I Think Inductively, Therefore I Know

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By Robin Craig

December 29, 2014



One of the important questions philosophy tries to answer is: can we know anything, and if so, how do we gain reliable knowledge?

Is there some way to learn the true nature of reality from the clues provided by our senses? There is. And our primary tool for doing it is inductive reasoning.

At the base of all our knowledge are our sense perceptions. It is through them that we detect what is ‘out there’. But how exactly do we get from what we see, hear, touch, taste, and smell to knowing anything deeper or broader about the things we are detecting? Are we blind men feeling an elephant, never to know the actual nature of the beast we are studying? Or is there some way to learn the true nature of reality from the clues provided by our senses?

There is. And our primary tool for doing it is inductive reasoning.

The Primacy of Induction

Induction is the art of deriving the general from the particular. It is complementary to deduction, which is the art of deriving the particular from the general.

It is often thought that deductive reasoning provides greater ‘certainty’ than inductive reasoning. The rules of deductive logic are ironclad: if an argument is valid and its assumptions are true, then its conclusion is guaranteed to be true. In contrast, the rules of induction seem more ‘rubbery’: they concern generalization of the ‘all’ from the ‘some’, from the known to the unknown, and involve evidence, probabilities, and best explanations – which can be wrong, even when the evidence is true.

However, it is critical to note those two requirements of a true deduction: “if an argument is valid and its assumptions are true.” In most cases, those assumptions are statements of general fact. And all ‘general facts’ are based on induction. Even if the immediate assumptions are the result of deduction, at base all judgment of the truth of propositions depends on induction. For example, take the classic syllogism:

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

How do we know all men are mortal? What is man – and how do we know Socrates is one? All these items of knowledge are a result of the inquiry method described in the earliest Philosophical Reflections: the application of reason and experiment to the evidence of our senses. They all depend upon induction.

In Douglas Adams’ The Hitchhiker’s Guide To The Galaxy, the super-computer Deep Thought started with “I think, therefore I am” and had deduced the existence of income tax and rice pudding before they could turn it off. The belief that you can start from introspection and by deep enough deduction come to truths about the universe is called rationalism. Such attempts are doomed to fail. The universe does not exist inside our heads, but outside: and the only way to learn about the external universe is to look at it. And the only way to learn by looking at things is by inductive reasoning. Trying to understand universal truths purely by introspection untested by reality has not given humanity new knowledge, only philosophies cut off from the actual requirements of human life (Immanuel Kant being a classic case).

Concepts, Induction, & Deduction

As noted in Immaculate Conceptions, valid concepts are derived from observed reality. We observe – we note similarities – we think – we identify – we combine and differentiate. Thus concept-formation is basically an inductive process.

Deduction is of course important. It gives concepts their predictive usefulness. Having generated the concept of ‘snake,’ and identifying a particular thing as a snake, we can apply our inductively acquired knowledge of the characteristics of snakes to deductively predict the nature of this snake. Having previously determined that taipans have a deadly bite, we don’t need to poke our finger in this one’s mouth to realize that we shouldn’t.

It is in the nature of concepts and reality that exceptions occur. And this is where deduction re-enters, refining our concepts. If the nature of a particular existent contradicts our understanding of the nature of its fellows, then we have learned that our concept is inaccurate, or this existent does not actually belong in it, or we have come across an exception that makes our concept less universal than we first thought. Which of these it is, is the task of our reason to determine.

Thus the logical certainty of deductive reasoning has a vital role in our thinking. All forms of deductive logic are some form of If A then necessarily B, whose converse is If not B then necessarily not A. The first lets us deduce the nature of particular instances of existing concepts: you don’t have to wait for Socrates to die to know that he is mortal. The second refines or refutes our concepts: if a thousand years pass and Socrates is still alive, we know that either he isn’t a man, or our understanding of the nature of man is incomplete. In Philosophical Reflections 24 I noted that the first rule of knowledge is that all our knowledge must be consistent without contradiction. Deduction is how we achieve this. Concepts are generated inductively and tested and refined deductively.

