What is the set of conditions under which a given knowledge can or cannot be acquired without testing (statistics) hypotheses?

Thoughts on different fields

Below is a list and definitions (and selected sentences of interest) of different field of knowledge and my opinion on whether it appears to me that the field in question is testing hypotheses to gather more knowledge.

Natural sciences

Natural science is a branch of science concerned with the description, prediction, and understanding of natural phenomena, based on observational and empirical evidence. Validity, accuracy, and social mechanisms ensuring quality control, such as peer review and repeatability of findings, are amongst the criteria and methods used for this purpose. (wiki)

In physics, chemistry, biology, geology (and other fields of natural sciences), it seems to me that acquiring knowledge can only be achieved through the statistical test of hypotheses.


Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),2 structure,3 space,2 and change.45 There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics

Mathematicians seek out patterns[9][10] and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. (wiki)

In Mathematics, knowledge is not acquired through testing hypotheses. I will note however, that any knowledge in mathematics is dependent on axioms that are assumed to be true. As natural sciences largely (or completely) depends on mathematics and of course, more generally speaking on logic, I think I could say that natural sciences also depend on axioms that are assumed to be true.


Psychology is the study of mind and behavior.1 It is an academic discipline and an applied science which seeks to understand individuals and groups by establishing general principles and researching specific cases.

Psychologists employ empirical methods to infer causal and correlational relationships between psychosocial variables. In addition, or in opposition, to employing empirical and deductive methods, some—especially clinical and counseling psychologists—at times rely upon symbolic interpretation and other inductive techniques. Psychology has been described as a "hub science",5 with psychological findings linking to research and perspectives from the social sciences, natural sciences, medicine, humanities, and philosophy.

In psychology, both hypothesis testing and other methods seem to be involved.

Applied psychology is the use of psychological methods and findings of scientific psychology to solve practical problems of human and animal behavior and experience.

Descriptive Geography

simply specifies the locations of features and populations (yahoo answer)

The only way I can think of descriptive geography as a field in which knowledge is acquired through testing hypothesis would be if we consider any possible set of characteristics of a given river as a given hypothesis in which, only the set that is observed is accepted. However, there is no statistical testing involved except for the evaluation of the characteristics of the river such as the measurement of the volumetric flow rate.


History (from Greek ἱστορία, historia, meaning "inquiry, knowledge acquired by investigation")2 is the study of the past, particularly how it relates to humans.3 It is an umbrella term that relates to past events as well as the memory, discovery, collection, organization, presentation, and interpretation of information about these events

History can also refer to the academic discipline which uses a narrative to examine and analyse a sequence of past events, and objectively determine the patterns of cause and effect that determine them (wiki)

There is a whole (and long) wikipedia article on the methods of inquiry in history: Historical method.

similarly to descriptive geography, I see history as a very descriptive science, for which I fail to think of it as a testing hypotheses. However I do recognize the use of statistical methods in history as described in the above wiki article (Historical method).


Ethics or moral philosophy is the branch of philosophy that involves systematizing, defending, and recommending concepts of right and wrong conduct (wiki)

I would doubt that much statistical testing would be involved in here.

6 Answers 6


Knowledge is typically defined with its roots in the definitions explored by the great Greek philosophers. SEP points out that the most common starting point is "Knowledge is Justified True Belief." For purposes of this question, the word "justified" is essential. Testing a hypothesis is a form of justification. Thus, your question might be what other forms of justification are there.

Of course, the answers are myriad. Religion knowledge is often justified without testing hypothesis, relying on other justification methods. Many martial arts include knowledge which could theoretically be traced back to millions of small tested hypotheses through one's career, but is typically justified in other ways. Knowledge of Self often comes without testing of hypotheses as well. Knowledge of Love also works this way. One does not find many arguments that you must test hypotheses to know if you are in love. The most common phrasing is simply "you'll know."

Those examples of alternatives in mind, scientific knowledge almost invariably involves the testing of hypotheses, by definition. The scientific method expressly requires the testing of hypotheses, so virtually all knowledge which is given the moniker "scientific" involved the testing of hypotheses.

  • Thanks. I realize how much of my confusion actually resulted from me not realizing I did not fully understood the concept of knowledge. Can you please give actual examples of how religion belief, knowledge in martial arts and knowledge of self are justified in absence of hypothesis testing?
    – Remi.b
    Feb 7, 2016 at 2:51
  • @Remi.b The justifications differ from person to person. Scientific justification (via testing hypotheses) is unique in today's society because most people agree that it qualifies as justification. Religious knowledge might be "transmitted" in a flash of light, or merely accumulated through years of "evidence" without actually intentionally testing any hypotheses. Much of the Oriental martial arts teach using an approach where the teacher provides what they "know" to be true, and the students learn it (one may presume hypothetical testing occurs on the side, as each student works at it...
    – Cort Ammon
    Feb 7, 2016 at 3:33
  • ... but it isn't the typical "justification." In fact, sometimes you can get in trouble by believing your tested hypotheses qualify as a justification in those schools. Knowledge of self is often justified because of just how hard it is to argue that you can know anything without first presuming some knowledge of self (its why Decartes started from "I think, therefore I am").
    – Cort Ammon
    Feb 7, 2016 at 3:35

I would reject the premise some: just because a problem isn't statistical in nature doesn't mean we can't (1) state what we know about the problem, (2) form a model for the problem and (3) see if the model fits the data.

