On Science

Empirical proposition vs Logical proposition

Empirical proposition (Synthetic truth):

1. All men are mortal

2. All objects follow the law of gravity

3. Humans are such and such.

Those propositions are called empirical proposition because there must exist some empirical evidence to support its validity. Hence, those propositions are all accidental and become truth by chance. Also you can never show that this proposition is true (you can only say that you have never seen any evidence that would reject the proposition) meaning you can only show them to be false. When you describe something about the world, the proposition becomes always empirical; therefore, there has to exist some actual correspondence which the proposition is referring to. Therefore, the empirical proposition that asserts something about the thing that does not exist in the world cannot be confirmed to be either true or false (in Kantian epistemological term, this is dialectic) because there is no actual correspondence to that which proposition asserts. If you say that all pegasus are white, it is senseless because the truth or falsehood of such proposition does not exist in the absence of the real correspondence. (Wittgenstein’s point)

Another weakness of empirical proposition is that it is extremely unstable to be used as a foundation of human knowledge. To demonstrate why, let me recall one example about the Black Swan.

Long time ago, in west, people had thought that all swans are white, so as an empirical proposition “all swans are white” gained certain degree of validity…until they discovered later on, as they travel around the globe, that there does exists a Black Swan!!! And in fact, it just took one evidence to kill the validity of this proposition!! This one instance showed the fallibility of the empirical knowledge and people have finally understood the unstableness of empirical propositions. Indeed, once a proposition is shown to be false by a single example, the entire validity of the proposition including the knowledge that built upon the false proposition will collapse!!

For example, Physics, Psychology, Chemistry, Biology, etc, all assert something about the world; therefore, they are all empirical proposition (hypothesis based) and the theory (or proposition) which does not agree with the evidence is ignored and dismissed as a false proposition easily! And even if it was found to agree with the evidence, one counter example is enough to kill the validity.

Those are the nature of empirical propositions.

Before we proceed, let me now summarize the weakness of empirical proposition.

1. Empirical propositions are always accidentally true. (i.e., it only holds the accidental general validity)
2. Empirical propositions always have to have correspondence to the actual world to confirm its validity. (i.e. it has to describe something about the world)
3. Empirical propositions are unstable because they are fragile and are susceptible to one counter evidence.

Let us now then proceed to the explanation of Logical proposition.

Logical proposition (Analytic truths):

1. There exists infinite number of prime numbers.
2. A v B, ~A > B. (A or B given that not A implies B)
3. (A v B, A > ~D ^ D) > B. (A or B given that A is D and not D implies B). A cannot be and not be D at the same time is called contradiction.
4. Any integer is a unique factorization of prime numbers.
5. For a^n + b^n = z^n, there is no solution for any integer n>=2. (Fermat’s last theorem)

Those are logical propositions. And to verify the truth of the proposition, you do not depend on the empirical evidence, meaning there does not have to exist an object which the proposition corresponds to in the world. For instance, number does not exist in the objective universe. It exists in human mind as a method to describe the countable discrete object — kind of analogous to our language in the sense that we need them to comprehend the world. It asserts nothing about the world because it is the tool to understand something about the world. Language is sort of like a game where there is rule as Wittgenstein said, and the general validity of logical proposition is guaranteed because their truth exists only by definition.

And all logical propositions follow from axioms. And axioms can be found by reducing our ideas or understanding to the level of irreducible, meaning you divide the understanding until it becomes indivisible, to the point of self-evident truth. Then, you hold this axiomatic proposition to be self-evidently true and use them as a foundation of all knowledge. For instance, one of the axioms of number system states as a proposition:

All non empty set with upper bound have a least upper bound.

This is self-evidently true because if you find something to be finite, there must exist a boundary to that thing. This axiom amounts to saying the same thing. If there exists a non-empty set with upper bound, there must have a least upper bound (least upper bound is a number in the upper bound of the set that’s closest to the set). Then, using this self-evident truth, mathematicians proceed to prove theorems which is far from self-evident. For instance, this particular axiom is used to prove all the of calculus.

