Friday, December 31, 2010

Induction of Objectivity (Aristotle)

[Previous post in the series: "Reduction of Objectivity (Aristotle)"]

Objectivity now being reduced, we can work through the steps Aristotle had to in order to induce his principle of objectivity. It’s essentially five steps:
  1. Grasp the distinction of percepts and concepts.
  2. Understand that concepts are capable of error, whereas percepts are not.
  3. Learn that the functioning of concepts is under our control, whereas percepts are not.
  4. Discover that we can somehow use percepts as a means to measure concepts.
  5. We’ll then know that a method is necessary, and that it is possible because we know what it would consist of, by reducing the fallible part to the infallible part.

Percepts and Concepts

The first step is to reach the distinction between percepts and concepts, what the Greeks called “sense” and “idea.” The distinction was originated by Socrates and Plato, depending on how one interprets his dialogues. What Plato had to do, and what Aristotle and all of us had to do, was to mentally observe similar instances of ideas in contrast to sensory experience, to our percepts. With the contrast, Plato was able to draw out a list of attributes that belonged to ideas as opposed to sense experience:
  1. Ideas were general or universal (Beauty, Justice, Virtue, etc.); sense experience was particular or concrete (the beauty of a maiden, the piety of a man, etc.).
  2. The One and the Many—we’re aware of countless things which nevertheless seem to have the same properties; for instance, John is the same person, no matter what age he is or any differences in his appearances. Plato realized that this physical distinction actually applied to these mental phenomena, ideas.
  3. Ideas are abstract, non-material, whereas the senses interact with our bodies and material objects.
  4. Ideas are immutable, changeless, whereas sensory objects are always changing, coming into being and going out of existence.
  5. And so on.
This first step itself consists of a great many inductions Plato had to make before even reaching this distinction. He had to realize that the phenomena of ideas were universal to man, but not to animals, which lead to the induction that animals possess senses, but not ideas. All men possess ideas—another induction. He had induce that all ideas have the same composite attributes—that anything that has universality would be immutable, non-material, etc.

These weren’t very difficult for Plato and Aristotle to induce, as these conceptions of ideas and the senses were easily integrated with the long-known view that man was the animal that reasons, argues, judges, etc. The field of epistemology started because Plato’s discovery led to the further discovery that reason, the special faculty of humans, was the faculty of ideas or universals, in contrast to other animals who had only the faculty of sense.

Error-free vs. Fallible

The next step: before we get to an idea of method, we have to discover something about error. Aristotle himself made the necessary discovery, following Plato’s distinction of ideas and senses: he states explicitly and on numerous occasions that the senses (specifically the “special objects” of senses) can never be in error, but that the intellectual interpretations of sense-data can be mistaken. He says for example that the seeing of the special object of sight, i.e. color, like “white,” can never be in error, while the belief that the white object seen is a “man” may be mistaken (On the Soul, Book 3, Chapter 3). He made this clear-cut induction without a clear knowledge of how the sense-organs operate or even how we form concepts, except that it involves abstraction and induction. But from examples like the white object seen being a man, and many examples of seeing, hearing, etc. being free from error, while the thought associated with the sense experiences was liable to error, it was relatively simple for him to generalize, thus grasping the fallibility of ideas, and the infallibility of the senses.

What We Control

The third step: We also have to know where we are in control, and where we’re not. The Greeks discovered this, and Plato and Aristotle knew that the senses were automatic, that they are an interaction of some material object and your body’s sense-organs, and no effort is needed on your part. And Aristotle knew implicitly that concepts functioned under our free will, and that we could deliberate, guide our mental and physical actions, make choices based on our circumstances, improve our skills, like in debate, etc. He knew that no act of will could affect our senses once our organs had interacted with the objects of sense, and that no mental effort was necessary for the interaction, and that the opposite was true for the level of ideas. (For instance, in the Topics, Book 8, Chapter 2, Aristotle advises that during a debate, when you present an inductive argument based on several cases and your opponent won’t admit the argument, you should cover all the cases with an already-known term, or a newly-coined one, which places the burden on the opponent to then disprove your argument.) Clearly, he thought that the use and creation of ideas was under our control, and he must have induced the restriction of free will to the conceptual level from observing numerous cases which discerned the role of choice.

