All our knowledge begins with the senses, proceeds then to the understanding, and ends with reason. There is nothing higher than reason. ~ Immanuel Kant
Reason is the capacity for, or the process of, making sense of experience and applying logic. Logic is the process of chaining symbols together – from one or more premises to a conclusion – in a way that the linkages are agreeable.
The sole object of logic is the guidance of one’s own thoughts. ~ John Stuart Mill
The application of reason is rationality. The ostensible employment of reason is judgment, and from that, making decisions.
Inference is the process of drawing conclusions from given premises by logical means. ~ Avron Douglis
Reason is often a social phenomenon, where arguments are made, and the validation of conclusions is consensual. What makes sense to one person may be considered irrational by others. Of course, reasoning is often used to convince oneself of something before proceeding to prove by experience a conclusion’s correctness, and thereby the rationale behind it.
Reason is not a search for truth, but instead a quest for a reason to think, believe, or behave a certain way. Rationality seeks a rationale.
The need of reason is not inspired by the quest for truth, but by the quest for meaning. ~ American theorist Hannah Arendt
Reasoning is typically bifurcated into deduction and induction, which come to conclusions via opposite routes.
The two operations of our understanding, intuition and deduction, on which alone we must rely in the acquisition of knowledge. ~ René Descartes
Deductive reasoning is top-down logic: reductively reaching a conclusion by applying generalized rules that narrows alternative considerations to a single result. Using assumptions (aka axioms, postulates) that are assumed true, deductive reasoning whittles away possibilities until only one is left: the conclusion.
Deduction has various forms, which are logical laws.
The law of detachment (aka affirming the antecedent, or modus ponens) is the simplest deduction: a conditional statement that determines whether a hypothesis is valid.
Condition: P → Q.
Condition: If it is raining, I will get wet if I go outside.
Hypothesis: It is raining.
Conclusion: I will get wet if I go outside.
A syllogism is a deduction that arrives at a conclusion from 2 or more related premises assumed true.
A classic exemplary syllogism:
Premise 1: All humans are mortal.
Premise 2: Socrates is a human.
Conclusion: Socrates is mortal.
The law of syllogism, as in the Socrates example, takes 2 premises and combines them to a conclusion. Its form is:
Premise 1: P → Q.
Premise 2: Q → R.
Conclusion: Therefore, P → R.
In a categorical syllogism, as above, the 2 linked premises concern classifications. Deduction to conclusion involves category memberships of the determining terms.
A linear syllogism posits a relationship between premises that invokes a qualitative or quantitative comparison.
Individuals differ in their approaches to linear syllogisms. Some do so spatially, through mental representations of a linear continuum. Others employ a semantic model of abstraction. Some combine both approaches.
Bias easily enters into the solution of a categorical syllogism. If there is at least one type of premise people prefer a particular conclusion. If there is a negative in a premise a negative solution is often sought.
In all kinds of syllogisms some combinations of premises fail to lead to a logically valid conclusion. Especially with categorical syllogisms, logically valid conclusions cannot be made from certain premises or those with 2 negative premises. For example, “Some politicians are corrupt. Some corrupt people are left-handed.” No conclusion can be drawn about the corruption of left-handed politicians. People are often flummoxed by such syllogisms, which may lead to erroneous conclusions that should not be made.
Another common error in logic is the belief that the terms of premises are equally valid when reversed: that “if A then B” is equivalent to “if B then A.” Premises are not necessarily transposable, though some may be; hence the easy error. There are no laws of logic on the transposability of premises.
The law of contrapositive (aka denying the consequent, or modus tollens) is the logical mirror of affirming the antecedent: a conditional statement that determines whether a hypothesis is invalid.
Condition: P → Q.
Hypothesis: not Q.
Conclusion: Therefore, not P.
Condition: If it is raining there are clouds in the sky.
Hypothesis: There are no clouds in the sky.
Conclusion: It is not raining.
Deductive arguments are adjudged by their validity and soundness. In application soundness trumps validity.
An argument is valid if it is impossible for its premises to be true yet its conclusion false. In other words, if the premises are true the conclusion must be too.
An argument is sound if it is valid and its premises true.
With false premises an argument can be valid but unsound. Fallacious arguments often take this form.
Everyone who eats carrots becomes a rabbit.
You eat carrots.
You will become a rabbit.