Blacked Out

A commonly used example of inductive reasoning is:

All observed crows are black.

Therefore all crows are black.

This does exemplify the nature of induction: inducing the universal from the particular. And clearly the conclusion is not certain. Unless we’ve seen every crow – and how do we know that? Maybe there are some rare blue ones.

And yet, whatever one says about the certainty of induction, one thing is clear and must be explained: induction works.

It is easy to show that induction works. If anyone claims it doesn’t, ask them to live without using any knowledge that was gained by induction or any related form of learning! Induction is simply a conscious application of the basic mechanism of learning, which can be summarized as once bitten, often shy; once rewarded, often repeated. This is the fundamental mechanism behind all learned behavior – and all instinctive behavior, for that matter. And there is one thing that we can be sure of: nothing that universal and fundamental would have evolved if it didn’t work.

Of course, this simple mechanism of learning is not completely reliable. That is why the rule is not “once bitten, forever shy.” It is just a rule of thumb, which is based on the fundamental rule of existence: a thing can only act according to its nature. Therefore if a thing has once acted in a certain way, that way is within its nature, and odds are it is typical of that kind of thing.

Inductive reasoning is the conceptual analogy and improvement of this basic mechanism of perceptual learning, and works for the same reason. That things act and can only act according to their nature is the fundamental basis of deductive reasoning – else no conclusion would follow from any assumption – and inductive reasoning – else we could induce nothing general from any particular – and of reality itself – because A is A and can be nothing else. This leads us to the proof of the validity of inductive reasoning.

Inductive Proof

Let us return to the common, but simplistic, example of inductive reasoning:

All observed crows are black.

Therefore all crows are black.

In fact the blackness of crows is a poor example of induction, because the nature of life (as we saw in Philosophical Reflections 24) includes genetic variability. So we actually expect there to be an occasional non-black mutant crow even if every crow ever seen is black! Crows are a subset of living things, and we can deduce from our much wider inductions about life in general that all crows will not necessarily be black. As proved by the occasional albino.

In Philosophical Reflections 24 we saw why concepts, which group multiple things into a single mental unit, are valid: because those things in fact share essential features. For example, fundamental particles such as electrons are all identical in their properties, and by virtue of the fact that A is A, this extends through all things in the universe (all being made of fundamental constituents interchangeable with their fellows). Similar considerations apply to living things, despite their inherent variability, because that variability is variation on a theme.

Since only individual things exist in reality and induction concerns generalities, the method and purpose of induction is to find out the qualities shared by the members of a conceptual group. For if they do not share qualities, no generalization is possible.

By virtue of the fact that A is A, a thing can only be and act according to its nature. From that springs the true foundation of inductive reasoning:

I observe an instance of B with the quality C.

Therefore, the nature of B allows C.

This foundation is certain. Further observations will reveal whether C is rare, common, or universal among B, from which we make the first level of induction: a hypothesis about the nature of B, what I shall call descriptive induction. But such hypotheses are far more certain than a simplistic and uncertain All observed B are C, therefore all B are C. There are subsidiary axioms of great import, and when these are made explicit, so is the true scope of inductive truth. For example in the simplest case, physical objects, the full reasoning is:

If all observed B are C,

And B is a simple physical system (i.e., without volition or genetic variability),

Then since A is A, all B are C under the conditions observed (that is, unless affected by some additional factor not yet encountered).

It is well known that our confidence in the conclusions of inductive reasoning increases with the number and quality of our observations.

It is well known that our confidence in the conclusions of inductive reasoning increases with the number and quality of our observations. This is implicit in the above. The quality determines the truth of “all observed B are C”, upon which our conclusion rests. The number determines not the truth of our hypothesis, which is guaranteed within the context stated, but its generality: how robust it is against those unknown additional factors. A single case, for example, might be the result of an unusual set of factors, and practically any other set of factors might change it! While a thousand identical outcomes under a wide range of conditions indicates great generality.

