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Nonphysical entities cannot be observed. Therefore such entities cannot be verified by observation. How could statements like "God exists" be even considered true? Why would anyone appeal to the metaphysical realm at all?

It seems to me that the best method by which we should go about in understanding the world is by initially ruling out the possibility of the metaphysical altogether for the simplest answer (a sort of null hypothesis). Once we can get a hold of a natural cause of some phenomenon, we should be satisfied that that is all there is to it. Formulating some nonphysical cause would be unnecessary, superfluously complicated, or even cluttered. Now if there was some problem that we were certain could not be solved by observation or experimentation or whose solution could not possibly exist in the observable realm, yet must be true, I would consider the possibility of a metaphysical cause.

That said, I don't think that if you can't empirically observe something, it doesn't exist; rather, I would declare total agnosticism and say that it is unknowable.

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Bacteria and viruses are not observable to the human eye; but they are through a microscope.

Atoms are not observable to the human and nor through an optical microscope but they are made visible via an electron tunnelling microscope.

The first extension of sight is via a means that is natural, the second though relies on our knowledge of how we interpret the world of the small.

What we both know and see is theory-laden; there is theory that is natural to us - it's part of us, there is also theory that is inferred; we might say its super-natural being over and above that which is natural.

The Isha Upanishad has something interesting to say about this:

Pin your faith to natural knowledge, and stumble through the darkness of the blind

Pin your faith to supernatural knowledge and stumble through a darkness deeper still.

Both kinds of knowledge is natural to human beings; both kinds of knowledge and understanding have been part of human thinking from the beginning; and as it has been in the past, so it is in the present, and also the future; human beings, move from one kind of knowledge to the other, not in any simple way, since the relationship between the two is vastly complex, as Hegel points out in his Phenomenology: Sense-Certainty is only the beginning, being immediate to us as also affirmed by Al-Ghazali (The Sense-Judge and Reason-Judge) and Descartes (his cogito).

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Nonphysical entities cannot be observed. Therefore such entities cannot be verified by observation. How could statements like "God exists" be even considered true? Why would anyone appeal to the metaphysical realm at all?

What you are describing here is the position known as positivism, which later evolved into logical positivism (also know as logical empiricism). One of the earliest and most famous formulations such a position was given by David Hume, in what became known as Hume's fork:

If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: For it can contain nothing but sophistry and illusion. -- David Hume, An Enquiry Concerning Human Understanding (1748) Section 12 : Of the Academical or Sceptical Philosophy Pt. 3

The Logical Positivists continued Hume's position, and were famously anti-metaphysics, which they considered to be a derogatory term. For them, the only statements that had any meaning were those that could be verified empirically, or analyzed using logic See the SEP article on Logical Empiricism - Section:4.1 Empiricism, Verificationism, and Anti-metaphysics, and the following quotes by notable Logical Positivists A.J Ayer and R. Carnap:

The criterion which we use to test the genuineness of apparent statements of fact is the criterion of verifiability. We say that a sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express — that is, if he knows what observations would lead him, under certain conditions, to accept the proposition as being true, or reject it as being false. -- A.J. Ayer , Language, Truth, and Logic, p. 16.

And

According to this view, the sentences of metaphysics are pseudo-sentences which on logical analysis are proved to be either empty phrases or phrases which violate the rules of syntax. Of the so-called philosophical problems, the only questions which have any meaning are those of the logic of science. To share this view is to substitute logical syntax for philosophy. -- R. Carnap, Logical Syntax of Language, p. 8

For the logical positivists, the end result such reasoning is that Philosophy should be just a linguistic tool to help analyze the statements coming from empirical sciences. Questions of metaphysics, philosophy of religion, etc,..but also of ethics (per your original question, ethical principles are also unobservables), aesthetics, etc...are strictly speaking, non-sense. See also A.J Ayer's emotivism.

A major problem with such a position is that it is self-defeating. Consider Hume's statement about throwing away anything that isn't either logic or empirical science: By his own reasoning, his own book "An Enquiry Concerning Human Understanding" should be itself committed to the flames.

Alternatively, we could state this problem in Logical Positivist terms:

The above mentioned statement by A.J Ayer

"The criterion which we use to test the genuineness of apparent statements of fact is the criterion of verifiability."

itself fails the criterion of verifiability -- there is no way to verify such a statement.