So, Aristotle knew that the part that can go wrong is in our control, and the part that was error-free was not in our control. With that knowledge, advances could be made in the science of epistemology, specifically an account of objectivity. The goal is to use our free will to correspond our ideas to the senses. Aristotle will propose to use the safe, error-free part as a standard against which to test the part that’s liable to error.

The Connection between Percepts and Concepts

This, however, leads to an interesting question: Since ideas and senses are opposites in so many ways, what could be the connection between the two? Plato is well-known for regarding ideas and the senses as so different that they occupy different realms, and thus that there are two worlds. Aristotle had to realize that there’s only one world, and that ideas come from sensory experience. He describes the process of ideas coming from sensory experience in Posterior Analytics, Book 2, Chapter 19 as a progression from perception to memory to experience (memories of the same thing) to a universal. The essence of objectivity is being able to reduce our ideas to the evidence of the senses. So Aristotle’s discovery that all ideas come from sense experience was an important and necessary induction.

How did he reach it? He had to directly observe the process he used in forming concepts. And the essential process of concept-formation, the one which he was the first to name, he termed abstraction. By abstraction, he meant a special focus on the similarities among things, while ignoring or not specifying the magnitudes of their differences. Certain things have similarities which we can cognitively focus on and “pull out,” separate in thought what can’t be separated in reality. Once mentally separated, we could discover an implicit universal that applies to all the particulars of a certain kind, and that allows us to form the concept, definition, or proposition. He performed this analysis on many concepts, concepts that he observed introspectively, and concepts he heard from other people. This insight into the nature of abstraction led to Aristotle’s induction that all ideas are formed by a process of abstraction from the data of senses, adding that higher-level abstractions were formed from lower-level abstractions that were initially formed from sense experience (see Posterior Analytics, Book 2, Chapter 19). For Aristotle, this corrected Plato’s original thesis that ideas do not come from the senses but are recollected from our previous existence. This in turn led to the deductive conclusion that there are no ideas apart from sensory evidence, and thus to the view now known as “empiricism,” the idea that all knowledge is based on sensory experience and the denial of innate ideas, a view which originated with Plato.

Here we could use the genus principle: knowledge above the level of a jellyfish, the level of discrete sensations, requires some sort of certification by perception, some validation. Higher animals (like tigers) already have perception, so their knowledge is directly validated. The distinctive method of people requires validation by perception because it is conceptual—concepts have to be reduced to percepts. This is what we have to know to form logic, because we now know that conceptual validation isn’t given without effort, but requires some kind of reduction to the level of percepts.

The fourth step would be to understand what basic things people did with concepts, so that we begin to search for a method to check our ideas against the senses. The key fact here that was known way before the Greeks is that people would argue, they would have structured discussions involving chains of ideas, which would lead to other ideas or other chains. The Greeks knew that propositions called “premises,” when linked together, would lead to a proposition called a “conclusion” and that this structure was called an “argument.” (Aristotle discusses “premises” and “conclusions” in Prior Analytics, Book 1, chapters 1 and 4, for instance.) The Greeks also knew that these arguments were a kind of reasoning, and that arguments were a crucial way of using ideas to gain knowledge.

There were many observations and inductive conclusions required before anyone could reach the ideas of “arguments,” “conclusions,” etc. and we’ll take them for granted here. People also knew in Plato’s time that you could unravel an argument, asking what a given premise depended on, which implies that there can be a chain of arguments. In this way, they learned that knowledge is relational and hierarchical: relational, because a person could gain important knowledge by relating one cognitive item to another (like, “a ‘tree’ falls under the idea of ‘plant’”) as opposed to starting in a void; hierarchical, because these relations among ideas can be organized into complex, protracted structures which go back to some kind of beginning or starting point.

It’s this context concerning arguments and their structures, and what Aristotle figured out about concepts that were prerequisites for Aristotle creating the science of logic.

A Method that was Both Necessary and Possible

Before we induce what Aristotle learned about logic, we should first reduce it, which will give us a clue into what discoveries he had to make.

