A Reply to Stefan on Induction and Deduction

On my blog Sye Ten Bruggencate vs. the Absolute Laws of Logic which I posted back in July, a visitor posting under the moniker StefanMach (to whom I will refer as Stefan henceforth) recently left a comment about the relationship between induction and deduction and presuppositionalism.

Specifically Stefan inquired about the consequences induction has for deductive conclusions given the view that “inductive argument conclusions are classified as either strong or weak and can never be classified as true or false.”

This is topical given that deductive arguments attempt to draw conclusions from at least one premise which, as a generalization, must be the conclusion of an inductive inference. Thus if an inductive inference can only produce a conclusion that is at best “strong” (as opposed to “weak”), then any attempt to draw a conclusion by means of deduction from an inductive conclusion would necessarily inherit the tentativeness already present in the inductive conclusion. Consequently, how can any deductive conclusion be accepted as reliably true or certain?

I will get into the details of this matter below, but I won’t keep readers in suspense. You see, I do not buy the supposition that ”all inductive generalizations are either strong or weak” for a variety of reasons, but hopefully the more observant readers can already spot one of the more obvious problems with this supposition right off the bat. (For those who cannot, I will elaborate below.)

Let’s turn first to what Stefan has stated. Stefan wrote:

You said that from previously derived generalizations ( conclusions of induction), we formulate deductive arguments and arrive at particulars. No challenge there. My question is this. Since inductive argument conclusions are classified as either strong or weak and can never be classified as true or false, wherein lies the strength to say the conclusion of a deductive argument derived from a previous induction concludes with a true answer? Seems to me that all true statements would lose their strength.

It is quite common these days to distinguish induction from deduction by characterizing the former as capable of leading at most to a conclusion that is probable while the latter leads to a conclusion that is certain. This is in contrast to the view that induction is the process by which a general conclusion is drawn from specific inputs while deduction draws a specific conclusion from at least one premise which is general in scope. For example, in his Dictionary of Philosophy and Religion, William L. Reese writes (sv. ‘Induction’):

The widespread distinction between induction as an inference moving from specific facts to general conclusions, and deduction as moving from general premises to specific conclusions is no longer respectable philosophically. This distinction distinguishes one kind of induction from one kind of deduction. It is much more satisfactory to think of induction as probable inference and deduction as necessary inference.

Now I realize that I am pretty old school on these matters, admittedly out of vogue with the recent trends in post-modernist deconstruction. In my mind, insofar as inferences are concerned, the drawing of a general conclusion from specific inputs is fundamentally different from drawing a specific conclusion from a general premise. Reese’s own statement confirms that designating the former as induction and the latter as deduction was commonplace in the past. This distinction goes back to Aristotle. H.W.B. Joseph, in the second edition (1916) of his mammoth An Introduction to Logic, also confirms this (p. 378):

The history of the word Induction is still to be written ; but it is certain that it has shifted its meaning in the course of time, and that much misunderstanding has arisen thereby. The Aristotelian term ὲπαγωγή, of which it is the translation, signified generally the process of establishing a general proposition not by deduction from a wider principle, but by appeal to the particular instances, or kinds of instances, in which its truth is shown.

Going back to Reese, we find an overview of Aristotle’s approach to induction (op. cit.):

The technical study of induction began with Aristotle. Although his writings carry suggestions of many of the forms of induction, he clearly describes at least two kinds, which have come to be termed perfect and ampliative induction. (a) In complete or perfect induction the general conclusion rests on knowledge of each instance covered. The conclusion does not go beyond the evidence. This form is also called induction by enumeration. (b) In ampliative induction the conclusion takes the instances as a sample of the class and generalizes from the properties of the sample to the properties of the class.

For the purposes of my present exploration, I will employ the convention of distinguishing induction “as an inference moving from specific facts to general conclusions, and deduction as moving from general premises to specific conclusions,” Reese’s concern for lack of respectability notwithstanding. Since my first order of business in the proceeding analysis is to dispel the notion that inferences moving from the specific to the general can always only yield at best tentatively true conclusions, it is important to keep this distinction in mind with respect to the terms of induction and deduction. Drawing on the objective theory of concepts, I will be seeking to establish the view that the approach described by Reese above as “ampliative induction” (as opposed to “enumerative induction”) can in fact yield conclusions which can confidently be accepted as certainly true. We do in fact draw general conclusions from specific instances regardless of what we call it.