Similar considerations apply to the more complex case of living things in which, as we’ve noted, the situation is complicated by inherent variability. In this case, the full reasoning is:

If all observed B are C,

And B is alive,

Then since A is A, the nature of B includes C under the conditions observed. But since life is life, variation is possible even under the same external conditions, especially if C is volitional.

Once again, our confidence in the generality of B are C depends on the quality and number of our observations. But genetic variability and the effects of volition – including both the rational volition of a human being acting according to his or her chosen values, and the lesser but still complex volition of an animal acting according to its experience and internal state – make prediction less certain than with simple physical systems.

Digging Deeper

In terms of practical knowledge, descriptive induction – a general statement about the qualities of certain existents – is often sufficient for our immediate purposes. The qualities of iron which enable its purification, alloying, and strength; how to make glass from sand; how to grow grain, thresh it, and bake it into bread – were all determined by descriptive induction, long before the why of all these things was understood.

However, it is the why which is the most important and powerful part of induction: what I call explanatory induction. Epistemologically, knowing why proves the what: because we know why diamonds are hard, we know that all diamond crystals are hard; because we understand why the chemistry of carbon is what it is, we know that pure carbon may be neither diamond nor hard. Practically, knowing the why gives us much greater power to reproduce and improve desirable qualities, and to predict new ways of making yet more useful things: and thus better achieve our values and improve our lives, which is the ultimate goal of all knowledge. It is our understanding of atoms and the materials made from them which has enabled us to make computers, cars, and aeroplanes; it is our understanding of biology and mechanics which has enabled us to feed an entire population on the work of a few farmers, to cure disease, and put us on the threshold of redesigning our own genes.

And that brings us full circle. In the early Philosophical Reflections I noted that the enquiry method by which we learn consists of observation, reason, and experiment. There are few experiments more rigorous than building a technology on the basis of our knowledge. Can you calculate the chance that a jumbo jet would fly if the physical principles on which it was based and the materials science by which it was constructed were incorrect? Likewise, it took many careful experiments to learn that DNA – and sometimes RNA – is the molecule of genetics, and to uncover the genetic code by which it works. That we can now make a gene from simple chemicals, put it in a cell, and thereby make that cell do our bidding – to make a product we want, kill a virus, or cure a genetic disease – is the final seal of approval on that knowledge. That knowledge might not be complete – but it is true.

© 2001 Robin Craig: an earlier version of this essay was first published in TableAus.


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  • Bruce Caithness

    A.J. Ayer introduced logical positivism into England but in his interview with Bryan Magee he was asked about how he felt about it now.

    Ayer said ” Well, I suppose the most important of the defects was that nearly all of it was false.”

    Magee replied “I think you need to say a little more about that.” (Magee, B. “Men of Ideas” 1978)

    My reaction to Robin Craig’s argument for induction is that nearly all of it is false.

    The point is that a lot of our thinking is conjectural, reason has a role to play in checking the validity of our arguments, not inventing them. David Hume and later Karl Popper made the problem of trying to pin a logical overlay onto induction painfully clear, but Ayn Rand never got the point, nor evidently has Robin Craig.

    • Robin Craig

      Yet here you are, writing your reply on a computer with more transistors you can count in something the size of a postage stamp. I do like the way people who think that way not only miss the point, they disprove it with pretty much every breath they take.

      • Bruce Caithness

        Science as with the other arts begins with problems, not with data that somehow induces theories or works of art in general. How can minds or their technological surrogates even perceive data if they do not possess modifiable expectations or propensities to solve problems?

        Rather than having a focus on the justification of beliefs, some sort of attempt to rationalize induction, it is more astute as Popper points out to focus on reaching a critical preference between choices. Better theories explain more than lesser theories, predict more precisely, articulate with other theories and they stand up to tests.

