On the Impossibility of Objective Scientific Truth

I can imagine the title of this blog post to be polarizing. I can understand and appreciate why. There are many reasons, and I feel that I can address each of them accordingly, however the scope of each fall far beyond what I am willing to communicate in a given blog post.

It was Aristotle who said it was the sign of an intelligent man who can entertain an idea that he doesn’t hold to be true. With that said, let’s entertain an idea and see what comes from it.

As someone who has been so closely tied to science, sometimes I cannot get a good picture of what the general public’s view of it is. Likewise, people would ask me about the general public’s view of MMA. It was hard for me to answer. I thought I had an idea, but because I was so entrenched, it was hard for me to really get an idea what the lay persons view was. I had to make an effort to get an idea of what people think of science, and what scientists think of science and what the general view of what science is held to be.

Though science, as a concept, (in the same way that capitalism or democracy as concepts) could take on various forms and have different meanings, generally, I believe it is held to be a mechanism/process/methodology of acquiring objective truthThis objective truth is always of something, meaning truth is a predicate of something which we ascribe to. This objective truth is of nature, the universe, reality, the world, etc. It is of what is. Now, in order for there to be even a possibility of an objective truth of nature, the universe, reality, the world, etc, then there would have to be an objective truth. There is an objective truth to reality, the world, the universe, nature, etc. That is what is postulated by science and the scientific pursuit. The entire pursuit rests on this postulate, this belief, this hypothesis, this assumption. If there did not exist any objective truth to the universe, reality, the world, nature, etc, then this would be an untenable pursuit/methodology/ideology. 

(Though, I am not sure it would be a pointless pursuit, as the experience of scientific pursuit, though it might be an endless chase, it provides focus, meaning, structure, and clarity. It provides pursuit and aspiration, and this is an exercise of one of our greatest valued traits and qualities.)

We do not believe that science is without purpose, that it is not a vain pursuit, and that it brings truth into our body of knowledge, knowledge that guides our world views, our actions in the world and our beliefs on what is possible or not possible. We don’t believe this to be the case because we think that it can accomplish its task, and that it is accomplishing its task. We then must also accept, intrinsically, that the universe operates in an objectively knowable way. That must be a necessary belief in order to accept scientific knowledge to be possible.

I am lead to believe that whether intrinsically believed, or explicitly stated, most people would agree that science is about the pursuit of objective truth. Now, since this truth can only be communicated, it must be represented and communicated through language. No body of objective scientific knowledge can be known or knowable from introspection, from intuition or any personal, subjective manner, such as through a personal experience. Though the knowledge gained through personal experience might also match the truth of a unit of scientific knowledge, to say that it must be true (based solely on the personal experience without any previous knowledge, scientific or otherwise) would be wrong. I might have a personal experience that I feel is “objectively true” of something, and perhaps 10 or 100 years from now science will demonstrate it to be “true”, but this does not mean I can say I objectively knew, or that I truly knew about that “truth”.

The only way to personally arrive at and experience an objective scientific truth is to be the person performing, witnessing and interpreting the scientific experiment. All other members of the populace (of the entire world, and all throughout the future history of the world) who acquire that knowledge take it as an accepted truth of the universe, nature, reality, the world, and do so through learning. This learning is done through communication, and this communication can only be done through language.

So every piece of scientific truth is communicated through a truth statement. Grammatically, a truth statement (though the structure may differ depending on the language and form of language) is a sentence.

All scientific truth statements are communicated as/in sentences.

I will return to this later.

Now, we in our scientific pursuit of finding truth or coming to determine something to be true, we must have a means of doing so. We must have at our disposal a criteria from which we can judge something to be true or not true. Otherwise, we can never make the proper judgement of what is a scientific truth. So, there must be an objectively agreed upon definition/concept of what truth is. It must be objective, because if it was not, then the entire enterprise of arriving at an objective truth would not be possible. So, our criteria for judging whether a statement is true or not must be objectively true. But how can we do that? Would this not be a circular process? How do you get an objectively true criteria for judgement for what is objectively true?