Thus logical proposition stemming from the axioms makes itself valid on the concrete ground. And unlike empirical propositions, axiomatical knowledge does not have to concern about the actual existence of things which the proposition is supposed to correspond, as long as it exist by definition.

The validity of truth for the logical proposition however is said to be necessarily true.

Let me now explain what is meant by necessary truth.

Truth is said to be a necessary truth if the negation of a given proposition will lead itself to a self-contradiction. In other words, when it comes to the necessary truth, you have no choice but to hold it to be true (meaning you cannot deny that this proposition is true); therefore, the truth will be necessary in the sense that you can never deny it. If you deny it, you will contradict yourself.

Thus, logical propositions are all necessary truth and it’s unchanging and never swaying, which makes itself qualified to serve as a foundation of human knowledge.

Ever since we have found the fallibility of empirical knowledge, we have searched for the truth on which we can build other knowledge — such knowledge must not depend on inductions from empirical evidence but on the pure deduction from axioms. And so far, there has never been any scientific processes invented that can offer as much stability as the axiomatical approach. Thus, scientists have thought that we have the mechanism necessary to know about the universe.

To summarize, quickly:

1. Logical propositions do not necessitate the objective existence of things which the proposition asserts. Thus, true logical propositions do not have to depend on empirical evidence.
2. Logical propositions follow from axioms and self-evident truth.
3. Logical propositions makes itself true by definition; therefore, they are a priori.
4. All true logical propositions are necessarily true in the sense that in denial of it, you will be led to the contradiction.
5. Logical propositions can offer the stability which allows scientific development.

Let’s say you verified the truth and falsehood of all propositions. Then, once you aggregate all of the true Propositions, you create a complete picture of the world, meaning you successfully reconstructed the world in language and essentially in our understanding. Once we have that, we can claim that we have transferred the phenomenal world into our language (propositions) and humans will finally conclude its scientific endeavor. Thus, science is a describing activity and the process to verify the propositions either logically or empirically.

Empirical propositions can be thought of as a hypothesis which needs empirical confirmation, whereas hypothesis in logical propositions can be thought of as a proposition that needs a priori logical proof.

But to return to the definition of science, let me list out the things we have discussed:

1. Science is a describing activity in which we reconstruct the world in language by means of empirical or logical verification.
2. Aggregation of all TRUE propositions can allow us to claim that we understood everything about the world and the things that exist.
3. Empirical propositions are founded on the principle of induction therefore it is only probabilistically credible and sadly, it can never be shown to be necessarily true.
4. Logical propositions are necessarily true by definition but you can never confirm the actual existence of the things which asserts because of its a priori ground. (It has to embrace the fact that all of a priori knowledge MIGHT be just an inner human construct and that it can never have a NECESSARY correspondence to the actual world — Kant’s point.)

But human endeavor does not just end here. We have other means to answer other particular questions about the nature of things, such as good and evil, whether God exists, and so on. Such questions are treated as metaphysical propositions. What it means is that it asserts something about the world, but truth or falsehood of its claim cannot be confirmed neither empirically nor logically. However, it does not mean that we can never know and understand about such propositions. How to turn this situation around? Can we still use our human logic and this principle of induction to know something about that propositions? Sadly, the answer is No. Logic has its boundary just like our existence has its boundary.

In fact, at this point, it is safe to say we hit the boundary of logic there. In other words, our ability to be able to comprehend the validity of metaphysical propositions does not depend on logic and induction principle. Sorry to say but, the logic is bounded and is essentially quite useless when it comes to answering things about human nature or something that transcend our experience. Thus, we must depend on the other means to answering this questions, which we call is spirit and faith.

The elaboration of this topic will be discussed in my later article: On Religions. (still in the process of writing.)