Induction and Deduction

This is an excerpt from the book series Philosophy for Heroes: Knowledge.

How does the process of deduction supplement the process of induction?

Now we know how to design concepts and a concept hierarchy, and how to assign to the concepts corresponding definitions. We have also learned how we perceive reality and how we can protect ourselves from errors and external influences. So far, we have left open the question, how we can apply this knowledge, especially our concept hierarchy, in specific situations. In relation to this, philosophy discusses two concepts, induction and deduction:

‍INDUCTION ·  With induction, we conclude from the special case (a number of concrete perceptions) the general case (the concept). With this, we create new or refine existing concepts, on the basis of sense data and the logical integration of a number of perceptions of entities. For example, if we see a number of cars with different colors, we create from this observation the more general concept “car” by using induction.

DEDUCTION ·  With deduction, we conclude from the general case the special case. For this, we use the knowledge that we gained from induction, check if a certain perception fits the definition of a concept, and conclude for the corresponding entity that it has all the properties of the corresponding concept. In short, deduction is the process of subsuming new instances under a known concept . Deduction thus operates in the opposite direction as induction. For example, if we notice that cars can drive on the street, and we see a parked car, then we can deduct that this car is able to drive on the street as well, because we have assigned the parked car to the known concept “car.”

What we have discussed in the previous chapters relates to induction. We have made sense perceptions on the basis of sense data, integrated those, and finally created concepts. Figure 1.10 shows us the central element of the acquisition of new knowledge (induction) on one side, and the application of familiar knowledge (deduction) on the other. With induction, we conclude from the special case the general case. On the other hand, with deduction, we conclude from the general case the special case. For this, we use the knowledge that we gained from induction, check if a certain perception fits the definition of a concept, and conclude for the corresponding entity that it has all the properties of the corresponding concept.

Rationalism

The earlier [concepts are] required to get to the later, but the later is required thoroughly to understand the earlier. So the only time you get a complete understanding of any element is when you know every element, and that is what it means to say it’s a system of philosophy, an integration, and not simply a series of discrete items. —Leonard Peikoff, Understanding Objectivism [Peikoff, 2012, p. 167]

The idea that knowledge can be obtained by the mere deduction from concepts that originate from one’s mind or some place other than the external world is called rationalism. Is it possible to simply take our thoughts as a starting point and then reach conclusions about reality step by step, as rationalists like Descartes with his famous quote “Cogito, ergo sum”—“I think, therefore I am”—suggested?

RATIONALISM ·  Rationalism is the attempt to create knowledge without induction and to deduce from this knowledge.

Are we spirits who discovered their bodies, or the other way around?

Naturally, it is true that if we think, we also exist. We do not, however, exist because we think. In order to be aware of something, we first must exist ourselves and something must exist we can be aware of; thus, something must exist in the first place. Our actual existence hence does not follow from simply being aware. [cf. Peikoff, 1991, pp. 17–23]

In Objectivism, this statement is referred to as “primacy of existence” (as opposed to “primacy of consciousness”). We are aware of something because we exist. The entity of which we are to become aware must first exist before we can become aware of it. Our consciousness observes reality; it does not alter reality by our thoughts. Correspondingly, knowledge can be acquired only by directing our consciousness to reality using our senses. Likewise, as rationalism does not start with sense perceptions, one can usually find rationalists among those who doubt the validity of our senses.

Despite its name, the concept “primacy of existence” simply means that existence is not derived from consciousness. It does not mean that it stands in the first place or that you can derive the other axioms from it. Consequently, in Ayn Rand’s argumentation, it never stands on its own and is instead used primarily as a counter-argument to the “primacy of consciousness” argument where people argue that things can come into existence via mere thought. A more fitting term would probably be “non-primacy of consciousness.”

However, even if the result of an induction is drawn upon, but deduction is then used exclusively in the investigation of a certain fact, we can nonetheless still attribute it to rationalist thinking. Deduction is a very powerful tool, but the proper usage of logic does not happen automatically. As we will see in the following chapters and books, the risk of error is great if we cannot, or do not want to, check results from logic objectively each time by means of observations of reality. [cf. Peikoff, 2012, pp. 209–41] So we see that induction and deduction ideally always go hand in hand. [cf. Rand et al., 1990, pp. 94–111] We have to constantly go back and forth between the application of logic and the actual observation of reality.

We are not spirits that deduce from their consciousness that they also must possess bodies. We are also not bodies who have learned to perceive the world and form a consciousness. We are both at the same time and we need to discover both at the same time.

