Sherlock Holmes & Deductive Reasoning: How to Become a Brilliant Detective! I

Sherlock Holmes &

 
Deductive

Reasoning:

How to Become a

Brilliant Detective! I

(In 2 Easy Lessons)

Originally Published August 21, 2005... Republished June 4, 2009 (H: 3,755, C: 3)

Recently I heard my young tenant shout an obscenity in a pained manner. Subsequently, I went into the bathroom and found a spot of blood on the vanity counter. I went to his room; the door was open. A friend was in the room with him. He was holding his left hand in his right hand while in obvious discomfort. I abruptly, and with unreserved pleasure announced to his surprise, “You cut your left hand!” He looked up and asked, “How did you know?” Of course I recounted the series of events, which brought me to the obvious conclusion, just as Sherlock would have done. And no, I did not say, “Elementary, my dear Watson”.

All devotees of Arthur Conan Doyle’s master sleuth can appreciate my feelings at that moment when my tenant asked, “How did you know?” An opportune moment to show off unapologetically, while making him feel quite ordinary. Sheer bliss indeed!

Have you ever seen a baseball player attempt to keep a long drive that he just hit, from going foul with body language? How about a golfer using body language to guide an already struck putt into the hole? These are examples of illogical thinking or invalid reasoning, better known as superstition.

Why we draw invalid conclusions!

1-Most times, when we incorrectly interpret someone’s actions, it’s because we have failed to consider all possibilities.

2-There is also the possibility that our gathering of facts includes unnecessary information, which has caused us to err.

3- Insufficient information will likely elicit an erroneous conclusion.

4- Misinterpretation of the facts can cause us to go awry.

5- And then we sometimes draw a conclusion, which is not valid. That occurs when we do not understand logic fully.

Example: “If all men wear shoes, and Jose wears shoes, is Jose a man?” If your answer is “Yes”, you may be correct, but not necessarily. Jose may be Joseph or Josephine. Or Jose might be a dog that some peculiar pet owner has fitted with booties. So while you may be correct, your assumed conclusion is INVALID!

If instead I had proposed, “If all men wear shoes, and Jose is a man, does Jose wear shoes?” The correct and valid answer is YES!

The first example illustrates how we sometimes may draw invalid conclusions, which do not necessarily evolve from the stated conditions.

If you return home, find the front door unlocked do you think a) I forgot to lock it, or b) the kids must have forgotten to do it? Well, don’t forget c) a burglar might have done it, and, more importantly, he may still be inside!

First, look for evidence of breaking and entering since most pro burglars, who pick locks, are probably after Madonna, Oprah or Donald Trump. You probably get the crowbar variety burglar. If you don’t see any crowbar evidence, it may be safe to go inside without screaming “Help, police!” at 120 decibels.

Why do we need to think logically like Sherlock Holmes? To stay one step ahead of the kids and grandkids, of course. They already think like Columbo. Before we tackle the task of becoming Holmes, let’s first review the basics of logical thinking or syllogistic reasoning.


Definitions


GENERAL TERMINOLOGY

Logic: the study of arguments to advance an account of valid and fallacious inference to allow one to distinguish good from bad arguments. Traditionally, logic is studied as a branch of philosophy.

Term Logic: Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century.

The basics:

The fundamental assumption behind the theory is that propositions are composed of two terms - whence the name "two-term theory" or "term logic" – and that the reasoning process is in turn built from propositions:
The term is a part of speech representing something, but which is not true or false in its own right, as "man" or "mortal".
The proposition consists of two terms, in which one term (the "predicate") is "affirmed" or "denied" of the other (the "subject"), and which is capable of truth or falsity.
The syllogism is an inference in which one proposition (the "conclusion") follows of necessity from two others (the "premises").

A proposition may be universal or particular, and it may be affirmative or negative. Thus there are just four kinds of propositions:

A-type: universal and affirmative or ("All men are mortal")
I-type: Particular and affirmative ("Some men are philosophers")
E-type: Universal and negative ("No philosophers are rich")
O-type: Particular and negative ("Some men are not philosophers").

This was called the fourfold scheme of propositions. The syllogistic is a formal theory explaining which combinations of true premises yield true conclusions.

Aristotelian Logic: Aristotelian logic, also known as syllogistic logic, is the particular type of logic created by Aristotle. It later developed into what became known as traditional logic or term logic.

Aristotle's logical system

Aristotle recognized four kinds of quantified sentences, each of which contain a subject and a predicate:

Universal affirmative: Every S is a P.
Universal negative: No S is a P.
Particular affirmative: Some S is a P.
Particular negative: Not every S is a P.

There are various ways to combine such sentences into syllogisms, both valid and invalid. In Medieval times, students of Aristotelian logic classified every possibility and gave them a name. For example, the Barbara syllogism is as follows:

Every X is a Y.
Every Y is a Z.
Therefore, every X is a Z.