        We should attempt to state the universal claims of our creative imagination in a form that will invite refutation by existential statements (if true). Thus falsifiability is a LOGICAL property of a statement. Falsification is the process of DEMONSTRATING that a proposition has been falsified. Unlike the clear logic of the process, the real-world process of falsification can never be decisive due to implications of broader assumptions, the uncertainty of observations and the ways that people can willingly or unwillingly protect their views.

        Furthermore, building tools is not the same as doing science. Scientific theories may be instruments but they are not only instruments. They explain. A shovel or an electron microscope is not true or false, a scientific theory can be; mind you any claim to be true is only tentative – otherwise it is not science!

        Our conjectures come first as in all arts. The primacy of perception or induction is a fantasy. Let us praise the imagination that discovers our ideas, but remain humbled by our propensity for error. It is the humility of science that gives us hope that we will not be consumed by technological hubris nor the hubris of scientism.

        • Robin Craig

          Conjectures – on what? Conjectures are dependent on perceptions to conjecture about, and induction is the tool by which we determine the truth of conjectures. Obviously induction is a process of thinking, not something that generates itself out of random data. That in no way affects the truth of my arguments why induction is primary (over deduction – for without induction, deduction has no material to deduce from) and why induction gives true knowledge.

          • Bruce Caithness

            You seem to be making a claim for immaculate perception. Strange.

  • Robin Craig

    Yes, to clarify, what I mean by “explanatory induction” is discovering causes. The question “why is it so?” is pretty much the same as the question “What causes it?”

  • Bruce Caithness

    Just a few points, I do not want to over-stay my welcome on this web page:

    1. It is a world of propensities. Living cells and multicellular organisms are disposed to interact with the outside world.

    2. These dispositions or propensities, articulated or not, collide with reality rather like a blind person extending a walking stick. When the probe meets an unexpected barrier then the earlier disposition is modified, and the exploration continues.

    3. How many people observed fruit fall from trees before Isaac Newton? Newton did not have a blank mind, he was wrestling with problems as he interacted with the world. Kant was a bit off the mark in that he thought dispositions were valid or true without the testing of experience. It is the testing against reality plus the possession of language and that builds primitive dispositions into articulated theories. It is continued testing that hopefully leads us closer to the truth of these statements.

    4. We must observe the world to test our fumbling expectations, but be critical towards even our interpretations of reality, what we believe are facts. Facts are statements that reflect reality. Perception can deceive.

    • Thomas M. Miovas, Jr.

      I’m not really sure of what you are trying to say by the term propensity. We observe the facts of reality. Our minds do not create them when we observe them to be what they are. It is not “theory laden observations” that make the world what it is. It is what it is independent of any consciousness being aware of it. No one starts off with theories in their minds or even propensities, if I understand your position correctly. What exists exists, and we observe it, then we organize what we observe mentally into identifications of that which we observe, and from there come up with concepts, propositions, generalizations,and finally theories. Newton did not start off with a theory in mind when he made his observations. He observed how things interacted, measured the results, and then finally organized them in such a way as to come up with the Laws of Motion inductively. I can’t go into the whole details of how he did this, you would have to read “The Logical Leap,” but in essence he measured various aspects of that which he observed, organized according to causes, and then came up with the generalizations of how things interacted, and then formalized his theory and tested it. At no time did his theorizing control that which he observed, which is why he was so successful. The facts of reality are directly observed by the sense, such as the letters on this page you are reading. Your knowledge of the English language does not make them what they are. They are what they are regardless of whether or not you even understand English.

      Unfortunately, the idea that ideas make reality what it is is a very old mistake in philosophy and it will be some time before that false notion is eradicated from our ideas about how the world works for many people. Our senses do not conform to our ideas; reality does not conform to our senses nor to our ideas. We observe what exists and then we think about it to come up with concepts, principles, and theories. The inductive method of observing the world before conceptualizing it is why that method is so successful because it recognizes the independent nature of existence, and simply comes to understand it.

