Abstract: Occam’s Razor (OR) establishes that one must eliminate “unnecessary” hypothesis from theories. This essay intends to establish some rules that conceptualise the “no-necessity” criterion in OR. A new version of the classic Inductivism is also proposed and later used to solve this problem.
Key-words: Epistemology, Occam’s Razor, Philosophy of Science, Science, Inductivism, Logic, "Inductivist Hierarchy”, Inductive Method.
Occam’s Razor (OR)  is a logical-philosophic criterion used virtually in every knowledge acquisition process as well as in our everyday life.
Succinctly, OR establishes that we must eliminate unnecessary hypothesis from our theories. The criterion by itself is almost a tautology, that is, an absolute logical truth, since the hypothesis understood as unnecessary are by definition not necessary to the theory. That way OR must be considered an incontestable truth. Therefore, the whole problem is not really in OR, but in the criteria concerning the “unnecessity” of the hypothesis.
Let us use some examples to exemplify. Consider the following theories:
1a- For a car to move, it must have fuel.
1b- For a car to move, it must have fuel, and its occupants must pray the “Our Father”.
2a- For cough syrup to work the patient must ingest it.
2b- For cough syrup to work the patient must ingest it and, besides that, sing “hula-hula” while turning around for three times.
This way we could include an infinity of other craziest as possible hypothesis in each of our theories.
Similarly, the reader knows he does not have to recite a children’s poem each time he drinks a glass of water in order to avoid pouring water out of the glass. That shows OR is present in our everyday life, even in an imperceptible way.
But how should we know whether a hypothesis is really unnecessary?
How should we know we actually do not have to pray the “Our Father” for the car to move, nor turn around singing the “hula-hula” for some medicine to be effective, or recite a children’s poem so water does not shed from the glass?
Indeed, all these apparently absurd and clearly unnecessary hypothesis given in the examples could be absolutely necessary in some other universe, or even in our own universe since the moment the reader finishes this sentence. That is, we cannot guarantee that the laws of physics have changed and those hypotheses that were before seen as absurd are now totally necessary.
In short, what is the criterion of necessity (or not) of a hypothesis or any theory?
Before we answer to that important question, let us create a new theoretical framework: “The New Inductivism”.
2- The New Inductivism
The main process to connect our minds to the external world and elaborate theories about our universe, that is, the way we acquire knowledge is known as “induction process”.
The induction process, or Inductivism, establishes that experiments, occurrences or events that always have the same results will probably have the same results under the same conditions. And the more times these results repeat, that is, the more favourable observations about the hypothesis or theory are obtained, the more reliable the hypothesis or theory is.
2.1- Hypothesis Formation
Obviously, the simple observation of phenomena repetition does not produce by itself any theory. To exemplify, a monkey can observe some repetitive phenomena for its whole life as “the Sun rises in the East”, and it will not formulate a theory about that.
Therefore, the inductive process does not elaborate finished theories. Instead, it provides us with important clues so that we or some kind of processing can create hypothesis or theories about reality. That way, it is perfectly possible that different people elaborate different theories or hypothesis using the same data obtained from inductive observation.
2.2- First Results
From the inductive process we create the basic hypothesis that our universe is logical, that is, it works logically according to the aristotelic logic. And also, the laws of Physics must be stable. These first results give us the trust that our universe must not have changed its laws so that water would pour out from our glasses if we did not recite some children’s poem!
The Induction process is very criticized by many scientists and science philosophers under the true statement that this process not always produces correct results.
However, that will rarely happen under the “New Inductivism”. There is an inductive hierarchy in the New Inductivism. This hierarchy establishes that new inductive rules must be subordinate to pre-existent inductive rules.
Thus, there is a law hierarchy based on more basic and reliable inductive processes, where some have more power and privilege than others. That way, it is not possible to interrupt an inductive hierarchy without a good reason for that.
So a new inductive rule can only be considered satisfactory if it does not break the hierarchy of stronger inductive rules.
In this manner, the “New Inductivism” can be defined as the classical Inductivism linked to subordination of an inductive hierarchy.
It is possible to create an inductive hierarchy in a decreasing degree of power, in a way that a law with a less elevated level of power must not go against the superior hierarchical levels. Our inductive hierarchy can be defined in a decreasing level of importance in the following way:
- The most basic and powerful inductive rule is that our universe is logical. No illogical event has ever been observed. We can suppose then, by induction, that the universe follows logic. Any theory that goes against this first rule must, in principle, be considered false.
- The laws of Physics form the second class of our inductive hierarchy. Obviously they must not oppose the first level of hierarchy. And, for that reason, the laws of Physics can use mathematics, which is totally based on logic. The laws of Physics are created by observation of the most extense set of observations on regularities of our universe. For that reason, they must be among the most reliable rules built by mankind. The power of these rules resides in the fact that they must be verified, direct or indirectly, in every observable universe and they should not be limited to our planet, nor even to our solar system.
- The laws of Chemistry could form the third level of our hierarchy.