The first premise is false, and so the argument unsound, even as its logic is valid. Generalizations are often the basis for unsound arguments.
While most people have little difficulty using the simple logic of modus ponens (affirming the antecedent), the contrapositive (modus tollens) is something else altogether: few recognize the need for contrapositive deduction. Many do not recognize logical fallacies in not denying the antecedent, at least with abstract reasoning.
Fallacious and misleading arguments are most easily detected if set out in correct syllogistic form. ~ Immanuel Kant
Kant’s optimism withstanding, human logic is error prone. There is a tendency to employ favored strategies that work in some syllogisms on ones where the heuristic is inapt (overextension error). It is also common to reach a conclusion without considering all the logical possibilities (the foreclosure effect).
Mood affects reasoning. People pay more attention to details when less sanguine.
Deduction is essential to rationality. Yet it is not directly taught in schools, as it is considered a skill that develops without teaching. This unsound reasoning is one reason that specious logic is so common.
But even training in logic leads to mixed results. While awareness of mental models and rules improves, deductive reasoning is not often used.
Conditional reasoning is usually employed in 2 circumstances: to resolve linguistic ambiguities and in activating schemas that provide a meaningful context for reasoning. In short, people reason only when the demands of the situation leave no other resort to make sense of what is going on.
Rather than employing formal logic, people typically use pragmatic rules of thumb, which are sufficiently broad to cover a wide variety of situations. Such heuristics are typically goal oriented, or pertain to social mores, especially deontic contexts.
Not only do people anticipate the immediate consequences of actions (for example, whether an action is likely to achieve a desired goal), but also more indirect consequences related to social roles and regulations. For a person acting within a social context, the evaluation of actions is guided in part by a complex web of contract-like regulations. ~ Canadian American cognitive psychologist Keith Holyoak & Chinese American cognitive psychologist Patricia Cheng
In our reasonings concerning matters of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence. A wise man, therefore, proportions his belief to the evidence. ~ David Hume
Inductive reasoning is bottom-up logic: reaching a conclusion by generalizing or extrapolating from premises. Induction is inherently uncertain: a probability rather than a certainty.
A classic example of induction (from David Hume):
Premise: The Sun has risen in the east every morning up until now.
Conclusion: The Sun will also rise in the east tomorrow.
Unlike deduction, inductive conclusions can be false even if all of the premises are true. Instead of soundness, inductive arguments are strong or weak, depending upon how probable the conclusion.
People use inductive reasoning as a simplifier: to collate and congeal the diversity that comes to them into mental models and usable rules of thumb. A goodly portion of induction aims at rendering the environment more predictable, thereby reducing uncertainty.
Innumerable observations make up the gumbo which is baked into a generalization via induction. Inference does not account for all the covariations in the stew. People come to a conclusion that appeals to them, or at least makes some sense, and plow on from there.
The human mind is no logical computer. Instead, it looks for shortcuts: straightforward heuristics that work well much of the time. The fly in the ointment is that these shortcuts are subject to biases which short-circuit the reliability of conclusions.
Though analogy is often misleading, it is the least misleading thing we have. ~ English author Samuel Butler
Most everyday inferences are by analogy. The basis for assuming continuity – that the past presages the future – comes by analogy. Such tidiness can be comforting.
Analogies prove nothing, that is quite true, but they can make one feel more at home. ~ Sigmund Freud
In drawing general conclusions from specific examples, empirical science studiously employs inference.
When they propose to establish the universal from the particulars by means of induction, they will effect this by a review of either all or some of the particulars. But if they review some, the induction will be insecure, since some of the particulars omitted in the induction may contravene the universal; while if they are to review all, they will be toiling at the impossible, since the particulars are infinite and indefinite. ~ Roman philosopher Sextus Empiricus
In its obsession with classification via resemblance, science holds fast to analogy. Categorization is itself hypothesis. Evolutionary biology is especially beholden to classification in smoothing over dissimilarities and giving the facile appearance of orderliness.
The scheme of classification adopted depends upon the purpose or interest of the classifier. ~ American logician Irving Copi & American philosopher Carl Cohen
To describe any object as having a certain attribute sets it with others that share that characteristic. Once confined by category, academic inertia sets in to leave it where it sits.