Since deduction derives specific conclusions from at least one general premise, we need that general premise before we can proceed deductively. The question boils down to: How do we get that general premise? And in light of the concern which Stefan has raised, we must also ask: Does the process by which we got the general premise indicate that inductive conclusions can at best be strong, or are there different species of inductive inferences (of the “ampliative” sort), some of which can and do in fact produce conclusions that are certain?

My view is that while there are different types or applications of induction, some inductive inferences in fact draw general conclusions from essential information already implicit in one or more of the concepts involved in the inference such that they can be accepted as certainties, and that the lion’s share of the inductive work is already accomplished in the very formation of the concepts in question. Yes, I realize that this may strike some thinkers as a rather bold move, but I think there is good warrant for this view in the objective theory of concepts.

Consider the following examples:

(I) The standard model of a basic deductive syllogism:

P1: All men are mortal.  

P2: Socrates is a man.  

C: Therefore, Socrates is mortal.

(II) I have a bag full of marbles and after pulling out 20 blue marbles, I infer that the next marble I pull out will also be blue.

(III) My wife was recently cooking on the stove, so I infer that if I touch the surface of the stove that it will be hot enough to burn me or at least cause pain.

Now I readily grant that I am not an expert on the varieties of inductive application; it’s been quite a while, for instance, since I’ve studied Mill’s methods. But the three examples I’ve given here are distinct from each other in my mind given the relation between the conclusion derived and the inputs used to derive them.

Obviously (I) is a deductive argument. But P1 is clearly a broad, all-inclusive generality about an entire class of objects and thus must be examined for its strength, cogency or, perhaps, its truth value. It is the kind of generality that we find in P1 of (I) that I would say is incontestably certain, and I think the objective theory of concepts supports this entirely (I’ll get into some of the details below).

Example (II) is the classic “what could come next?” scenario. Now it very well could be that the next marble I pull out of the bag will be blue. But in fact, all things being equal, what guarantee do I have that the next thing I pull out of the bag will be a marble in the first place? Unless I packed the bag myself or at least observed it being packed, how could I know what is in the bag? Perhaps there is a label on the bag indicating that it is a bag of marbles. Fair enough. Of course, I could squeeze the bag around in my hands and tell that at least much of its content is marbles. But this would not ensure that there might be other small objects included with them, let alone provide a basis for supposing that the next marble I pull out of it will be of a certain color. Here the strong-vs.-weak scale of measuring inductive reliability seems appropriate.

In example (III) I am drawing on past firsthand experience. I know that using the stove to cook food (such as stir fried vegetables, which uses high heat) makes the stove top very hot, and that its heat does not dissipate suddenly. The stove top retains its heat for some time. But perhaps it’s been enough time since my wife used it for the stove to have cooled down. Here again the at-best probable outcome of an inductive inference seems to be a reasonable expectation.

Since examples (II) and (III) do not cause us to question the notion that inductive arguments can produce only strong or weak conclusions, let us look at (I) again, specifically the premise “all men are mortal.” P1 is clearly a general premise – it applies to all men. And yet, how did we acquire this knowledge?

Some might say that P1 is true simply “by definition.” But I think this falls short of providing a suitable explanation, and whether intentional or not, saying that something is true “by definition” strikes me as readily granting the license to stipulate that something is the case. Moreover, it does not explain how we got the definition in question in the first place. Rather, the “by definition” defense seems to preclude the supposition that P1 is the product of inductive inference.

Also in that case, we must ask: “by definition” of which term? Is it the case by definition of ‘man’ or by definition of ‘mortal’? Presumably it would be involved in the definition of ‘man’, but what exactly is that definition and where did we get that definition?

Definitions do not come to us out of the blue. We do not pick them up off the ground. We do not find them buried in the soil and then say, “We’ve unearthed the definition of ‘man’ near Crater Lake, so going forward we need to abide by it.”

The objective theory of concepts teaches us that definition is the final step of concept-formation. We do not begin forming concepts by first defining them and then looking for units which satisfy their definitions. This would be a reversal: what would we be defining in such a case? It would be a concept without units, which is a contradiction in terms. And what gave rise to a concept without units?

