The Nature of Objective Reality

The Nature of Objective Reality

There is a fashion nowadays for a school of thought variously called “post-modernism” or “cultural relativism”, which claims that there is no such thing as objective reality, and that theories of objective reality (i.e. science) are nothing more than “cultural constructs”. This Essay will attempt to prove that such claims are logically inconsistent, and hence they cannot be true.

What Is Objective Reality?

Let me propose my definition of objective reality:

Definition 1: Objective reality is whatever remains true whether you believe in it or not.

Many people may claim that the above definition is insufficiently precise, or perhaps even circular: for instance, what do you mean by “true”? And what do you mean by “believe”? For that matter, what do you mean by “mean”?

For the purposes of my argument, ultimate precision in the meanings of the terms is not important—their common, everyday meanings, with their common, everyday precisions, are good enough. In mathematics (and engineering), there is the concept of sensitivity analysis: a result is often more crucially dependent on certain input parameters than on others, so more imprecision can be tolerated in the less crucial parameters. Later on, I will give a sensitivity analysis to demonstrate that the truth of my argument is not crucially dependent on the precise meanings of any of the above terms.

Another point is that I will be using the terms “objective truth” and “objective reality” completely interchangeably: as far as I’m concerned, what’s true is real, and what’s real is true.

Proof of Objective Reality

This proof is about giving a definite answer to the following question Q:

Q: Is there such a thing as objective reality?

Objective realists would say that the answer A to question Q is:

A1: Yes.

while the cultural relativists would say that the answer is:

A2: No.

So let us ask the meta-question Q':

Q': Is there an answer to question Q?

To which both objective realists and cultural relativists would agree that the answer A' is definitely:

A': Yes.

All parties must be united in accepting that this answer is objectively true, not a matter of someone's individual or cultural belief, for if they did not, then there would be no basis for their dispute. Therefore answer A' is itself an example of objective reality—something that remains true whether anybody believes in it or not. Therefore the answer to question Q is A1 (yes)—there is such a thing as objective reality.

That, in a nutshell, is the basis of the proof of objective reality. But some may argue that the above conclusion is too pat. What if there isn’t a definite answer to meta-question Q'? So now we have a dispute over the answer to meta-meta-question Q'':

Q'': Is there an answer to question Q'?

to which the objective realists say the answer is “yes”, while the meta-cultural-relativists say the answer is “no”. However, all have to be in agreement that the answer to meta-meta-meta-question Q''':

Q''': Is there an answer to question Q''?

is

A''': Yes.

which itself becomes an example of something objectively true, from which the answer to the original question Q is again A1 (yes).

It is clear that the above sequence can be extended ad infinitum: the objective realists always answer “yes” to every question, while the metan-cultural relativists (n = 0, 1, 2 ...) answer “no” to the first 2n+1 questions, and agree with the objective realists thereafter.

Objections to the Proof

What Do the Terms Mean?

I promised above that I would present a sensitivity analysis to demonstrate that the validity of my proof is not crucially dependent on the meanings of any of the terms used in Definition 1.

Let us assume that some reader of this Essay (let us call this individual “A. Reader”) uses some definitions of one or more of the terms used in Definition 1 such that my proof is invalid. For the purposes of this argument, it doesn’t matter what those definitions are, how different they are, or how exactly they result in the proof becoming invalid. In all cases, we can simply sum up the conclusion of A. Reader’s argument as follows:

Hypothetical Refutation 1: A. Reader uses definitions of one or more of the terms mentioned in Definition 1, perhaps together with variant forms of logical argument, that render the objective-reality proof invalid.

In order for this to be a valid objection, it must be objectively true. It shouldn’t matter whether or not I believe that A. Reader uses such definitions or forms of logical argument; it must be true regardless. (After all, if it were possible for me to invalidate the refutation simply by disbelieving it, then I do.)

It follows from this that Hypothetical Refutation 1 itself becomes an example of objective reality. Which means there is such a thing.

The Law of the Excluded Middle

My proofs rely heavily on the reductio ad absurdum technique—that is, assume a proposition is false, show that this leads to a contradiction, therefore the proposition must be true. Implicit in this is what’s called the “law of the excluded middle”—that is, if a proposition can be shown not to be false, then it must be true, and vice versa. But some people might object: “what if the law of the excluded middle is not valid?” To which I have only this to say: even if the law of the excluded middle is not true, that doesn’t mean it’s false.

Alternative Logics?

The law-of-the-excluded-middle objection is just one of a family of objections based on the idea that there are other kinds of logical reasoning besides the traditional, two-valued, either-true-or-false kind that I have used in my proof. And under these alternative kinds of reasoning, it is claimed, my argument might not necessarily be valid.

Trouble is, these objections are all based on a fallacy. To expose the fallacy, consider the following question:

Question L: Are there other kinds of equally valid logical reasoning besides traditional two-valued logic?