Aristotle also recognized the various immediate entailments that each type of sentence has. For example, the truth of a universal affirmative entails the truth of the corresponding particular affirmative, and the falsity of the corresponding universal negative and particular negative. The square of opposition lists all these logical entailments.

Famously, Aristotelian logic runs into trouble when one or more of the terms involved are empty (has no members). For example, under Aristotelian logic, "all trespassers will be prosecuted" implies the existence of at least one trespasser.

Syllogistic Reasoning: In traditional logic, a syllogism is an inference in which one proposition (the conclusion) follows of necessity from two others (known as premises). The definition is traditional, but is derived loosely from Aristotle 's Prior Analytics, Book I, c. 1.

Syllogisms consist of three things: major, minor (the premises) and conclusion, which follows logically from the major and the minor. A major is a general principle. A minor is a specific statement. Logically, the conclusion follows from applying the major to the minor.

For example, this is the classic "Barbara" syllogism, given by Aristotle:

If all humans (B's) are mortal (A), (major)
and all Greeks (C's) are humans (B's), (minor)
then all Greeks (C's) are mortal (A). (conclusion)

That is,
Men die. (general principle)
Socrates is a man. (specific statement)
Socrates will die. (application of major to minor)

Syllogisms may also be invalid if they have four terms or the middle term is not distributed.

Categorical Syllogism: A categorical syllogism is a deductive inference in which all the premises are categorical propositions.

Example:
All life has value.
Even a murderer is a living thing.
Therefore even a murderer has value.

The first two propositions are called the premises. If the syllogism is valid, the premises logically imply the last proposition, called the conclusion. The truth of the conclusion is established by the truth of the premises and the relationship between them: the middle term must be distributed at least once in the premises, forming a connection between the subject and predicate in the conclusion.

Note that a categorical syllogism can be valid but the conclusion can still be false if either of the premises is false. The above syllogism is valid, but some might disagree with the conclusion because they disagree with either or both of the premises.


Memorize six rules using the information presented thus far. While Johnston Diagrams are good tools for illustrative purposes, it may be preferable for some to test validity with the following rules:

1- As noted before, categorical syllogisms must contain exactly three terms, no more, no less (cp. fallacy of four terms). As a cautionary note, beware that synonyms and antonyms can create the illusion of invalidity, but can sometimes be rectified by substituting the interexchangeable terms for one of choice.

2- If either premise is negative, then the conclusion must be negative (cp. affirmative conclusion from a negative premise).

3- Both premises cannot be negative (cp. fallacy of exclusive premises).

4- Any term distributed in the conclusion must be distributed in either premise.
 
5- The middle term must be distributed once and only once (cp. fallacy of the undistributed middle).

6- You cannot draw a particular conclusion with two universal premises (cp. existential fallacy).


List of syllogisms:

The following is a list of fourteen syllogisms whose names were given to them during the Middle Ages, but which are all based on Aristotle's Analytics. For the names, see term logic.


Barbara
Every B is an A.
Every C is a B.
_ Every C is an A.

Celarent
No B is an A.
Every C is a B.
_ No C is an A.

Darii
Every B is an A.
Some Cs are Bs.
_ Some Cs are As.

Ferio
No B is an A.
Some Cs are Bs.
_ Some Cs are not As.

Cesare
No B is an A.
Every C is an A.
_ No C is a B.

Camestres
Every B is an A.
No C is an A.
_ No C is a B.

Festino
No B is an A.
Some Cs are As.
_ Some Cs are not Bs.

Baroco
Every B is an A.
Some Cs are not As.
_ Some Cs are not Bs.

Darapti
Every C is an A.
Every C is a B.
_ Some Bs are As.
(This form needs the assumption that some Cs do exist.)

Datisi
Every C is an A.
Some Cs are Bs.
_ Some Bs are As.

Disamis
Some Cs are As.
Every C is a B.
_ Some Bs are As.

Felapton
No C is an A.
Every C is a B.
_ Some Bs are not As.
(This form needs the assumption that some Cs do exist.)

Ferison
No C is an A.
Some Cs are Bs.
_ Some Bs are not As.

Bocardo
Some Cs are not As.
Every C is a B.
_ Some Bs are not As.

Deductive and Inductive Reasoning

Originally, logic consisted only of deductive reasoning, which concerns what follows universally from given premises. However, it is important to note that inductive reasoning —the study of deriving a reliable generalization from observations—has sometimes been included in the study of logic. Correspondingly, we must distinguish between deductive validity and inductive validity. An inference is deductively valid if and only if there is no possible situation in which all the premises are true and the conclusion false. The notion of deductive validity can be rigorously stated for systems of formal logic in terms of the well-understood notions of semantics. Inductive validity on the other hand requires us to define a reliable generalization of some set of observations. For the most part our discussion of logic deals only with deductive logic.