Concepts serve man’s mental needs by maximizing cognitive economy. The task of a concept is to “unite things that share an essential similarity” (Peter Schwartz, Why Is The Tea Party 'Extremist,' But Democratic Support For Big Government 'Moderate'?). We form concepts for a purpose – to group like things into a mental unit which is open-ended in its scope of reference and distinguished by a definition for the purpose of identifying and integrating the objects we perceive. The process begins with perceptual awareness, and through the process of abstraction we advance to a new level of awareness, conceptual awareness - the level which expands our awareness beyond the perceptual level.

But we do not begin the process of forming concepts with the process of supplying definitions. This step only comes after we have isolated and integrated units to inform the concept. Only then do we have something to define. Ayn Rand explains:

A definition is a statement that identifies the nature of the units subsumed under a concept.  

It is often said that definitions state the meaning of words. This is true, but it is not exact. A word is merely a visual-auditory symbol used to represent a concept; a word has no meaning other than that of the concept it symbolizes, and the meaning of a concept consists of its units. It is not words, but concepts that man defines—by specifying their referents.  

The purpose of a definition is to distinguish a concept from all other concepts and thus to keep its units differentiated from all other existents.  

Since the definition of a concept is formulated in terms of other concepts, it enables man, not only to identify and retain a concept, but also to establish the relationships, the hierarchy, the integration of all his concepts and thus the integration of his knowledge. Definitions preserve, not the chronological order in which a given man may have learned concepts, but the logical order of their hierarchical interdependence.  

With certain significant exceptions, every concept can be defined and communicated in terms of other concepts. The exceptions are concepts referring to sensations, and metaphysical axioms. (Ayn Rand, Introduction to Objectivist Epistemology, p. 40)

Clearly then, before we can define a concept, we need the units which that concept subsumes, and we need to have formed the concept itself. Just as we do not “interpret” concrete objects like rocks or chairs (we interpret symbols, statements, facial expressions, etc.), we do not define the units which a concept subsumes, but rather the concept which subsumes a distinguished class of objects. Definitions make it possible to differentiate one concept from another. And since definitions of concepts consist of other concepts, definitions help us map out the hierarchical relationships in which concepts are contextually embedded. Peikoff explains:

If a concept is to be a device of cognition, it must be tied to reality. It must denote units that one has methodically isolated from all others… A definition cannot list all the characteristics of the units; such a catalogue would be too large to retain. Instead, a definition identifies a concept’s units by specifying their essential characteristics. The “essential” characteristic(s) is the fundamental characteristic(s) which makes the units the kind of existents they are and differentiates them from all other known existents. (Objectivism: The Philosophy of Ayn Rand, pp. 96-97)

Thus definitions are not and thus cannot rightly be treated as self-sufficient primaries. To say that something is “true by definition” does not ensure us that the definition is ultimately tied to reality. The ontological argument, for example, begins with the affirmation that “It is a conceptual truth (or, so to speak, true by definition) that God is a being than which none greater can be imagined (that is, the greatest possible being that can be imagined).” If any notion were to be taken as “true by definition,” what accounts for the supposed truth of the definition in question? Where is the tie to reality? One could just as easily say “By definition, Blarko is a being than which none greater can be imagined.” If we accept the initial premise of the ontological argument, on what basis could we reject the statement about Blarko? If we begin with definitions without concern for their conceptual legitimacy, we are in for intellectual hazards of Obamacare proportions.

Luckily we have the objective theory of concepts to protect ourselves from such catastrophes, at least so far as our own thinking is concerned. In fact, the “true by definition” approach is not sufficient to settle all questions. Thus while the notion that P1 is “true by definition” overlooks the relationship between concepts and their definitions, we are right to explore the nature of the concepts involved in P1 and ask: Where did we get these? To address this question, we need the objective theory of concepts.