Induction and Empiricism

In our discussion of cognition, the question still remained whether induction is a valid process at all. Similar to what we have already found, namely that ontology (the axioms) and epistemology are closely intertwined, and similar to how we have to reflect on our process of cognition, the process of induction is not structured in a strictly hierarchical manner. The validity of induction depends on the validity of induction itself, which leads to the so-called “problem of induction.” Here, we want to examine this issue more closely and examine the positions of various philosophers concerning empiricism. The discussion serves to provide different points of view and the contradictions that lie in them in order to arrive at a clear statement about how we can answer the question of validity of induction.

EMPIRICISM ·  Empiricism states that the source of all knowledge lies in sense data (empirical evidence). In empiricism, deduction from knowledge which is not based on sense data is not possible.

TABULA RASA ·  Tabula rasa refers to the view that we are born without any innate knowledge and that our minds can create knowledge only with the help of sense data.

A PRIORI KNOWLEDGE ·  A priori knowledge is knowledge that was acquired without first engaging in an experience.

Empiricism says that the source of all knowledge lies in sense data. This can go to the extreme by denying induction—for proving induction you first would need induction itself. At the same time, it is assumed that our mind is tabula rasa and contains no a priori knowledge, and therefore any knowledge can only be created with the help of sense data. Formulated this way, it would constitute a circular argument because you would have to have the knowledge about gaining knowledge before gaining knowledge in the first place. On the other hand, if we were to ignore sense data as the only source of knowledge and thus not apply induction, we would suddenly face a conundrum: how to prove without induction that an external reality exists at all. [cf. Rand, 1963, p. 173]

A World Without Induction

How would the concept of “concept” lose its meaning in extreme empiricism?

Let us first take a look at a world without induction. Here, every situation would have to be considered anew, making the knowledge that we have so far acquired (using induction) useless. For an extreme empiricist, every realization is independent of the next, so everything is an independent, separate part of reality. Acquiring new knowledge would be a new challenge each time, since we could not build upon, or classify our observations into, already existing concepts. This extreme empirical mode of thought becomes particularly recognizable with the use of the so-called “cliff-jumper” argument.

Example The “cliff-jumper” argument involves the notion that we can only judge something if we have experienced it ourselves. If that were the case, we would first have to jump from a particular cliff in order to be able to argue for or against jumping from that cliff. This view originates from extreme empiricism, according to which there are supposedly no general principles in nature, but only statements applicable to a given situation. For an extreme empiricist, each new jump from a cliff would always be a new unknown—we could not draw conclusions from past observations that we could apply to the future or other similar situations.

In extreme empiricism, the concept hierarchy tree would be completely flat and the concept of “concepts” would lose its meaning, because every concept would correspond only to one single instance.

The Problem of Induction

The question of whether or not when you see something, you see only the light or you see the thing you’re looking at, is one of those dopey philosophical things that an ordinary person has no difficulty with. Even the most profound philosopher, sitting eating his dinner, has many difficulties making out that what he looks at perhaps might only be the light from the steak, but it still implies the existence of the steak which he is able to lift by the fork to his mouth. The philosophers, who were unable to make that analysis, and that idea have fallen by the wayside from hunger. —Richard Feynman, 1979, University of Auckland

Can statements be shown to be true without induction? Why or why not?

In his Critique of Pure Reason , Kant wished to argue against the extreme empiricism of David Hume, and to overcome the antagonism between empiricism and rationalism. Hume claimed that induction in relation to causality could not be a means of learning anything about nature, since the justification of the validity of induction would, in turn, require induction. According to Hume, it is not valid to posit that the identity of an entity at a future point in time (without external influence and with attention paid to internal processes) is the same as in the present. This problem increases even further if we think about how this would mean that we could no longer rely on a constant structure of our sense organs and that we could perceive random disconnected static from the world.

Kant attempted to solve this problem by creating the term “synthetic a priori statement.” [cf. Kant, 2008, pp. 43–56] By that, he intended to show that there are statements about the world which would not require induction, meaning that certain truths about the world could be found without the need for sense data. His attempt failed, but it is helpful to understand his train of thought in that regard:

ANALYTIC STATEMENT ·  An analytic statement is a statement whose assertion is given by the definition of the subject. As a result, measurements are not necessary to determine whether it is true or not (e.g., “Triangles have three vertices”).

SYNTHETIC STATEMENT ·  A synthetic statement is a statement whose assertion is given not by the definition of the subject alone; i.e., measurements are required to determine whether it is true or not (e.g., “This form has three corners”).