Inductive Reasoning: Induction or inductive reasoning, sometimes called inductive logic, is the process of reasoning in which the premises of an argument support the conclusion, but do not ensure it. It is to ascribe properties or relations to types based on limited observations of particular tokens; or to formulate laws based on limited observations of recurring phenomenal patterns. Induction is used, for example, in using specific propositions such as:

a) The ice is cold.
b) A billiard ball moves when struck with a cue.

to infer general propositions such as:

a) All ice is cold. - Or - There is no ice in the Sun.
b) For every action, there is an equal and opposite re-action.

Deductive Reasoning: In traditional Aristotelian logic, deductive reasoning is inference in which the conclusion is of lesser or equal generality than the premises, as opposed to inductive reasoning, where the conclusion is of greater generality than the premises. Other theories of logic define deductive reasoning as inference in which the conclusion is just as certain as the premises, as opposed to inductive reasoning, where the conclusion can have less certainty than the premises. In both approaches, the conclusion of a deductive inference is necessitated by the premises; the premises can't be true while the conclusion is false.

Examples

Valid:
All men are mortal.
Socrates is a man.
Therefore Socrates is mortal.

The picture is above the desk.
The desk is above the floor.
Therefore the picture is above the floor.

Invalid:
Every criminal opposes the government.
Everyone in the opposition party opposes the government.
Therefore everyone in the opposition party is a criminal.

This is invalid because the premises fail to establish commonality between membership in the opposition party and being a criminal. This is the famous fallacy of undistributed middle.


Rules of inference and replacement in deductive logic

Retroductive Reasoning: Similar to induction, but predicated on a known or assumed relationary rule(s) and an observation(s) that contains at least one of the predicates (predictors) of the rule. Another predicate(s) of the relationary rule is then generalized to the observation due to the coincidence of the other predicate(s) in both the observation and the rule.

This is commonly applied in police work to determine the initial suspects of a crime via means, motive and opportunity.

The most common forms of logic systems built up through retroductive reasoning involve or are related to complexity theory.

Scientific Method: Scientists use observations, hypotheses and deductions to propose explanations for natural phenomena in the form of theories. Predictions from these theories are tested by experiment. Any theory, which is cogent enough to make predictions, can then be tested reproducibly in this way. The method is commonly taken as the underlying logic of scientific practice. A scientific method is essentially an extremely cautious means of building a supportable, evidence-based understanding of our natural world.

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NOMENCLATURE


Logical Argument: An argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. The process of demonstration of deductive and inductive reasoning shapes the argument, and presumes some kind of communication, which could be part of a written text, a speech or a conversation. Arguments can be valid or invalid, although how arguments are determined to be in either of these two categories can often itself be an object of much discussion. Informally one should expect that a valid argument should be compelling in the sense that it is capable of convincing someone about the truth of the conclusion. However, such a criterion for validity is inadequate or even misleading since it depends more on the skill of the person constructing the argument to manipulate the person who is being convinced and less on the argument itself.

Less subjective criteria for validity of arguments are clearly desirable, and in some cases we should even expect an argument to be rigorous, that is, to adhere to precise rules of validity. This is the case for arguments used in mathematical proofs.

In ordinary language, people refer to the logic of an argument or use terminology that suggests that an argument is based on inference rules of formal logic. Though arguments do use inferences that are indisputably purely logical (such as syllogisms), other kinds of inferences are almost always used in practical arguments. For example, arguments commonly deal with causality, probability and statistics or even specialized areas such as economics. In these cases, logic refers to the structure of the argument rather than to principles of pure logic that might be used in it.

Proposition: Proposition is a term used in logic to describe the content of assertions, content which may be taken as being true or false, and which are a non-linguistic abstraction from the linguistic sentence that constitutes an assertion.

Aristotelian propositions take forms like All men are mortal and Socrates is a man. Propositional logic is so named because its atomic elements (the expressions of complete propositions) are often simply called propositions. The sentence A and B expresses both proposition A and proposition B.

Premise: A premise is a statement presumed true within the context of a discourse, especially of a logical argument. Often premises are explicitly stated. The accuracy of the conclusion depends on the truth of the premises.

Major Premise: The major premise in a categorical syllogism is the premise whose terms are the syllogism 's major term and middle term.

Minor Premise: In a categorical syllogism, the minor premise is the premise whose terms are the syllogism's minor term and middle term. It is also called the subsumption.

Conclusion: In logic, a conclusion is a proposition inferred from premises.

Inference: Inference is the act or process of drawing a conclusion, based solely on what one already knows. Suppose you see rain on your window - you can infer, quite trivially, that the sky is grey. Looking out the window would have yielded the same fact, but through a process of perception, not inference (note however that perception itself can be viewed as an inferential process).