      • Bruce Caithness

        A blank slate cannot learn.

        • Robin Craig

          Whatever that is intended to mean, the fact remains that by applying our reason to the evidence of our senses (including when we deliberately experiment) we can gain true knowledge of what’s out there in reality.
          As proved by everything from cooking a meal to landing a space probe on a comet.

          • Bruce Caithness

            The evidence of our senses is useful, not because it is incontrovertibly proven to be true, but because our agreement to accept it is relatively unproblematic. What is it useful for in science? For testing our universal theories and like many experiences as triggers for fresh guesses (theories).

            Cooking and landing space probes are examples of technology, the making and using of artifacts, not science. The conflation of technology and science is part of the same problem as that of glorifying generalization into a pseudo-logical word, “induction”.

            One develops technologies to do things, like test theories or make diagnoses. Near enough is good enough. One develops scientific theories to seek the truth (pure). Science endorses ideas as preferred against others, but never releases them from susceptibility to further criticism e.g. Newton’s theories were not as broad as Einstein’s and even the latter are not the last word.

          • Robin Craig

            You have some Platonic ideal of “truth” – where in science, you need full and complete knowledge before you will acknowledge that any of it is true?
            You have it round the wrong way. Technology would not work if the science behind it were not true. That we later refine our theories does not disprove them, it extends and, er, refines them. For example, that there are blood antigens beyond A and B was not disproved by the discovery of the Rh factor. The A and B antigens still exist and that knowledge is, was and will be true even if we later discover the X factor exists as well.

          • Bruce Caithness

            One can agree that knowledge of universal scientific theories as contrasted with existential facts can tell technologists what will not work, but the corollary is not true that scientific theories are necessary to develop technology or engineering projects. This applies even today. Technology has preceded science by many thousands of years.

            I was not aware that recognizing the limitations of my own perceptions and theories as proper reflections of reality means my view of truth is Platonic. As certain as I may be about how well my views reflect reality, this does not inoculate them from error in actually reflecting what is going on in the universe.

          • Robin Craig

            I never said science was necessary for technology. In fact the article says quite the opposite in the bit on descriptive vs explanatory induction.
            However *true understanding* is necessary for technology, even if the understanding is only partial. You can’t even make a living making stone tools, let alone a bow and arrow, without some true understanding of the nature of the things you are converting.
            However high technology is another matter and while it can advance beyond theoretical understanding, it is still based on true understanding of the nature of reality to a far greater precision than making primitive tools or machines.

  • Wow, I loved this piece! Thank you Robin!

  • Guest

    Robin, are your Just Hunter books available hard copy anywhere? Thanks, Roslyn

    • Robin Craig

      Hi Roslyn,
      You can order hard copies of “The Geneh War” and “Time Enough for Killing” through Amazon, not just the Kindle versions.
      However “Frankensteel”, since it’s a shorter novella, is not yet available in hard copy. I do recommend you read it first if possible.

  • Kurt Keefner

    I think there are at least three kinds of valid deductions: 1. “Explanatory” deductions whereby we appeal to the factors that cause our examples to be alike, for example, “gold is ductile” is a valid generalization if we understand what about the atomic structure of gold makes it ductile. 2. “Identity” deductions in which we say “gold is ductile” EVEN IF we do not understand the atomic structure of gold, but we know that our new examples of gold are indistinguishable from examples we have observed to be ductile and we conclude that it would a contradiction for them NOT to be ductile. (I know this needs beefing up.) 3. “Population” deductions, which are primarily applied to biology and state that since members of the same species share a common ancestry and a limited gene pool, it is reasonable to generalize that they will consistently share certain traits, barring mutation. Note that I said reasonable, not certain. I don’t think certainty is the goal here, unless you mean “contextual” certainty.

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