But, in any case, we do have to decide on a criteria. Science as a methodology is not the criteria, rather, it produces data for the criteria. The criteria we use is based off of empirical data. The criteria, aside from convention, belief and aesthetics, is logical. It is either inductively reasoned to be true, or deductively reasoned to be true. Now, only one of these reasoning methods is necessarily true, while the other we induce it to be true, we say that it is true based on a finite number of past experiences which we infer to be representative for all the future. Deductive inferences are necessarily true (the 9 in the row of sudoku must be in that spot) while inductive inferences are not (I studied the effects of pesticide use on crops on mice for 8 weeks and since I see them to be “healthy” (what is my criteria again?) then I state that forever in the future, definitively, that the pesticides are safe).

Now, I will argue that in order for scientific knowledge to be true, then our scientific deductions, our scientific discoveries, our scientific statements must have then been arrived at through deduction. Inductive reasoning does not necessitate truth, so it is not a valid criterion for judging truth value. That is simply convention and belief (in a certain aesthetic preference).

In order to meaningfully say that we have a body of scientific knowledge that is true then these truth statements must have been arrived at through deductive means. In order for something to be deductively true, it must be necessarily true. Now, aside from a deductive argument in the case of mathematics and geometry, most of our scientific knowledge comes from the observation and interpretation of events/occurrences/phenomena in the world via experiments. How are we to deduce that the interpretation of the results, that the explanation given, that the results obtained are necessarily true, objectively, of nature? It seems to me that in order to arrive at necessary truth via empirical evidence and experimentation, one must arrive at every possible experiment, every possible empirical evidence and do this by testing every possible hypothesis. Once all competing possible hypotheses have been tested and refuted, the one left standing can be deduced to be true. If there is another hypothesis that has yet to have been tested, how can we say, necessarily, that the one that is held to be “true” is in fact true? And so all hypotheses, no matter how seemingly improbably or far-fetched, must necessarily be tested in order to validly state that any given scientific statement (knowledge) is necessarily true. 

So, in order for a hypothesis to at some point be removed of hypothetical status and be acquired as a true statement of the objective nature of the universe, of valid scientific knowledge, then all other possible hypotheses must be tested first and all are discredited/shown to be false.

If this is the case (and it appears that it is) then is it possible to arrive at a true empirical and objective scientific statement (i.e. model, explanation, paradigm, etc)? This seems like it might be an impossible task. There need not necessarily be an infinite number of hypotheses in order for this to be impossible, rather, there only needs to be just one more possible hypothesis. Always, just one more. As long as there is just one more hypothesis that requires our testing, then there can be no deduced true scientific truth statement.

At first glance it might seem intuitive that we could always pose another hypothesis, no matter how far-fetched it is. There could always be another possible means of explaining a process or empirical phenomenal experience. But can this be shown necessarily? 

In order to address this question, it can be approached from how science progresses.

The entire body of the pursuit scientific knowledge can be visualized and modeled as a tree (infinitely?) growing.

science tree

The trunk of the tree could be viewed as the set of all axioms, definitions, postulates, etc, that science is based off of. Some underlying assumptions of scientific knowledge have already been covered, such as that the universe is objectively knowable, and that we can arrive at that knowledge. Other assumptions would be cause-effect relations, mathematics and geometry, that nature is regular such that once we see a pattern in nature we can infer that the pattern will continue into the future, etc.

From these axioms springs forth our body of knowledge. Each unit of knowledge could be seen as a growth of the tree branch, a line in the diagram, or a sentence in the truth statement. Each unit of knowledge represents a hypothesis. A hypothesis might not be tested yet, and so no growth past that part of the tree, no extension of that scientific theory, can be made, until the hypothesis withstands verificationism/disprovability(I.e. the hypothesis stands up to scientific rigor). Some branches on the tree, some models and theories, will grow and then come to a stop. Some models can only go so far, and then they die, forcing a growth from a more initial part of the tree, a more basic and fundamental scientific truth statement. Sometimes scientific models and theories take wrong turns, and once determined to be wrong, the scientific community responsible for those models and theories have to take a few steps back and take a new direction.

Now, every hypothesis is a hypothetical truth statement. That is to say, it is a statement of hypothetical truth. The statement, in order to no longer be classified as a hypothetical statement and be considered a member of the class/set of all truth statements must be judged to be true, and as we have seen that can only be done through deduction (which is to say, by testing all other hypothetical truth statements first, i.e. testing all possible hypotheses).When the tree grows, it rests on the previous parts of that branch that it has extended from connecting it to the trunk (axioms) which provide it with nutrients (validity/means for being true). Just in that way, any hypothesis to be tested also takes all previously non-refuted hypotheses (i.e. currently accepted models/theories) into account in order for that given hypothesis to be possibly/plausibly true.