A classification scheme made for narrowly practical purposes may tend to obscure important similarities and differences. ~ Irving Copi & Carl Cohen
The problem, of course, is that different things are never quite the same. What is overlooked in the classification process often turns out to be the most interesting thing about an object. Genetics is an especially apt example. Time and again, instead of helping, categorical lumping has retarded our understanding of Nature, which incessantly produces diverse uniqueness.
Inferring causal relations among the constituent elements of this world, be they physical objects or living things, is one of the most important tasks the cognitive system has to perform. ~ Israeli psychologist Ran Hassin
Causal reasoning is the faculty to identify causality: the relation between a cause and its effect. It is a critical facility in rendering the world predictable.
Causal reasoning ability is innate, though its display depends upon developing the necessary mental leverage to appreciate causality. In experiencing the world, an early fascination of infants is observing situations of cause and effect.
Children develop core concepts of causality at a very early age. Basic causal processes can be activated automatically or implicitly, with minimal effort.~ American developmental psychologists Roberta Corrigan & Peggy Denton
Humans are not alone in this ability. Crows, rats, and apes are known to suss cause and effect. It would be unsurprising to find that all organisms become seasoned in causal reasoning.
English philosopher John Stuart Mill described 5 methods of induction from correlation that suggest causality: agreement, difference, joint, residue, and concomitant variations. While helpful, the study required to comprehend Mill’s methods shows that they are not natural mental mechanisms.
For the method of agreement, the commonality among phenomena that have similar effect indicates cause.
If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon. ~ John Stuart Mill
A B C D occur with w x y z
A E F G occur with t u v x
Therefore: A is the cause or effect of x.
For the method of difference, the element missing in 1 of 2 entities being compared suggests the factor that may be causal.
If an instance in which the phenomenon under investigation occurs, and an instance in which it does not occur, have every circumstance save one in common, that one occurring only in the former; the circumstance in which alone the two instances differ, is the effect, or cause, or an necessary part of the cause, of the phenomenon. ~ John Stuart Mill
A B C D occur with w x y z
B C D occur with w y z
Therefore: A is the cause or effect of x.
The joint method combines the agreement and difference methods.
If two or more instances in which the phenomenon occurs have only one circumstance in common, while two or more instances in which it does not occur have nothing in common save the absence of that circumstance; the circumstance in which alone the two sets of instances differ, is the effect, or cause, or a necessary part of the cause, of the phenomenon. ~ John Stuart Mill
A B C occur with x y z
B D E occur with x v w
B C occur with y z
Therefore: A is the cause or effect of x.
The method of residue helps identify an effect, or possibly a cause, by a process of elimination.
Subduct from any phenomenon such part as is known by previous inductions to be the effect of certain antecedents, and the residue of the phenomenon is the effect of the remaining antecedents. ~ John Stuart Mill
A B C occur with x y z
B is the known cause of y
C is the known cause of z
Therefore: A is the cause or effect of x.
The method of concomitant variations finds a causal association between variations in an element or factor and a circumstance.
Whatever phenomenon varies in any manner whenever another phenomenon varies in some particular manner, is either a cause or an effect of that phenomenon, or is connected with it through some fact of causation. ~ John Stuart Mill
A B C occur with x y z.
A± B C results in x± y z, where ± represents variance.
Therefore: A and x are casually related.
Water toxicity is exemplary. Various samples of water with both salt and lead are found to be toxic. If the level of toxicity varied in tandem with the level of lead, but not so for salt, toxicity is attributable to lead.
Unlike other methods, concomitant variation is an issue of magnitude, and does not involve induction by elimination.
Mistakes in inference and attributing causality are common. Ignoring the law of large numbers is a prevalent error. While people generally understand the significance of having a representative sample size, there is a tendency to infer association or causality from a relatively few observations. The main reason for this is, of course, that life seldom presents statistically-sound sample sizes. Over time, people accept what they must, and may make more of it than they should. Further, everyone has experienced success despite the law of large numbers. Language learning is an exercise in generalization from a few examples.
Most people tend to ignore base-rate information (the typical), instead focusing on odd variations or unusual anecdotes. Besides the sample-size dilemma, it is natural that the norm is ignored while the unusual grabs the attention; but such is a poor basis for inference.
People tend to gather information before making judgments. As information is often unlimited, a decision has to be made as to when the data is sufficient to reach a conclusion. The decision to stop gathering data is influenced by whether the data points towards the desired conclusion.