Now, those who believe in the validity of multiple kinds of logical reasoning still think of the answer to this question as either yes or no. That is, either it is, or it isn’t, valid to reason in other ways besides that of traditional two-valued logic. It’s got to be one or the other. Thus, even when reasoning about alternative forms of logical reasoning, there is still a special reliance on two-valued logic. No matter how you try to argue otherwise, you cannnot escape from the fact that two-valued logic is more basic, more fundamental than any other kind of reasoning—that it in fact underlies all other forms of reasoning.

To put it another way, consider the difference between logic and mathematics. Mathematics is about exploring the consequences of axioms: given a set of axioms (starting assumptions), which are accepted without proof, a mathematical theory is built by following the chains of deduction that follow logically from those axioms. Different mathematical theories are built from different axioms: thus, the theorems of topology are very different from those of geometry, which are in turn different from those of number theory, and so on.

But regardless of the different axioms which are used as starting points, all mathematical theories are built by following the same kind of logical reasoning. In order to be universally applicable, this logical reasoning must be independent of any particular axioms—otherwise, it could only be used to build certain mathematical theories, but not others.

Thus, the difference between logic and mathematics is that mathematics is always built on axioms, but logic is not. And so those “alternative logics”, which are supposedly built on different starting points from conventional logic, are not really logics at all, but are mathematical theories. True logic has no axioms.

No Logic At All?

This would seem to be a fatal objection: how do you know that logical reasoning is valid at all? Aren’t you simply assuming that it is so?

In fact, it is possible to prove that logical reasoning is valid, in a non-circular fashion (that is, without having to assume that it is valid to begin with). Here is the proof:

  1. Assume that logical reasoning is invalid to begin with.
  2. Since logical reasoning is invalid, it follows that illogical reasoning is valid.
  3. Therefore, since logical reasoning is invalid, it must illogically follow that logical reasoning is in fact valid.
  4. QED.

Note that any attempt to poke logical holes in this proof implicitly assumes that there are logical steps that I am not correctly following. In other words, all objections must themselves be based on the assumption that logical reasoning is valid.

Did I Slip Up Somewhere?

What if I made a mistake in the proof? That is, your definitions of terms and forms of logical argument are sufficiently congruent with mine, but I slipped up in applying them somewhere? Let us consider:

Hypothetical Refutation 2: There is a mistake or gap in the proof that renders it invalid, or at least lacking in rigour.

The same reasoning applies as with the previous objection: this mistake must objectively exist, not simply because somebody believes it is there. In which case, we reach the same conclusion: the Hypothetical Refutation itself becomes an example of objective reality. Which means there is such a thing.

More Than One Reality?

This objection is a little more subtle, and deserves discussing at greater length.

Let the number of possible objective realities be N. I have proven that N cannot equal zero, but does that mean it has to equal one? So let us consider the proposition:

There is more than one objective reality.

Now, what does it mean for there to be more than one objective reality? Let us define an “objective reality” as “a collection of statements which are true in that reality”. So what does it mean to come up with more than one collection of such statements?

Given any collection of more than one such statements, you could easily construct another such collection by leaving out one of those statements. Let us ignore such subset realities, and consider only maximal ones, that contain all the true statements they can contain, and are not subsets of any other reality. For if the only way to come up with different realities is by subsetting, then there must be one ultimately maximal reality that contains all the others, and the others are simply incomplete versions of this reality.

Clearly, then, the only possible difference between two different maximal objective realities is that they must disagree on the objective truth of some statement. Consider two of these objective realities, R1 and R2, and the statement S, such that

Statement T: Statement S is demonstrably true in reality R1, and demonstrably false in reality R2.

Aside: It is true that not every statement may be demonstrably true or demonstrably false. This doesn’t matter. For suppose that statement S is demonstrably true (or perhaps demonstrably false) in reality R1, but cannot be shown to be definitively true or false in reality R2. Then we simply construct the statement:

Statement S': Statement S is demonstrably true (or demonstrably false).

and statement T simply becomes “Statement S' is demonstrably true in reality R1, and demonstrably false in reality R2”. In other words, every statement about a difference between two objective realities can be put into the original form we have given for statement T.

Before proceeding any further with the consequences of statement T, let’s ask a more fundamental question:

Question H: Can different objective realities contain true statements about one another?

Before we even try to answer this question, consider this: to which objective reality (or realities) does the answer to question H belong? Clearly, whichever one (or ones) it belongs to does contain at least one true statement that applies to the others (namely, the answer to question H). Therefore the answer to question H must be “yes”.

Is it possible for different realities to disagree about the answer to question H? Consider an objective reality called RX, in which the answer to question H is “no”. In other words, “no objective reality can contain a true statement about another”. But this is a true statement, within RX, that applies to realities other than RX! In other words, the statement contradicts itself.