Logic allows you to validate or prove an idea by showing you how to establish valid relations among your knowledge, leading back to axioms, to sense-data. How did he discover that “validation” is something established by leading an idea or chain of ideas back to axioms or sensory data? That presupposes that he discovered the principle of validity, whatever it is that makes an argument valid. Once he knew it, he would know what makes a valid argument, and could realize that a chain of valid arguments is what a proof consists of. We thus need to discover the basic principle of validity. To determine the standard or basic principle of validity, we’ll need to create a list of valid arguments on one side and compare them to a list of invalid arguments on the other side. And from there, we can abstract what the valid ones have in common.

But before that separation can happen, we’ll have to discover that we need rules to guide us in relating ideas, since up until now we’ve been focusing on a general guide of validating concepts as such, not specifically their relations to other concepts. Aristotle’s validation of concepts will progress by analyzing concepts as combined into statements, and discovering rules to guide us whenever we combine these statements to draw a conclusion.

So, to induce all this: how did Aristotle discover that we need rules to direct us into combining propositions to reach a conclusion? The Greeks before Aristotle knew that some arguments followed from their premises and some did not, and philosophers from the beginning of philosophy would criticize each other for drawing unwarranted conclusions, or denying what they admitted in their premise. The Sophists were well-known for deliberately using invalid arguments and convincing people to accept them. They knew that reasoning was the means by which we learn (or at least one important way), and they knew that a person’s reasoning could get off-track and the reasoning could be criticized as a result. All of this was known before logic, and people could grasp that arguments didn’t follow before studies on arguments like that of Aristotle’s, and Aristotle used this knowledge to devise the method of reasoning.

Aristotle knew that a method was necessary because he knew that the mind’s reasoning can go wrong, that this wasn’t direct observation of the self-evident. And he knew that this method was possible because he knew that the area of reasoning was the area under our control, and that we’re not merely reactors. People argued, and they couldn’t figure out how or why arguments would fail, and yet Aristotle devised an ingenious universal method for checking chains of ideas in our consciousness. He set out to formulate a set of principles that an argument could follow and could insure that the argument was valid, and if an argument disobeyed the principles, it was then invalid. Thus, he abstracted a method of thought that pertains to everything and anything: books, teachers, ships, houses, ideas etc. The result would be the largest induction that could ever be made.

But even the discovery that we need these rules was itself inductive: how did he know that we need rules in every case of reasoning? He knew that every case of reasoning was volitional and fallible, liable to some kind of fault. He couldn’t examine every case of reasoning; he rather examined exhaustive numbers of arguments (simply read the Prior Analytics for a sample of his study!), and generalized that all reasoning required rules. There’s no other way to reach this generalization except by induction, neither by enumerative induction and inspection of every case, nor by deduction.

His goal was to find rules to determine valid and invalid arguments. The results of his efforts can be read in his Prior Analytics, which inductively presents each argument type (Aristotle calls the premise-conclusion structure that arguments are presented in "syllogisms"), even providing examples for the reader to work through his argument structures, which uses variables. I’ll add that the idea that variables could be used to teach argument structures was another innovative induction of Aristotle’s. His amazing discovery was that all the valid argument structures were related by having certain forms, rather than validity depending on the content or material of the argument. Without Aristotle’s discovery of this, logic would have been impossible, as people would think that only certain structures would work for certain content, or that the content determined the validity of the argument.

Here is an example of a valid argument (the syllogistic figure that the medievals called Baroco, in which “a” means a universal affirmative proposition, like “all men are mortal,” and “o” means a particular negative proposition, such as “some pigs are not messy”):
  1. “a”: M belongs to all S
  2. “o”: M does not belong to some B
  3. “o”: S does not belong to some B
To give an example of this argument:
  1. All swamps are murky.
  2. Some books are not murky.
  3. Therefore, some books are not swamps.
The major premise (M belongs to all S) states a universal property of a subject, the minor premise (M does not belong to some B) states that some members of a different subject don’t have this property, and the conclusion (S does not belong to some B) is a conversion of the two premises: it infers that those members of the second subject do not belong to the class of the first subject. (A conversion occurs when we infer a proposition from different proposition by interchanging the subject and predicate.) Aristotle, by using variables, holds that arguments like this, and the other figures he discusses in his book, are structurally valid no matter what their content.