An example might be good. Let’s say for example any and all currently investigated hypotheses based on dark matter and dark energy. The truth value of any and all such hypotheses rest on the truth value of the hypothesis that there exists dark matter and dark energy. That is a hypothesis, as it has not been proven to be true. It has not been proven to be true because it has not been held up to deduction. It has not been held up to deduction because not every possible hypothesis to explain why mathematical predictions for the masses and energy in the universe (which rests on other hypotheses such as the universe being a closed system, the accuracy and truth value of our proposed laws, concepts of forces and geometry of the universe) do not match what has been observed empirically. Every hypothesis made rests on another hypothesis. It rests on it because it grows from the hypotheses that precedes it. Like a tree branch, the newest growth proceeds from the older branch. The older branch must remain alive in order for the newest segment to remain alive. A current hypothesis rests on an older hypothesis that has not been refuted. At any time a hypothesis is refuted, like a point along a tree branch, any further growth from that hypothesis (or tree branch) will also be refuted (die).

And so as more and more experiments are done, more and more hypotheses will be refuted (branches die off or stop growing). If we were to follow our visual model for the growth of scientific knowledge, then ultimately, a deductively arrived at empirical scientifically objective truth would look like a tree with a single branch on it. As all other branches would act as competing hypotheses, and they would all be refuted, necessarily, in order for there to be a single objective truth.

Now, each growth along the tree occurs in bursts. In the same way that a model or theory or knowledge in science extends by units. These units are single hypotheses. Each hypothesis is a statement of hypothetical truth, and thus, is a statement communicated in language. So, we can say that each hypothesis is a sentence.

So, if we model each hypothesis (aka potential truth statement within the body of scientific knowledge) as a sentence, then we can view each successive growth along that tree branch, along that hypothesis, as another sentence. Therefore, once the single branch is arrived at and modeled in language, it would represent to us a series of sentences about the truth of all scientific knowledge, which is to say, a complete theory/model/explanation of the universe/nature/reality/the world/etc. This series of sentences could be turned into a single sentence. Each sentence could be connected to the other in order to form a single sentence simply by ligating the two sentences via the use of the conjunction word “and”. So instead of having the following sentences: A. B. There would be the single sentence: A and B. Where A/B represent sentences of hypothetical truth value (hypotheses/scientific truth statements). This process could be continued such that the entire body of scientific knowledge was contained within a single sentence which contained within it each and every truth statement, conjoined together via the use of the conjunctive “and”.

If this is the case, then we must then consider the simple a priori truth that any and every sentence can be extended indefinitely. Each and every sentence can be extended by the addition of another “and”. This is exactly the same as saying that another hypotheses can always be posed. There is always one more hypothesis that someone can pose. In the same way, given any sentence, no matter how long or what the content is, it can always be extended with the use of “and”.

This sentence can be extended and it will continue and then it will get longer and it will end up being a run on sentence but it won’t matter because in the end it will still be one single sentence and that sentence can either be true or false and the truth or falsity of that entire sentence can be judged and so if it is found to be false then the entire sentence is false and if it is found to be true then the entire sentence will be true and if that is the case then that sentence will be true but if we extend from that true sentence another segment by adding and to it then that will form a new sentence altogether which has its very own truth value and then we will have to judge that new sentence for its truth value and and and and…

If that is case, then that sentence can increase indefinitely, as it can always be increased once more. Since every increase of the sentence represents a new hypotheses to be tested, then the extension of the sentence directly means an extension to the number of experiments that must be done (test of hypothesis). This necessarily means that there can always be one more experiment needed to be done in order to come to a deductive statement regarding the truth value of a scientific statement. If this is the case, then no deductive empirically scientific truth statements can be made. This means that science can never produce a single true sentence. This means that science cannot produce a single truth statement. This means that not a single scientific truth can be arrived at via deduction, through scientific experimentation (this does not necessarily dismiss mathematics and geometry, though that is a separate topic).

So. What does that mean? What meaning can we derive from this?