This points to a larger problem that Logical Positivists faced, and that is the fact no matter how hard one tries, it is impossible to completely separate empirical statements from the theoretical presuppositions they are based on.

As Mozibur Ullah mentions in his answer, everything is theory laden (see this post and answers within). W.V.O Quine, who considered himself a Logical Positivist who had worked with Carnap and Ayer, pointed out this problem of the Logical Positivist stance, and also offered a pragmatic solution out of the problem with his confirmation holism (a pragmatic view of science: science is a useful tool that works, religion and other forms of metaphysics aren't) in his 1951 paper "Two Dogmas of Empiricism", which he concludes with the following statement:

As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer . . . For my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing, the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conceptions only as cultural posits. (emphasis mine)

Finally, I don't have references or quotes to back this up, but another argument in defense of studying metaphysical unobservables is the following:

  • Democritus' atoms were definitely unobservable metaphysical objects back in his day. Yet the atomic theory of matter is firmly grounded in observable physics now. If we were to subscribe to a logical positivist stance, we would be depriving ourselves of useful metaphysical exploration that might lead to future developments in science.
  • All right. Besides my positivist stance, what of my proposed null hypothesis? I think my original questions could count just as well without the positivist language. Also, could atoms really have been classified as metaphysical? If atoms are in the world, that would mean that they are definitely not metaphysical. I'm guess I'm fine with postulating that what might be metaphysical now could be natural and researchable in the future. I'm just suspicious of positing the existence of a purely, absolutely metaphysical entity like God. – cortez1403 Mar 26 '16 at 17:01
  • @cortez1403 atoms and gravity waves seem less metaphysical now only after the fact. Consider a 17th century layperson, for whom the concept of microscopic atoms that could trigger city sized explosions or of mysterious invisible forces tying the earth to the moon were just as fantastically metaphysical as gods or angels. I'm not defending the existence of the latter (I don't believe in any), I'm just showing per the text quoted from Quine, that is impossible to draw the line between "reasonable" unobservables and "unreasonable" unobservables a priori. – Alexander S King Mar 28 '16 at 23:01
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So, there are three approaches I've seen (that one is free to disagree with!):

  1. Arguments from internal experience. These arguments attempt to show the metaphysical by appealing to one's internal dialog. As one example, CS Lewis makes an argument like this in Mere Christianity: by appealing to our emotional state and how we react internally to slights, he reasons that there must be a Natural Law.
  2. Arguments from reason. There are a few of these (eg: God as the first mover), but they all take the form of extrapolating the existence of real metaphysical objects from what we can observe about our normal, day-to-day existence.
  3. History/Divine Revelation. As one example: Christians believe that God is observable, and that He humbled Himself to become man, and that he died on the cross, and then was bodily resurrected. For Christians, belief in God is a consequence of a historical fact that was observed and communicated.
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I completely agree with your diagnosis. Notably your proposal to start with as less metaphysical assumptions as necessary is convincing. The consequent implementation of your approach is building worldview simply from natural science.

How would you know if nonobservable entities exist?

You cannot know whether non-observable entities exist. One can speculate about them, e.g., currently about multiverses.

But sometimes one can introduce non-observable entities as hypothesis, cf. the atom hypothesis in the time from Democritus until the end of 19. century. Possibly a later time detects the existence of previously unobservable entities.

How could statements like "God exists" be even considered true?

I think the wish was father to the thought.

The domain of gods is a screen of projection. Often these projections are anthropomorphic. In Europe this insight has been uttered the first time by Xenophanes (6./5. century B.C.E.) in fragment B15.

Why would anyone appeal to the metaphysical realm at all?

The first attempts to explain the world around are not due to science, based on observation, experiment, and mathematics. The first attempts are speculation and metaphors taken from every-day experience.

In Europe metaphysics started with Plato and notably with Aristotle’s lecture notes, later named “Metaphysics”. It is the attempt to find fundamental principles valid for all sciences.

Science knows it boundaries. But human thinking likes to go beyond all boundaries, not only concerning questions, but also concerning answers. On the opposite, science accepts that today not all questions can be answered. Hence questions must be left open and answers must be postponed to future generations.