Here’s an example of an invalid argument:
  1. C does not belong to B
  2. C does belong to some X
  3. B belongs to all X
Or, to particularize this argument:
  1. All bathtubs are not made of cardboard.
  2. Some boxes are made of cardboard.
  3. Therefore, all boxes are bathtubs.
We supposed in the major premise that no bathtubs are made of cardboard (C does not belong to B), and this is convertible with the statement that no cardboard things are bathtubs (B does not belong to C). But in the minor premise, we also supposed that some boxes are made of cardboard (C does belong to some X); to make the argument valid, we would have to conclude that some boxes are not bathtubs (B does not belong to some X), but that isn’t the conclusion we reached in the argument. The conclusion that all boxes are bathtubs does not follow from its premises, and it clashes with what the premises present. (What this “clash” is will be discussed a little later.) In fact, the argument structure will always be invalid, no matter what the content is, with the result being that “there will be no syllogism,” as Aristotle often remarks about invalid arguments.

Aristotle’s Predisposition towards Forms and Rules

How did Aristotle find out that validity in arguments is an issue of form? Here, Dr. Leonard Peikoff has two speculations, as he finds the idea that Aristotle merely observed instances of arguments and induced his discovery to be too simplistic.

Two factors may have predisposed Aristotle to see validity as a formal issue rather than a material one, prior to his induction about arguments and validity. One was his knowledge of mathematics; the other was his philosophical distinction between “form” and “matter.”

The science of mathematics, especially geometry, was already well-developed as a deductive system, and this was a critical model to work with for someone working on an even more abstract science, which is what logic is. Geometry was a well-suited deductive model, with well-defined rules regarding how you approached a subject matter, the axioms you must start with, and how each theorem and proposition would unfailingly follow from the preceding, and the presentation would end with QED—“what was to be demonstrated.” He understood that broad geometric reasoning was possible because the science dealt with abstractions and not specific concretes. You could reach universal conclusions about equilateral triangles or right angles, but not about a triangle whose sides were 10 feet, 8.4 feet, and 3 feet. This might have led Aristotle to figure out that we make logical connections in accordance with abstract rules, not rules with specific contents contained within them. So in developing logic, he searched for universal rules, even more universal and abstract than geometry, which deals with space, size, shape, and figures, whereas his logic could cover everything that exists.

The second factor was that his entire philosophy rested on the distinction between form and matter. Practically on every issue or subject, he states that there is something with matter, its composition, and a form or structure in which the matter exists. He wasn’t always correct in applying the distinction, but it was a brilliant thought, and he used it to analyze God, the soul, perception, elements of the physical world, all kinds of animals, and even cause-and-effect (the well-known "formal" and "material" causes). With that in mind, what would make more sense than to apply the distinction to chains of thought as well, splitting every argument into its form and matter, structure and content, use abstraction to consider the greatest possible range of arguments that could exist, and conclude that in each case, the validity depended on the form and was independent of the matter? This discovery led to Aristotle’s induction that the validity of all arguments is dependent upon their form, which was the discovery of logic.

Non-contradiction, the Excluded Middle, and Objectivity

We have yet to find the unifying principle, however. What is common to all of the valid forms of arguments, and thus defines validity? He discovered that in every case of invalid reasoning, there was a contradiction, a mistake, a violation of the law of noncontradiction. No matter the form of the argument, an invalid argument always fails due to some sort of contradiction, some attempt to claim “A” and “non-A” at the same time and in the same respect. This led to Aristotle’s application of the principle of noncontradiction to all thought, including arguments: “…the most indisputable of all beliefs is that contradictory statements are not at the same time true” (Metaphysics Book 4, Chapter 6).