- The laws of Biology, the forth level.
- The other norms, rules or laws must not oppose the theories of the classification above, unless they are exhaustingly verified.
It is possible to notice that the degree of strength in the inductive hierarchy is based on the extensibility, that is, the quantity of favourable observations in space and time in which the theory approaches in a favourable way. Inductive rules of short range in space and time have fewer favourable cases than large range ones. For that reason, such rules must be subordinate to the most general ones that had been tested and, because of that, present a greater level of reliability.
2.4- Inductivist Response
Now, with that classification, we can rebut the argument against the inductive principle: “The Sun Rising Argument”. It says that if we use the inductive process about the rising of the Sun every morning we will create a law establishing that:
“Today and always, every 24 hours the sun will rise in the East and set in the West”
However, we can “rebut” (*) this argument by showing that it goes against the inductive principles of the second hierarchy (the laws of Physics), since according to these laws, the hydrogen of the Sun will end in four billion years and our star will explode. That way, one day, unfortunately, the Sun will not rise anymore and therefore this principle cannot be considered satisfactory.
2.5- “Inductivist Refutationism”
We must make it clear that the inductive process, as any other process, does not necessarily lead to the truth. Something that has always been stable and reached the same results can have these results changed by some new condition or some new observation. We will never be sure about the ultimate truth of the universe.
That way, it is natural that a law or rule created by an inductive process stops being valid in case a new observation “rebuts” (*) the inductive regularity. In that case, evidently, the induction does not exist anymore, since this refutatory event did not pass through induction. The induction, in that case, was broken and therefore it is not an induction, it is not valid. We can clearly notice the brakeage of the inductivity by an unfavourable event as analogue to “popperian refutationism”, where evidence contrary to a theory is its own rebuttal element.
2.6- The Deductive Hypothetical Method
The Deductive- Hypothetical Method (DHM), in which hypothesis and theories are released to be later tested, does not go against the inductive method. If not, see:
In DHM a theory (or hypothesis) – not necessarily of inductive basis – is proposed. From this theory we can use logic and verify the consequences that it causes. If any observation “refutes” (*) the consequence of this theory or this theory itself, then the theory will be “refuted” (*). But clearly if the consequence of a theory is “refuted”, then the theory that originated it will also be refuted, since the strongest inductivist rule is the logical one, and by logic (more specifically by “modus tollens”) if the consequent is false then necessarily the antecedent will also be.
That way, we can verify that if DHM shows some case which results in a “refutation” of the consequence of a theory, this fact will also break the Inductivism of the theory that originated it. The opposite is also clearly true: a flaw in Inductivism by an observation would also “refute” (*) the theory.
2.7- The Evidence
An evidence is an observation, fact or event that corroborates or not a theory. The inductive method, in general, elaborates its theories from evidence, that is, inductivity has its basis on reality as a starting point. Thus, Inductivism has advantages over other creation processes.
It is important to notice that theories or hypothesis generated by creation processes that do not come from empirical observation will also need to go through some kind of validation process, that is, a sequence of tests and empirical observations will also be necessary for the theories to be reliable.
Obviously in principle a newly created non-inductive theory, and yet with no favourable evidence can be true, while another that has been tested can be false. However, until the observations or experiments decrease or enhance the reliability of the theories, we must credit the theories that have already been through some observational test. In that case, inductive-based theories would have the initial advantage and therefore must be taken as more reliable than the non-inductive ones.
2.8 – Degree of “Inductive Reliability”
As a particular case, but not less important, we could say that a theory that does not have any favourable evidence, that is, the number of favourable inductions is zero, must have in principle, zero reliability.
As the amount of favourable evidence (quantity of valid inductive events) increases, the inductive reliability degree must also increase.
3- Necessity Criterion in Occam’s Razor
From this new theoretical base we can now answer the question in the beginning of this essay:
What is the necessity (or not) criterion of any hypothesis or theory in OR?”
The answer to this question can be given according to the “inductive reliability” degree (IR) presented by the hypothesis concerning the theory. The lower the inductive reliability (IR), the more unnecessary the hypothesis is.
Take the following theory as an example:
1b- For a car to move, it must have fuel, and its occupants must pray the “Our Father”.
The hypothesis of the necessity for the prayer for the car to move has a very low IR and therefore can be considered unnecessary. But in case our universe changes or the fact happens in another universe, this hypothesis can have a high degree of IR and then be a hypothesis that is not unnecessary. It all depends on associated inductive reliability.
(*) “Refute” is between inverted commas because, according to P.I.F , it is never possible to know whether an observation is true or not. Therefore, it is never possible to know whether something was refuted or not.
 A Navalha de Ocam – Occam’s Razor
 Ciência Expandida – Expanded Science
 O Princípio da Incerteza Filosófico – The Philosophical Uncertainty Principle
 O Argumento Indutivista – The Inductivist Argument
Portuguese version: http://stoa.usp.br/cienciaexpandida/forum/42550.html