A PRIORI STATEMENT ·  An a priori statement is a statement that can be substantiated independently of experience (e.g., mathematical statements).

A POSTERIORI STATEMENT ·  An a posteriori statement is a statement that must be substantiated through experience (for example, “bodies are heavy;” we must first lift a body to determine its weight).

In his work, Kant sought synthetic statements which were at the same time a priori statements and, as a result, could be substantiated without sense data (empirical knowledge) of reality. His lengthy explanation in his Critique of Pure Reason did not help to clarify what he—knowingly or unknowingly—actually meant by his notion of analytic and synthetic statements, as well as by the distinction of a priori and a posteriori statements.

The point is that his synthetic statements concern nothing other than measurements. A synthetic statement is thus nothing other than a statement about the effect of a representation of a concept—an entity. The statement “All chairs are made of material” refers to a property of the concept “chair, ”while the statement “All chairs are made of the material wood” relates to the tangible effect of the property “material.” A synthetic a priori statement thus would be nothing other than a statement whose assertion is not given by the definition of the subject (i.e., a measurement!), but can be substantiated independently of experience (i.e., not a measurement!). A measurement that is not a measurement is obviously a contradiction; for this reason, by the Axiom of Identity, synthetic a priori statements cannot exist. Thus, his “solution” is not a solution and the problem persists.

By the Axiom of Identity, Kant’s synthetic a priori statements cannot exist. That means that there are no statements that can be shown to be true without induction. Kant’s examination does not solve the problem of induction.

What does Hume’s problem of induction have to do with omniscience?

If a question seems unsolvable, the question itself should be inspected more closely. In regard to induction, Hume concerns himself with the future, and hence with the question of whether knowledge we acquire about the world can be applied to future events. “Time,” however, is ultimately merely a construct of the mind. In more general terms, it deals with the question of whether knowledge acquired from a past situation is also valid in a situation at different points in time. Still more generally, his position could be seen as a criticism of the use of concepts.

If we have established that when dropping a certain apple, it falls downward, who is to say that the same must also hold for a different apple (or at a different but comparable location or point in time)? Possible answers to this problem include that we may have erred in constructing the concepts in question, and there are still many more significant properties we might have not yet discovered. But that is not what Hume aims at; he is concerned about the validity of concepts, whether we can acquire general knowledge about the world when we exclude such special cases. We have defined “concept” in this way for the very reason that it includes entities that, for example, possess the property of falling downward. It makes no difference whether we now consider other apples in our fruit basket or apples existing far in the future. In both cases, we are referring to the same concept, “apple.” If future apples possess other properties than our present apples, we just have to diversify our concept “apple.” When defining the concept, we have to either restrict the selection of entities or include a dynamic component which adds the factor of time into the description of the properties.

Exactly such a discussion is currently going on in the sciences concerning the gravitational constant. If, for instance, in the future, the gravitational constant should change, it would say nothing about the validity of concepts per se but instead would speak to our potentially incomplete definition of gravitation, where we should have included a change of the gravitational constant depending on the time and location. Hume himself stated the example that we could not know that the sun would continue to rise in the East just because we have observed so in the past. But the point is that we can expand our concept and knowledge about the stars and planets to include irregularities without having to declare them as special cases (think of a morning solar eclipse).

Ultimately, we see that Hume’s argument is a matter of nonexistent omniscience in the formation of concepts. We can, therefore, compare it with Kant’s “things in themselves”: potentially, there is always a level further on, an unknown “true reality,” which was as yet unknown to us when we defined our concepts. We could also formulate the question in more general terms: does carrying out a deduction depend on sense data (empirical evidence)? Can we perform experiments which can determine whether we can determine things? This approach leads to an endless cycle of questioning—to answer the question we must first be able to answer the question. It has come to this recursion, since we cannot ask a question which attacks the very presupposition for the question itself—this would be a fallacy of the stolen concept. We could not then bring into question the validity of concepts if we pose a question that uses concepts.

Hume’s problem of induction is ultimately directed at the fact that we are not omniscient when we establish concepts.