Aristotle didn’t invent the principle or law of noncontradiction; Plato or Socrates before him might have, because in the Republic Plato writes: "It is obvious that the same thing will never do or suffer opposites in the same respect in relation to the same thing and at the same time" (4:436b). (Correction: the ancient Greek philosopher Parmenides was the first person known to state the principle of noncontradiction: "Never will this prevail, that what is not is." Plato in Sophist writes: "The great Parmenides from beginning to end testified...'Never shall this be proved--that things that are not are.") Aristotle words the principle: “the same attribute cannot at the same time belong and not belong to the same subject and in the same respect” (Metaphysics, Book 4, Chapter 3). But Aristotle discovered the law’s role in thought, that it is the law which governs all thought trains. And he did this by another grand induction; the law’s application to thought is not deducible from the definition of knowledge or from the statement of the law. From the fact that nothing can be a contradiction, it would not follow that the invalidation of all reasoning consists in the attempt to maintain a contradiction. (In fact, Aristotle doesn't regard the principle of noncontradiction or its application to thought as something that must be proved; rather, it is an axiom, a starting point of all thought, inductive or deductive/syllogistic, and thus the basis of all proofs.)

Though he wasn’t the discoverer of the law of noncontradiction, he did discover its corollary, the law of excluded middle, as well as that law’s role in thought. The law of excluded middle states that: “…there cannot be an intermediate between contradictories…” (Metaphysics, Book 4, Chapter 7). Its application to thought states that: “…of one subject we must either affirm or deny any one predicate” (Ibid.). Everything is either A or non-A at a given time and in a given respect; in thought, only the assertion or the negation of something can be true at a given time and in a given respect: there is no third alternative to assertion or negation, or to existence or non-existence, in reasoning. The laws of noncontradiction and excluded middle state the basic rule of reasoning and the principle of logical validity, non-contradiction, and the basic rule applied to all assertions: all reasoning must either affirm or deny something about some subject at a given time and in a given respect.

We can now consider the final point: we know what a valid argument is, but what is full validation of a series of arguments—what is proof? Aristotle knew our ideas came ultimately from our sense experiences, and that the purpose of his method of logic was to conform our thinking to reality. His focus on tracking reality can be seen from this instance, while he was discussing the ambiguity of names: “the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can be [a man and not a man] in fact” (Metaphysics Book 4, Chapter 4; italics and brackets mine). Because of what he knew, he reached another induction: that proof is taking arguments step-by-step back to sensory data and axioms.

The medium for the progression of a chain of ideas was what Aristotle termed a conversion, such as the one used in my deduction above, that some books are not swamps by relating them to the quality of murkiness. And the validity of a series of arguments was determined by testing the constituent propositions against the law of noncontradiction: “It is for this reason [i.e. the possibility of contradicting oneself] that all who are carrying out a demonstration [i.e. an argument that leads to knowledge] reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms” (Metaphysics, Book 4, Chapter 3; brackets mine). The conversions allow us to reach the inferences we seek to prove using pre-established knowledge (or presumed knowledge); the syllogistic forms give us the necessary valid structures to present our reasoning; and the axioms of logic; the laws of noncontradiction and excluded middle, provide a means for us to check if our reasoning is contradictory at any step.

Gaining knowledge by choosing to adhere to reality through this method of proof which goes backward until we reach axioms and sense experience, i.e., by the use of logic, keeping in mind that the overarching principle is: noncontradiction. This is what Aristotle conceived objectivity to be.

Conclusion: Objectivity vs. Subjectivism

One last issue: to help clarify objectivity as Aristotle understood it, we should contrast it to an opposing idea: subjectivism. What would Aristotle’s definition of subjectivism be? Instead of “choosing to adhere to reality,” he would most likely say, “volitional indifference to or departure from reality.” Instead of “by the use of logic,” he would say, “by the disdain of logic.” And Aristotle knew plenty of examples of these, and could easily use them to fill this understanding of “subjectivism.” He discusses many instances in which people would deliberately use ambiguous words in arguments, or ask many distracting questions, or offer a proof that actually doesn’t follow, and a number of other ways in which arguments were made using some criteria other than or opposed to logic; Aristotle discusses many broad examples of logical fallacies in his Prior Analytics and On Sophistical Refutations, showing that fallacies could pertain to the form of an argument, or to the material or content of an argument.

Aristotle then could have contrasted his view of objectivity with case after case of people being non-logical or illogical, and then induced the principle that if you use something other than logic, then you cannot claim to be adhering to reality.

[Next post in the series: "Reduction of Objectivity (Ayn Rand)"]

No comments:

Post a Comment