People start with an assumption that their favored conclusion is more likely true and weight each piece of evidence supporting it more than evidence opposing it. Because of that, people will find no need to gather additional information that could have revealed their conclusion to be false. They will stop the investigation as soon as the jury tilts in their favor. ~ Dutch psychologist Filip Gesiarz
Confirmation bias is the tendency to interpret or prioritize information in a way that confirms a held hypothesis or belief; information to the contrary is shunned. A self-fulfilling prophecy is confirmation bias at work.
Confirmation bias leads to determining causality from correlational evidence alone, and illusory correlations. Cherished beliefs are especially prone to confirmation bias.
Confirmation bias can have a major effect on our everyday lives. ~ American psychologist Robert Sternberg
First impressions are often lasting impressions, and those first impressions often owe to expectation. The way we treat people when we first meet them greatly affects a first impression, as people interactively respond to how they are treated.
The tone of a first meeting, and hence a first impression, is often set beforehand, by what we have heard from others, or information otherwise obtained. Finding that we do not like someone we expect not to like can be confirmation bias, as we treat them less civilly than when our expectation runs to the affirmative, in which case our own cordiality can be contagious, and we again confirm expectation.
Causal analysis provides absolutely no value judgment, and a value judgment is absolutely not a causal explanation. ~ German sociologist Max Weber
If formal logic is to be treated as a model of competence, we need to know which logic or logics human beings have internalized, and the nature of their mental formulation. ~ American psychologist Philip Johnson-Laird
Arguments, like men, are often pretenders. ~ Plato
Logic as applied is often problematic. Most commonly the premises upon which conclusions are based are fallacious.
A fallacy is an error in reasoning, whether by dint of false assumptions, or by connection of arguments which lead to a conclusion. If any of the premises are unreliable, then so too the conclusion, even if the chain of reasoning is impeccable.
Sometimes the premises are insufficient to infer the conclusion: there is an overlooked, and thereby missing link, in the reasoning chain.
Aristotle, an early systematic logician, identified 13 fallacies. The list has since grown to over 300. Fallacies bifurcate into 2 groups: of relevance and of ambiguity.
Fallacies of Relevance
A fallacy is of relevance when an argument relies upon premises not pertinent to the conclusion.
Premises may be logically irrelevant but not psychologically so. These are appeals to emotion. Such “emotional logic” is ubiquitous but is logic only in the sense that anything is logical which appeals to one’s reason.
Many fallacies are so old as to have Latin names. The best known is ad Hominem: “against the man.” Rather than attack a conclusion or the arguments that support it, a retort is directed to demean the debate opponent, and so undermine the credibility of the message through its messenger.
The argument from ignorance (ad Ignorantiam) posits that a proposition is true simply because it has not been proved false. This fallacious appeal to ignorance most commonly appears in misunderstandings of developing science, and in religiously oriented pseudoscience.
You could claim that anything’s real if the only basis for believing in it is that nobody’s proved it doesn’t exist! ~ English novelist J.K. Rowling
The Christian creationist argument for the existence of God known as intelligent design, which subverts evolutionary theory to its own ends, uses ad Ignorantiam as its springboard. The intelligent design argument is clever in that adaptation is teleological. Goal orientation suggests design, which implies a designer. The problem with intelligent design is that any conception of God as an entity presents at least one insolvable contradiction (having nothing to do with evolution), depending upon how God is imagined. (The glossary has an extensive entry on intelligent design. Evolution is explained in Spokes 3. God is refuted in Spokes 8.)
Appeal to authority (ad Verecundiam) posits that expert opinion renders an argument axiomatic, needing no further proof. It is a logical fallacy twist to the old saw that “it’s not what you know, it’s who you know.”
A common fallacy is posing a question in a way that presupposes the truth of the conclusion. This is, essentially, a leading question, with presumption thrown in; very popular with lawyers, who ask such things as “when did you stop beating your wife?”
The fallacy of accident is applying a generalization to a specific circumstance. The fallacy of converse accident is drawing a conclusion based upon a categorical generalization.
Ignoratio elenchi is of an irrelevant conclusion: arguments purporting to prove one thing but are instead directed to a different conclusion. The reasoning may be valid, but it misses its intended target.
Fallacies of Ambiguity
Arguments become sleazy by having ambiguous words or phrases whose meanings shift during the course of argument. Such sophisms are often crude but can at times be subtle.