Peter Kreeft is a current philosopher in ethics and religion, and if you see his talks (he has many on YouTube) he often follows the pattern of starting with what we know and trying to work out ethical "hypotheses" that fit that data.

For mathematics, it also is important to note in math that propositions can be disproven by single examples. So, very often, you can gain knowledge of something without constructing a full proof.

You can also see this pattern at work in Plato's Republic: obviously not a statistical treatise, the Republic does include thought experiments, by which the characters in dialog gain knowledge through testing "models" of ethics against what data they have.


Descartes borrowed a thought experiment from Avicenna, his floating man thought experiment, which for Descartes became the starting point for his cogito, the foundation stone for his theory of knowledge.

Here, no hypothesis is being tested; merely an act of the imagination philosophically thought out; and equally importantly, founded upon and following the thought of other philosophers, the philosophers that preceded him, of whom one is, as mentioned, Avicenna, but there will have been others for philosophers read other philosophers. They are in touch with the philosophical canon.

  • +1 I changed al-Ghazali to Avicenna based on the Wikipedia link, however, I don't know if Descartes read either of them. Please correct this edit if you think it is wrong. Jul 24, 2018 at 14:12

First I take over the definition of knowledge as quoted by Cort Ammon: “Knowledge is justified true belief.”

Because you ask in which cases the justification can or cannot be achieved by statistical tests, I would like to point to the following properties complementing Cort Ammon's answer:

1) Statistical tests presuppose that the hypothesis refers to a general statement, not to a single case. Science always refers to general cases. This holds for all sciences from your list.

In the case of history it is under discussion: Do general laws of history exist or does history always investigate single cases? And descriptive geography is no science if it really restricts itself to description. Description can only be the first step, the next important step of a science is to formulate hypotheses and a theory.

Justification or refutation by tests is necessary for all natural sciences on your list, but not for mathematics, where one has the stronger means of proof.

2) It is common to make a difference between knowing why as giving an explanation and knowing how as having a certain capability. “Knowing why” is characteristic for scientific knowledge from your list. While “knowing how” often refers to a practical capability, e.g. how to drive a car, how to act in martial arts etc.

3) There is a subtle point concerning the definition of knowledge above, named the Gettier problem. It refers to the fact that in certain cases a person’s statement in fact fullfills the three chacteristics of the definition: the statement is true, the persons believes that the statement is true, the person argues why the statement is true. Nevertheless we deny that the person has knowledge. See http://plato.stanford.edu/entries/knowledge-analysis/


Nirvana is the well known to be a certainty, which means that if you feel the need to verify that you have the fruits of it, you do not have it...

Any other result are got by induction, over at least space and time (since most people choose to think through these categories), and therefore cannot yield certainty. People feel the need to verify, more less individual by individual, these kind of results, precisely because they are not sure that they hold beforehand. Thus they verify that the result hold statistically, with personal margins of statistical significance, to better choose to claim, out of laziness (or pragmatism (to sound less adhering to subjectivity), for those who choose to see themselves as pragmatists), that if the result holds, according to a few individuals, a few times, it holds more than a few times (sometimes forever, without statistical margins as in mathematics, for a few philosophers of mathematics (well, until somebody with good reputation claims to have found a mistake in a accepted proof old of a few years !)) and for everybody, therefore fulfilling their dream of truth by universality and necessity. Of course, they choose not to question their clinging to the concept of universality and necessity.

  • Welcome to Philosophy.SE! This attempts to answer the question, but is rather poorly written. "People feel the need" - which people? Can you make your main point more obvious? "Nirvana is the well known to be a certainty" (sic): certainly many people hold that it exists, but many others hold that it (1) doesn't exist, (2) is not a certainty, or (3) something like it exists but in a different form. You should say more about why some say it exist (divine revelation? experiential reasons?) Feb 9, 2016 at 12:06
  • I highly doubt the existance of (any!) Nirvana. Do not infer from peers to objectivity, this would be a fallacy within justification and disqualify the proposition as knowledge.
    – Philip Klöcking
    Feb 9, 2016 at 22:08

I would argue that theories of knowledges can be acquired without statistical testing in fields such as metaphysics, ethics (as mentioned in the question) and other fields where there it is impossible to test hypotheses.

For example, "René Descartes, with je pense donc je suis or cogito ergo sum or "I think, therefore I am", argued that "the self" is something that we can know exists with epistemological certainty" (wiki). However I doubt, he used statistics to come to that conclusion. Furthermore, arguments such as the ontological argument cannot be tested and cannot be proven (at least with the current technology and most likely the technology for the next hundred years) and are simply fathomed with purely hypothetical reasoning.

Note: I deliberately wrote "theories of knowledge" because I consider knowledge as a certainty or something proven with testing (some people may disagree).

  • I think the question is trying identify "the set of conditions under which a given knowledge can or cannot be acquired without" testing hypothesis. I am not sure what those would be. You do add metaphysics to the list already provided. If you have people you can reference who take a similar view as you do they would help strengthen your answer and give readers a place to get more information. Jul 25, 2018 at 4:25

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