The process by which concepts are formed involves isolating objects that are essentially similar and uniting them into a mental unit by means of measurment-omission. Measurement-omission is the principle that “omitted measurements must exist in some quantity, but may exist in any quantity” (Ayn Rand, Introduction to Objectivist Epistemology, p. 18). Thus the concept ‘man’ includes men who are 5’5” tall as well as those who are 6’4” tall; those who weigh 160 lbs as well as those who weigh 260 lbs; those who have beards as well as those who are clean-shaven; those who are professionals like doctors and lawyers as well as homeless beggars and couch potatoes, etc. All these measurements are included in the concept ‘man’, but they are not specified as criteria which must exist in some specific measure in order to qualify something as a legitimate unit of the concept ‘man’. Also notice that among the measurements that are omitted in forming concepts denoting concretes are both time and place. The concept ‘man’ includes all men who live now, who have lived in the past, and who will live in the future. Thus the concept ‘man’ is open-ended - it is not quantitatively restricted.

So already at the very level of the concept ‘man’, we are seeing pervasive generalities emerge. Once we formulate a definition – e.g., “the rational animal” – the process of forming the concept is complete. But the process as a whole does not end there. We continue adding new units to the concept ‘man’ as we encounter more individuals and learn more things about specific men. The concept includes all attributes of every man, even those we have not met firsthand. The meaning of the concept is not restricted only to its definition; its definition is simply a means of distinguishing the essential characteristics of its units from those belonging to other concepts.

But given the essential isolated in the definition of the concept ‘man’, we can without any hint of doubt affirm that all men are biological organisms. As a result we have a generality that applies to all units of a concept based on the essential characteristic(s) specified in that concept’s definition – in this case “rational animal.” Thus we can know that something that is not a biological organism cannot be subsumed under the concept ‘man’. Animality is an essential characteristic of all units subsumed under the concept ‘man’. Anything lacking this characteristic already cannot rightly be considered a man and consequently cannot be subsumed in the concept ‘man’.

The point here is that already at the very formation of the concept ‘man’, certain general characteristics about all men can be immediately inferred given the essential characteristic(s) distinguishing its units. Thus “all men are biological organisms” is necessarily true given the fact that animality presupposes a biological nature. Another example of this would be the ready inference that “all men face the fundamental alternative of life vs. death,” since this too is a consequence of having a biological nature. Given such examples, we can rightly say that certain inductive generalities are implicit in a concept – not simply “by definition,” but rather by virtue of the essential nature of the units the concept subsumes – and that at least some of these inductively inferred generalities are certain in nature.

It is clear from her writings that Rand recognized the pregnant implications her theory had for induction and deduction. In her Introduction to Objectivist Epistemology, for instance, she wrote (second edition, p. 28):

Thus the process of forming and applying concepts contains the essential pattern of two fundamental methods of cognition: induction and deduction. The process of observing the facts of reality and of integrating them into concepts is, in essence a process of induction. The process of subsuming new instances under a known concept is, in essence, a process of deduction.

Consider also the points Tom Porter makes in his book Ayn Rand’s Theory of Knowledge (p. 93):

Induction produces universal knowledge from other knowledge, especially from particular knowledge. Concepts are universal knowledge. We do have some knowledge about people we don’t know, about their ranges of shapes, heights and weights (but not about unknown and unconceptualized existents). We couldn’t have this knowledge if we didn’t distinguish those attributes from their measurements, within human ranges. Or if we didn’t know there are human ranges. We couldn’t do this without forming the concept “man”, and we’d have this universal knowledge once we’d formed it. Forming concepts must somehow produce universal knowledge. It must be induction

The general point here is that just by forming a concept – since its reference is open-ended and inclusive of all units of a class of objects regardless of when or where they exist or how many there might ultimately be – is in essence an inductive process. We form concepts on the basis of only two or more units which we have observed, and yet the concept so formed includes all units of the same class even though we have not observed nearly all of them. This is an unprecedented power, an ability we should not take for granted or attribute in ignorance of how it works to some supernatural realm which we can only imagine. To understand induction, we need to understand how the mind forms concepts.

Given these points, then, it would not be the case that all deductive arguments would consequently lose their strength given the supposition that all inductive inferences are necessarily less than certain. Inductive inferences which draw on information already included in a concept may in fact, given the nature of the particulars involved, lead to conclusions which are unassailably true.