Caveat: I expect that your position and my answers to your three questions will be criticized by several participants from the philosophical and religious fraction. But I will not anticipate their objections. :-)

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The very definition of non observable tells you that you can't know if something non observable exists! However, we have the capabilities of deduction, induction, and logic. With these capabilities, we are able to infer the existence of "something" by its effects.

Lets say we detect some "effect," then we try to find its cause. If we are able to detect some cause, then we can confidently say that the "cause" exists. If we are unable to find a cause, we can still infer that something must exist that caused the effect, even though it is - non observable.

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The interesting question arises when one of your statements is called into question:

Once we can get a hold of a natural cause of some phenomenon, we should be satisfied that that is all there is to it.

Sometimes there's more to a phenomena than simply understanding the general forces that caused it. To give a very concrete example, I'd like to turn to cryptography. In particular, public key encryption. We can define the "natural" behavior of the RSA encryption method in terms of two keys, Key_public and Key_private. I can give you a Key_public and say "There is a Key_private such that any message encoded with Key_private can be decoded with Key_public." That's just the natural behavior of RSA. It's defined within the math. You can "get ahold of the natural cause of that phenomenon" with a small amount of math.

Now, I don't think it's extreme to say that there is a big difference between knowing that "natural cause" and actually knowing what Key_private is. In practice, knowing what Key_private is is actually quite a big deal. If you could know Verisign's private key, you could wreak quite a bit of havoc.

So this suggests that there is more to satisfaction than just knowing the causes. We also need to know the state of the universe that is being affected by these natural causes. Unfortunately, the empirical approaches humans have today cannot fully know the state of the universe. Every approach leaves unknowns in its wake, and they will continue to do so until someone discovers the meaning of everything (or disproves its existence). As an example, science runs into very interesting conundrums when their observer cannot observe systems without perturbing them.

If I may make a claim without a justification, the supernatural tends to do a better job of describing things close to one's "self." The way it handles the unobservable tends to be rather helpful for dealing with the unobservable nuances of one's own self. This is important for the rational result you are asking about: a reliance on supernatural claims would be rational if the rational entity could argue that the belief in those supernatural claims is valuable enough to warrant using non-empirical approaches to arrive at their decisions. You will find, hidden deep in that sentence, a self-referential phrasing: "the belief ... is valuable enough." Such self-referential phrasings show up quite often in places where more methodical approaches falter.

Another approach, which limits the need to explore self-referential issues, is to suggest that you don't need to know nonobservable entities exist to find it valuable to believe they exist. There are some cases where the cost of learning a law is simply too great.

Consider a case involving your only child. They are eying a thin beam over a deep crevasse. Protective instincts surge over you and you state, "Get away from that! You'll fall and hurt yourself." Did you actually mean the second sentence? It is well recognized that children will accept a statement issued with confidence more than they will accept one which accepts the possibility of being wrong, so you can maximize your value better by appearing confident. However, faking confidence is not an easy skill. It may be more valuable to actually believe your child might fall than to try to fake such a confident belief.

Likewise, consider the case where the child got half way out across the narrow beam before their confidence began to falter. You encourage them from the other side with, "Come on! You can make it!" Did you actually mean the second sentence? By the same rules as before, you can maximize your value by appearing confident, but faking it is difficult. Thus, it is in your best interests to actually believe you child can make it.

In both cases, the belief is of an unobservable. You have never seen your child fall into a crevasse. In fact, you've never seen them deal with this particular crevasse with this particular wind condition. You don't have a model of what your child will do. You cannot observe the information you need, because you only have one firstborn child (if the solution is to sacrifice the first one to science and then have another, I dare you to suggest that solution to a parent. Get a head start :). Yet, in both cases, there is value in believing a statement about the child's future, regardless of whether it can be observed. It is even possible to show that it can be valuable to believe the child can make it, or the child will never make it, in different circumstances!

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You would not know if non observable entities exist. There are no such things. (If so, show me one.)

My rationale: Any effect, to be known about, must be observed, even if its cause is yet unknown.
But each effect has a cause.
Thus, 'non observable' must also mean that no effects have occurred or exist.
No effect means no cause.
No cause means no entity.

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