When a word or expression has more than one literal meaning, and the meaning is used in various ways, the fallacy is equivocation. Prevarication falls under this fallacy.
The fallacy of amphiboly is arguing ambiguous premises because of grammatical construction. Dangling participles and phrases can present humorous amphiboly.
The farmer blew out his brains after taking an affectionate farewell of his family with a shotgun.
Deception by accent occurs when words take on different meaning via various emphases. Propaganda, including news headlines and advertisements, commonly take this tack of self-promotion. They are fallacies in being misleading.
You got it buddy: the large print giveth, and the small print taketh away. ~ American musician Tom Waits in the song “Step Right Up” (1976)
The fallacy of composition comes to a holistic conclusion based upon the sum of the component parts. Blaise Pascal’s argument about God falls under this fallacy.
If there is a God, he is infinitely incomprehensible, since having neither parts nor limits, he has no affinity to us. ~ Blaise Pascal
English film director Alfred Hitchcock once defined a “great movie” as “a few good scenes and no bad scenes.” A lot of silly and illogical films fit that bill of decent individual scenes, but few viewers would call such a movie good, let alone great. Instead, a great movie has an interesting story, is emotionally engaging, and has no bad scenes.
The fallacy of division is the reverse of the fallacy of composition, in arguing that what is true of the whole also applies to the parts.
Our first naïve impression of Nature and matter is that of continuity. Be it a piece of metal or a volume of liquid, we invariably conceive it as divisible into infinity, and ever so small a part of it appears to us to possess the same properties as the whole. ~ German mathematician David Hilbert
The classic syllogism…
All humans are mortal.
Socrates is a human.
Therefore, Socrates is mortal.
…becomes a parody via the fallacy of division with
American Indians are disappearing.
That man is an American Indian.
Therefore, that man is disappearing.
The above example is fallacious by arguing that the attributes of a collection apply to the elements that comprise the collection.
◊ ◊ ◊
There are analogous resemblances between the fallacies of accident and division, and between converse accident and composition, but the distinctions are clear.
In the fallacy of composition, the argument is that since each member has a certain attribute, so too the set/group/class. A converse accident argument is that all members of a group have an attribute that can be attributed to only some atypical members.
The fallacy of division is arguing that an attribute of a class applies to all its members. The fallacy of accident argues that because a general rule applies, there are no circumstances where it does not.
Human beings are the only creatures who are able to behave irrationally in the name of reason. ~ English American anthropologist Ashley Montagu
In human situations, which are usually confused through too little reliable information or too much information of questionable validity, logic may find little scope. Common sense seems better adapted to such situations, since it draws on intuitive insights, is sensitive to intangibles, makes use of both experience and knowledge, and benefits somehow from unconscious wisdom. Thus, common sense is a serviceable guide in the ordinary affairs of life, while logic often is not. ~ Avron Douglis
It is a happy faculty of the mind to slough that which conscience refuses to assimilate. ~ William Faulkner
Cognitive dissonance is mental stress from simultaneously holding contradictory ideas, values, or beliefs. In 1957, American social psychologist Leon Festinger noted that the mind strives for consistency (the principle of cognitive consistency).
The mind mitigates cognitive dissonance in 3 possible ways: 1) change belief or behavior, 2) justify the dissonance through rationalization, or 3) deny or ignore information that creates dissonance, and, for good measure, avoid information and situations likely to augment the dissonance.
For instance, a man wanting to diet to lose weight falls prey to a jelly donut. To crack the dissonance between behavior and intent, he may: 1) stop eating the donut, 2) justify its consumption: by rationalization (need energy now), allowing latitude (cheating just this once), or compensation (promising to exercise it off later), or 3) deny the conflict (this donut is not especially fattening).
Decisions often arouse dissonance by bringing to the fore conflicting priorities and goals. Dissonance is reduced by augmenting the attractiveness of one alternative while degrading another.
Sometimes dissonance is created externally. Forced compliance is being compelled by someone to do something distasteful. The decision to submit is rationalized to reduce internal dissonance.
Cognitive dissonance sometimes soothes over an otherwise troubled psyche. People value most achievements or goods which required considerable effort or outlay to obtain. Rather than denigrate pursuit for something of low value, the tendency is to consider the effort worthwhile, even if only paying for one’s education.
Denial also works. If something turns out badly, convincing oneself that it was as good as circumstances permitted dismisses dissonance.