We started with the belief/assumption/postulate that science was in the business of arriving at objective truth statements. The experiments and results themselves are not the criteria for judging whether those results are true or not. Rather, we produce results and we must judge whether those results are true or not. The criteria of that judgement must be objective in order to maintain that science and scientific knowledge is objective. As Kuhn argued and as can be seen and experienced in the world, science progresses under convention, belief, aesthetics and some application of logic, logic being the sole basis for making scientific statements objectively true. The logic applied can be deductive or inductive. Since we are in the domain of truth, and not the domain of confidence or probable or anything short of necessarily the case, then inductive reasoning cannot grant us valid scientific knowledge. It is not necessarily true. Rather, we must use deductive reasoning.

A deductively arrived at explanation/model/theory must be necessarily true. In order for a single theory or model be necessarily true over every other theory or model, each and every possible model/theory must be tested, and all are found to be refuted except one. That single non-refuted theory/model can only then be accepted as true.

So in order to arrive at a deductively true scientific truth statement we must test all hypotheses (all theories and models of explanation). Every hypothesis rests on other hypotheses. No single hypothesis can be determined, by deduction, to be true, until all others are refuted. But since another hypothesis can always be posed, then there will always be another hypothesis to refute. Therefore it is impossible to truly arrive at an objectively true scientific statement. This is true only given all the definitions and assumptions and postulates that were put forward earlier. This truth statement is no different than a truth statement from science. The validity of its truthfulness must be judged based on a criteria, and must meet judgement.

I would be happy to see where the errors might be, but as of yet I am not yet aware of any. If we were to settle at any given scientific theory and decide to stop testing, we would necessarily have to stop hypothesizing as well. This would have to be something agreed upon, by convention. It would have to be an acceptance and perhaps an enjoyment and appeal to the aesthetic of the model/theory that science provides for the universe/reality/nature/the world/etc. But, logically speaking, it is always possible to pose one more hypothesis. So, science can arrive at something, but that is only based on non-objectively arrived at criteria such as aesthetics, belief and convention. Thus, the only “knowledge:” that could ever be arrived at via science would be belief/allegory/myth/folk lore, or a set of false beliefs (erroneous world views).

If you are satisfied with that argument you do not need to read any further. I will now approach this argument from a different method, one related to sets and set theory.

Let K be the set of all Knowledge. All the elements contained within K are all the knowledge in existence.

set k

Every single thing that we can determine/label as knowledge belongs to the set K. Knowledge of what I did yesterday for lunch belongs in K, knowledge of how I felt my bathroom renovations were finished is contained in K, and knowledge that for a triangle on a flat planar surface, the sum of the interior angles are equal to 180 degrees, while those of  a triangle on the surface of a sphere are greater than 180 degrees.

Now, we can group together some of those elements(units of knowledge) into separate sub-sets. We can call one sub-set, P, be the set of all personal/subjective knowledge (i.e. I have knowledge that I am hungry, that I need to brush my teeth, that I am going to do renovations today, etc). Let S be the set of all scientific and objective knowledge.

set s and p

Now, all of the knowledge, all of the elements within the subset P and the subset S are all contained within the greater parent set K. Some knowledge from P (personal/subjective) can overlap with that from S (scientific objective knowledge). This is visually represented by the area of overlap between the circles S and P.

Our current concern is science and scientific knowledge, and so we are only concerned with the elements contained within subset S. All elements within S are truth statements that convey scientifically derived objective truths. So, all elements within S are statements, and thus are sentences.

In order for a sentence to become a member of the set S, it must be found to be necessarily true via the methodology of science. This is to say, in order for a sentence to become a member of the set S, it must be necessarily true via experimentation. Again, as we mentioned above, in order for a scientific truth to be necessarily true (such as an interpretation, a model, a theory of science, an explanation) it must stand up to deduction. That is to say, that sentence can only be necessarily true if all other sentences (scientific explanations/hypotheses) have been refuted.

Let HS represent the set of all Hypothetical Scientific Truth Statements. All the elements/members of this set are all the possible hypotheses that can be posed. This set contains all possible hypotheses. Therefore, early on in scientific pursuit, it will contain many members (many possible hypotheses), but as experiments are carried out, and hypotheses are refuted and found to be untrue (not possible), then the set will have less and less members. This is the case because after a hypothetical truth statement is determined to be false, it is no longer a hypothetical truth statement and we can now classify it as a false statement.