So now let’s go back to the supposition Stefan affirmed in his above statement and take a closer look: is it internally consistent to say that “inductive argument conclusions are classified as either strong or weak and can never be classified as true or false”? This supposition seems to offer itself as an exception to its own stated rule. It is essentially saying that all inductive inferences are “either strong or weak and can never be classified as true or false.” How does one arrive at this (supposed) truth apart from an inductive inference? No explanation of this is even anticipated in what Stefan says, though in his defense it does seem to be a very common assumption. But it seems at best to instance its own refutation: if we accept the view that all inductive conclusions are tentative, for instance, then we could not affirm the inductive generalization that all inductive conclusions are tentative with certainty. Thus we would need to allow for the possibility that at least some inductive conclusions are certainly true. If this supposition is in fact a conclusion of an inductive inference, it can itself only be accepted as either strong or weak, not the incontestable principle that Stefan’s statement assumes it to be. To put it lightly, as a supposition which is not even consistent with itself, it needs to be considered more carefully.

Stefan writes:

I think one of the points that presuppositionalism is trying to make is just this.

I have never gotten the impression from any presuppositionalist text that their concern when raising the topic of induction has anything to do with the strength value of deductive conclusions given the consequences of inductively produced premises. In fact, presuppositionalism is not about identifying actual problems and posing rational solutions. Presuppositionalism is insidious in its habit of making use of problems arising ultimately from a false theory of concepts in the effort to undermine man’s confidence in his own mind. Stefan writes:

Unless one argues from a presuppositionally coherent starting point that understands knowledge as having objective primacy over objects, something like a supreme being "speaking" objects in to existence, than [sic] what you have said is accurate, and all true statements fall prey to their previous inductions as a chain does to its weakest link.

For one thing, my view has never been that all inductive generalizations must be either strong or weak (or somewhere in between), and never certain. I’m hoping that the points which I have elaborated on above will help clarify why I would be entirely reluctant to make such a claim – a claim which is not even consistent with itself!

Second, it is unclear what specifically Stefan might mean by “a presuppositionally coherent starting point.” Why not go with Objectivism’s starting point – the axiom of existence – which is objective, perceptually self-evident, incontestably true, implicit in all knowledge, and conceptually irreducible? I challenge Stefan or anyone else to identify a starting point which does not assume the truth of the axiom of existence.

Third, knowledge does not have primacy over objects. The objects of our knowledge do not conform to our knowledge of them. Rather, our knowledge needs to conform to the objects. Objectivity means the objects of consciousness have metaphysical primacy over consciousness, not the other way around. The opposite of objectivity – some form of subjectivism – is the view that the subject of consciousness holds metaphysical primacy over the objects – e.g., the objects of consciousness conform to the subject’s wishes, imagination, commandments, preferences, emotional eruptions, whims, etc.

Lastly, as I have established above, there is such a thing as inductive conclusions which can be reliably taken as certain, given the proximity of the inference in question to the information already contained in the concept(s) involved in that inference, such as “all men are mortal.” Even the dictum that “all inductive generalizations must be either strong or weak (or somewhere in between) and never certain” offers itself as an exception to its own stated rule. That doesn’t fly.

Stefan continued:

Deduction must come first, but for us it does not,

If deduction came first, what would be deduced, and from what would it be deduced? We have already seen above that, if deduction is the process of moving from general information to a specific conclusion, then clearly we need that general information first. And that general information must be known, which means: It must be conceptualized information. But the notion that “deduction must come first” denies this, and no attempt is made to justify this denial. Even the theist could not rightly say that this general conceptualized information is something his god has, for I have already shown that an omniscient mind would not have its knowledge in conceptual form.

Stefan wrote:

so without a revelation, any statement about ,say God, pro or con, is just opinion.

Why would we need “revelation”? Look at the power that the human mind has. We perceive the world and thus have awareness of objects as entities. Thus we can differentiate some objects from others. We can observe general similarities shared between some entities by differentiating them from everything else we perceive and integrate them into open-ended mental units using the process of measurement-omission. Thus through the process of abstraction, we have universal knowledge based on perception of just a few objects. There is no need for this to be “revealed” to us, as though our minds did not have an ability which they clearly do have.