The Truth

People say to me, “Are you looking for the ultimate laws of physics?” No, I’m not, I’m just looking to find out more about the world and if it turns out there is a simple ultimate law that explains everything, so be it, that would be very nice to discover. If it turns out it’s like an onion with millions of layers and we’re just sick and tired of looking at the layers, then that’s the way it is! But whatever way it comes out, it’s nature, it’s there, and she’s going to come out the way she is. And therefore, when we go to investigate, we shouldn’t pre-decide what it is we are trying to do except to find out more about it. —Richard Feynman, The Pleasure of Finding Things Out[Feynman and Robbins, 2005, p. 23]

One answer to the problem of induction is that knowledge is more than just an accumulation of instances. If we relied only on induction, our (inductive) claims of the world would be invalidated regularly by new discoveries and we would have to start again and again from scratch. Inductive claims are disconnected, they rely on a “traditionalist” view where the future will resemble the past. What we need to do is connect our knowledge, integrate it into a whole. When creating the concept of a swan, we should keep in mind that we might find outliers and irregularities, especially if we have no idea yet about how a swan becomes a swan (by biology, genetics, etc.). The same applies to the rising sun in the morning. After we gained knowledge about planetary movements, our inductive claim became an objective one because we could explain it not just with past data, but also with the principles that govern past data. And when we refined our knowledge later with the theory of relativity, it did not invalidate the principles we came up with before, as it was a more accurate description of reality.

Of course, this approach does not solve the problem of induction itself. And none of the so-called great philosophers like Descartes, Hume, or Kant were able to provide a solution for the problem of induction. And what we have seen is that there is no solution to it! It is a pseudo-problem which we actually should not use, especially not if it puts our ability to understand the world into question. Just because we can ask the question does not mean that there is a solution. Or that if we do not find a solution, there is something wrong with our perception of the world. The point is that the problem of induction is an impossible question whose only real answer is omniscience. So, at most, what we owe to Hume and others is that we should not assume that we are omniscient; we should require proof for scientific theories and re-examine existing knowledge when new insights are gained.

Did you know? As we are looking only at a part of the universe, our “truths” include the context in which we have found them. As one truth builds on many others, we have to guard carefully everything that we have discovered. Our tool for that will be the scientific method. Read more in Philosophy for Heroes: Continuum.

In the end, the question is what we want. Do we want the “absolute truth”? Should the goal be to attain all knowledge and create an exact replica of the universe in our minds? Already, there is a device in the world that can make 100% accurate predictions of the future. It’s called: the universe. It takes one second to calculate what it will look like in the next second. It uses all of its calculation power, all the atoms and molecules working together, creating a super computer which is faster and more accurate than anything built within that universe. We cannot compress the universe into our brains; we can perceive only one part of the universe at a time with our senses.

What we, as humans, can do is filter and abstract (concepts!) the information and focus only on parts of the universe at a time. We have to understand the principles of the known universe while hoping that the unknown parts will not interfere with our thinking. But because we are not omniscient, we cannot be sure and we have to expand our horizon constantly. We cannot take one piece of “absolute truth,” close our senses, and then deduct everything from that piece of information without ever checking with reality. Basically, this is what the rationalistic fallacy is about, and that is also the reason our axioms, if they stand independently from epistemology, are not “absolute truths.” We cannot say, “This is it, I have found the truth, I will ignore any new perceptions.” We have to go back and forth between induction and deduction and refine our understanding (our concepts) of the world.

Suppose that physics, or rather nature, is considered analogous to a great chess game with millions of pieces in it, and we are trying to discover the laws by which the pieces move. The great gods who play this chess play it very rapidly, and it is hard to watch and difficult to see. However, we are catching on to some of the rules, and there are some rules which we can work out which do not require that we watch every move. […] We do not need to watch the insides to know at least something about the game. —Richard Feynman, Character of Physical Law [Feynman, 2012, pp. 53–54]

Is it an unsatisfying answer that the universe does not consist of a set of independently perceivable truths? Well, nature does not care about whether she can be satisfyingly understood. We have to work with what we have. And what we do want, or should want, is a matter of ethics. Epistemology can only provide you with the means. Still, the question of what we want already implies that we have an identity. And philosophy teaches us to act in this world. Philosophy is not about discovering—as Kant put it—the “true reality.” Maybe we do not know everything, and if we knew more, something else would follow. But based on what we have, we can make statements. They might ultimately turn out to be inaccurate because we did not include all the data, but we did the best we could, and we built upon our knowledge. The alternative would be to make no predictions at all, and wait forever until we have gathered so much data that we are omniscient. Likewise, we need to welcome new and reflect on old ideas; this is what opens our soul to discovering reality. The challenge is striking the right balance between reflection and action. This is the first building block on your path from a student of philosophy to a teacher and ultimately a leader.