Visually, we could represent this as such:

set e

We now have an even greater/fundamental set, E, the set of all sentences. Within E, the set of all sentences, some sentences belong to the set of all knowledge, K, (meaning true sentences) some sentences are hypothetical truth statements, HS, and other sentences are false and thus belong to the set of all false sentences, F.

It is clear that in order for there to be a member of the set S (scientific objective truth statements), this can only occur when there is only a single member/element in the set HS (hypothetical scientific truth statements). This must be the case because deductively, a scientific hypothesis/statement can only be necessarily true if all other possible hypotheses have been refuted and discarded. So, the inclusion of sentence (member) within S rests on the membership of elements (sentences) within the subset HS. If there are at any point more than one member (sentences) within HS, then there can not be any members (true sentences) within S. Once HS has only a single member (which is to say there exists only a single hypotheses (or sentence of hypothetical truth value) that has not been refuted) we can deduce that it must necessarily be true (again, assuming there is an objective truth to be found). Then, and only then, can we then re-classify that hypothetical truth statement (sentence) as a sentence that belongs to the set/class of scientific truth statements.

So, the existence of ANY elements/members within S, which is to say the existence of any scientific truth statements whatsoever, rests on there being only a single member within the set HS.

However, since HS represents the set of all hypothetical truth statements, and since truth statements are sentences we run into two reasons why this set will never be reduced to a single member. First, we can always produce one more sentence. We can always produce one more hypothesis. The existence of just one more hypothesis will leave the set HS perpetually with more than one member/element. Secondly,a priori we know that any sentence can be extended by the use of the conjunctive “and”, then every sentence can be extended indefinitely, and thus this new extension of the sentence must be tested as a new and unique hypothesis of its own. This requires one more experiment. Since we can indefinitely extend any and every sentence by the use of the conjunctive “and” then we will always have at least one more experiment to perform. Thus, deductively arriving at a single truth statement is untenable.

So, HS can never have a single member, and this being the case, S, the set of all scientific objective knowledge can never have any members. This means that there can be no objective scientific knowledge.

The only time HS can have a single member is if we consciously decide not to pose any further hypotheses. Since, logically speaking, there can always be more hypotheses to be put forward, it is always possible to pose one more hypothesis. However, it is not necessary. There is nothing forcing anyone from posing a new hypothesis. Therefore, the fate of the set HS arriving at a single hypothesis rests solely on the decision to pose a new hypothesis. This being the case, then the criteria in which HS is found to have a single member (and thus S has a member) comes when, via convention, belief and aesthetics, it is found that the single member of HS and thus S are satisfactory and no further hypotheses are warranted or wanted. Convention – because it must be agreed upon, whether implicitly or explicitly, not to pose a new hypothesis. This would occur when the current hypothesis/explanation/truth statement/sentence is deemed acceptable and no other is necessary. Belief – because though it is not known necessarily, the hypothesis/explanation/truth statement/sentence that is deemed acceptable is done so under the belief that it is true and will be true in perpetuity, and it explains the objective truth of all phenomena. Aesthetics – because we have to accept the hypothesis/explanation/truth statement/sentence as something that fits. It is something that we think makes sense of the world. Logic alone can not be enough for someone to accept something as true. In the face of a logically sound argument whose conclusion is unpleasant and unwanted (aesthetically unpleasing) people will try to find a way to disprove it or find a way to circumvent the logic. To accept the logical argument is to agree with the aesthetic of it.

Now, though there can always be more hypotheses to be posed, one can simply be happy/content with not asking any more. This, under the axioms, assumptions and definitions agreed upon within this system, is the only means for arriving at an objective scientific truth. Which is to say, the only way that objective scientific truth is to be arrived at is through convention, belief and aesthetics. Something that most people would agree is not science itself.

And so, for there to be any membership within S, necessarily, logically speaking, the member of S would not actually be an objective truth statement, rather, it would be one agreed upon by convention, taken on belief/faith, and found to be agreeable in its aesthetics. It is for this reason, as well as others(such as how paradigm shifts occur and how science progresses) that I contend that science is no different than any world view that we would classify as allegory/myth/folk lore.

But what do I know. If there are errors in my reasoning, I would welcome being shown them. But at this point, I am pressed to find them.