Therefore, the answer to question H must be “yes” in all objective realities.

Now, another, slightly more tricky question: is it possible for one reality to contain false statements about another?

Remember our statement S, which was demonstrably true in reality R1. Is it possible for another reality RB (possibly the same as R2, possibly a different one) to contain the following statement?

Statement I: Statement S is false in R1.

But an objective reality is a collection of true statements—the only way we can distinguish one reality from another is by which statements are true in one but not the other. If all the true statements are the same, then the two realities are the same. Thus, if RB contains the above statement, it can’t be referring to R1, but to a different reality.

To make this clearer, the name “R1” is simply a shorthand for referring to the set of all statements which are true in R1. Thus, the expansion of this name looks like

{ ... Statement S is true; ...possibly other statements ...}

Or, substituting this expansion into statement I, we get:

Statement I: Statement S is false in { ... Statement S is true; ...}.

which is clearly a contradiction.

Now come back to our original statement, and consider the question: in which reality or realities is statement T true?

Clearly, it must be true in both R1 and R2. The first half, “statement S is demonstrably true in R1”, must be true in R1, otherwise that reality contradicts itself. The second half, “statement S is demonstrably false in R2”, must also be true in R1, otherwise R1 would contain a false statement about R2, and we have already shown that this cannot be. A corresponding argument applies to the two halves the other way round for R2.

In fact, statement T must be true in all realities. For in any reality R3 (distinct from R1 and R2), the first half must be true, to avoid containing a false statement about R1, and the second half must also be true, to avoid containing a false statement about R2.

Which leads to quite a powerful conclusion:

Theorem D: for any disagreement between two objective realities, all realities must agree on what that disagreement is.

So what is there left to disagree on?

To try to answer this, apply the following transformation to each objective reality: take the true statements comprising that reality and qualify them with its name. So for example the statements comprising R1:

{ ... Statement S is true; ... Statement T is true; ... }

become

{ ... Statement S is true in R1; ... Statement T is true in R1; ... }

And similarly R2 becomes

{ ... Statement S is false in R2; ... Statement T is true in R2; ... }

But if we substitute the definition of statement T, R1 becomes

{ ... Statement S is true in R1; ... Statement S is false in R2; ... }

while R2 becomes

{ ... Statement S is false in R2; ... Statement S is true in R1; ... }

which looks like they start to resemble one another, doesn’t it?

In fact, by Theorem D, for every point on which two objective realities disagree, all objective realities must contain exactly the same set of true statements spelling out what that disagreement is. While for points on which they agree, they obviously already contain the same set of statements spelling out those points. From which it follows that all objective realities must consist of exactly the same set of true statements. So the only difference between them is in their names, which are arbitrary anyway.

Thus, there is in the end only one objective reality.

Conclusions

To sum up:

  1. There is such a thing as objective reality.

  2. There is only one reality: a statement cannot be true in one reality and false in another.

  3. The proof I have given of the above is not merely an existence proof: it is a constructive proof, giving one or more examples of statements that are objectively true.

Where Do We Go From Here?

I will be the first to concede that not all of objective truth is as easy to uncover as the examples given above. We can’t always be sure whether something is objectively true or not. But that in itself is an objectively true statement! So we can sometimes be sure.

Even so, we often make mistakes and come up with wrong answers. But we only know this because we later discover the right answers! Thus, the pursuit of objective reality is a convergent process: it does get closer to the truth over time, rather than simply going around in endless circles, like that ultimate in cultural constructs, the fashion industry.

Some people accuse scientists of arrogance: “Who says Science has a monopoly on the truth?” they ask. “There are other ways of knowing besides Science”, they claim.

In fact, I like to turn this the other way round: if you come up with a new way of knowing (as opposed to merely believing), then it is worthy to be called Science. All you’ve got to do is prove that it works—that the truths you think you’ve uncovered can in fact be verified by others.

As human beings, we are notoriously prone to making mistakes. But another well-known human trait is that we find it easier to notice other people’s mistakes than our own. Science depends on this as a powerful tool: to get other people to accept your ideas as true, you have to show them all your reasoning, so that they can check it for themselves. If a fact is true for one, it is true for all.

Or, to put it another way, Science teaches us that nobody has a monopoly on the truth.

Exercises for the Reader

The essence of the proof is that any statement about objective reality, in order to be objectively true, must apply equally validly to itself. This technique can be used to uncover the illogic behind many other commonly-uttered statements. For instance, try applying it to uncover the fallacies behind the following:

Nothing is impossible.

Nothing is completely certain.

Everyone’s entitled to their own opinion.

Created 2000 March 27 by Lawrence D’Oliveiro <ldo@geek-central.gen.nz>, last updated 2002 September 22.

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