, Its Scope and Limits. New York: Simon and Schuster, 1948

  • Interesting, I'll check the source. I always like a bit of Russell, though never read him fully. – The very fluffy Panda Mar 2 '15 at 21:32
  • @PandaBear: Given a finite number of dots, there are infinite number of curves that can connect them. Replace dots with observations, curves with theories. – George Chen Mar 2 '15 at 21:36
  • That is bit of a stretch. I somewhat understand the analogy, but isn't that just a purely theoretical possibility? Are there any practical examples of this type of undertermination? – The very fluffy Panda Mar 2 '15 at 21:40
  • If you've never heard of 插值, then you are probably not a Chinese. en.wikipedia.org/wiki/Interpolation – George Chen Mar 3 '15 at 0:01
  • That was standard college stuffing. – George Chen Mar 3 '15 at 0:04
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Science does not need to postulate existence of anything. Science is the job of making predictions, going from one set of observations to another. Anything in between is just math or conceptual relationships. "Existence" has been going out of style since at least quantum mechanics, in particular Einstein's "elements of reality" in the EPR paper , Bells inequalities and it's offspring. Controversial perhaps, but in terms of your question science can't make claims that aren't empirical since predicting some set of observations is by definition empirical.

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