Moreover, since we can recognize the proper relationship between consciousness and its objects, we can recognize the metaphysical primacy of existence: i.e., the objects of consciousness hold metaphysical primacy over consciousness. Reality does not conform to consciousness; on the contrary, to have knowledge, consciousness must conform to the objects it perceives. Surely we can imagine an invisible magic being issuing what we want to believe in the form of “revelations,” but this is imagination, and the primacy of existence tells us that, just as wishing doesn’t make it so, there is a fundamental distinction between reality and imagination, and the rational individual is one who is prepared to observe and recognize this distinction consistently throughout all his knowledge.

What Stefan is offering here is simply more fallout from god-of-the-gaps thinking, which proceeds essentially as follows: Since inductive conclusions are necessarily only weak or strong (and never certain or necessary), deductive inferences drawing from inductive conclusions must likewise inherit induction’s tentativeness. Thus deductive conclusions can never be accepted as certain or necessary, so we need revelations from a supernatural source to provide us with reliable knowledge. All along the way there is a trail of ignorance of the nature of concepts and how they are formed leading to this mind-negating conclusion.

Stefan wrote:

Only if revelation were true could any predication take place concerning metaphysics.

I have already addressed this matter in my blog The Argument from Predication.

Stefan wrote:

Thus, the argument is made that arguments making declarations concerning the non existence of God become an odd sort of proof for God, in that they presuppose a worldview in which predication, which in form is inherently dogmatic, makes sense.

In the final analysis, there can be no such thing as a “proof for God.” To be sound, a logical proof must rest entirely on the primacy of existence. In contrast to this, the notion of “God” assumes the primacy of consciousness. The primacy of existence and the primacy of consciousness are entirely incompatible. Moreover, affirming the truth of the primacy of consciousness is self-contradictory. Attempting to prove the existence of a god is no different from trying to prove the existence of square circles. Stefan wrote:

By the way, I am at odds with where Bahnsen and his crew takes presuppositionalism, and I cannot for the life of me see why they replace God with the Bible, even though they say it is God who is self attesting. Seems oddly idolatrous to me.

This is not my problem.

Stefan wrote:

I just did not recognize in this article a serious dealing with presuppositionalism as the system that it is.

The article in question (Sye Ten Bruggencate vs. the Absolute Laws of Logic ) focuses on apologetic tactics of Sye Ten Bruggencate, as the title suggests. It was not intended as a once-for-all take-down of presuppositionalism as a system.

Stefan opined:

Fundamentally, you cannot justifiably attack a system piecemeal when it up front makes the point that world views need to be dealt with as a whole, and that coherence should be sought between metaphysical, ethical, and epistemological presuppositions so as to have a coherent takeoff point.

Actually, I don’t think things are so challenging as Stefan seems to believe here. As an apologetic method intended to defend Christianity, presuppositionalism assumes the truth of Christianity. If Christianity can be shown to be false, then, presuppositionalism as a system falls with it. Simply exposing Christianity’s system-wide assumption of the primacy of consciousness metaphysics is sufficient to show that Christianity is false. Notice how Christian apologists themselves often hasten to reply with statements like “Saying that X is the case doesn’t make X the case.” Indeed, they are right. But Christianity, a worldview which asserts that an invisible magic being “spoke” the universe into being – that whatever is the case is the case because a supernatural consciousness says it is, can in no way support such a declaration. The statement “Saying that X is the case doesn’t make X the case” is an instance of borrowing from Objectivism, specifically from the principle of the primacy of existence. This is completely at odds with Christianity, which rests on the primacy of consciousness – e.g., the notion that ‘wishing makes it so’. According to Christianity, its god wished, and made everything so.

Since I am not a Christian, these are not my problems.

Stefan wrote:

Perhaps at other points along the way, you have shown a working knowledge of presuppositionalism, I don't know.

I invite Stefan to explore my writings. They’re there for his and anyone else’s perusal. But I strongly suggest that Stefan not make the same mistake that so many others have. Countless Christians have visited my site attempting to refute Objectivism without first understanding what it is they are trying to refute. Stefan would be wise first to study what Objectivism is all about – he can begin with some of my blog posts and also consult Objectivist sources which I cite in my writings. Then he is welcome to come back with any questions he may have on what he’s has since discovered in Objectivism. A most profound and wonderful discovery awaits him.

So happy reading!

by Dawson Bethrick