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BASIC TERMINOLOGY


Validity: In logic, an argument is said to be valid if the truth of the conclusion follows from the truth of the premises.

A formula of logic is said to be valid if it is true under every interpretation.

Consider the following argument form in which the letters P, Q, and A represent unanalyzed or uninterpreted sentences.

All P are Q
A is P
Therefore, A is Q

We can determine the validity of an actual argument by translating it into an argument form, and then analyzing the argument form for validity. (The argument form above is valid.)


The two notions of logical validity are closely related.
(1) Every valid formula is the conclusion of a valid argument with no premises.
(2) For every valid argument, there is a corresponding valid formula.

For example, corresponding to the valid syllogism above is the valid (rather informal) formula:
If (all P are Q) and (A is P), then (A is Q).

Logical Fallacy: A logical fallacy is an error in logical argument, which is independent of the truth of the premises. It is a flaw in the structure of an argument as opposed to an error in its premises. When there is a fallacy in an argument it is said to be invalid. The presence of a logical fallacy in an argument does not necessarily imply anything about the argument's premises or its conclusion. Both may actually be true, but the argument is still invalid because the conclusion does not follow from the premises using the inference principles of the argument. By extension, an argument can have a logical fallacy even if the argument is not a purely logical one; for instance an argument that incorrectly applies principles of probability or causality can be said to have a logical fallacy.

Recognizing fallacies in practical arguments may be difficult since arguments are often structured using rhetorical patterns that obscure the logical connections between assertions. As we illustrate with various examples, fallacies may also exploit the emotions or intellectual or psychological weaknesses of the interlocutor. Having the capability of recognizing logical fallacies in arguments will hopefully reduce the likelihood of such an occurrence.


List of fallacies

The entries in the following list are neither exhaustive nor mutually exclusive, that is, several distinct entries may refer to the same pattern. As noted in the introduction, these fallacies describe erroneous or at least suspect patterns of argument in general, not necessarily argument based on formal logic. Many of the fallacies listed are traditionally recognized and discussed in works on critical thinking; others are more specialized.

Ad hominem (also called argumentum ad hominem or personal attack) Including:
...ad hominem abusive (also called argumentum ad personam)
...ad hominem circumstantial (also called ad hominem circumstantiae)
...ad hominem tu quoque (also called you too argument)
Amphibology (also called amphiboly)
Appeal to authority (also called argumentum ad verecundiam or argument by authority)
Appeal to belief
Appeal to consequences (also called argumentum ad consequentiam)
Appeal to emotion including:
Appeal to fear (also called argumentum ad metum or argumentum in terrorem)
Appeal to flattery
Appeal to the majority (also called argumentum ad populum)
Appeal to pity (also called argumentum ad misericordiam)
Appeal to ridicule
Appeal to spite (also called argumentum ad odium)
Two wrongs make a right
Wishful thinking
Appeal to motive
Appeal to novelty (also called argumentum ad novitatem)
Appeal to probability
Appeal to tradition (also called argumentum ad antiquitatem or appeal to common practice)
Argument from fallacy
Argument from ignorance (also called argumentum ad ignorantiam or argument by lack of imagination)
Argument from silence (also called argumentum ex silentio)
Argumentum ad baculum (also called appeal to force)
Argumentum ad crumenam (also called appeal to wealth)
Argumentum ad lazarum (also called appeal to poverty)
Argumentum ad nauseam (also called argument from repetition)
Argumentum ad numerum
Base rate fallacy
Bandwagon fallacy (also called appeal to popularity, appeal to the people, or argumentum ad populum)
Begging the question (also called petitio principii, circular argument or circular reasoning)
Cartesian fallacy
Conjunction fallacy
Correlative based fallacies including:
Fallacy of many questions (also called complex question, loaded question or plurium interrogationum)
False dilemma (also called false dichotomy or bifurcation)
Denying the correlative
Suppressed correlative
Dicto simpliciter, including:
Accident (also called a dicto simpliciter ad dictum secundum quid)
Converse accident (also called a dicto secundum quid ad dictum simpliciter)
Equivocation
False analogy
False premise
False compromise
Fallacies of distribution:
Composition
Division
Ecological fallacy
Faulty generalization including:
Biased sample
Hasty generalization (also called fallacy of insufficient statistics, fallacy of insufficient sample, fallacy of the lonely fact, leaping to a conclusion, hasty induction, secundum quid)
Overwhelming exception
Statistical special pleading
Gambler's fallacy /Inverse gambler's fallacy
Genetic fallacy
Guilt by association
Historian's fallacy
Homunculus fallacy
Ideology over reality
If-by-whiskey
Judgmental language
Ignoratio elenchi (also called irrelevant conclusion)
Inappropriate interpretations or applications of statistics including:
Biased sample
Correlation implies causation
Gambler's fallacy
Prosecutor's fallacy
Screening test fallacy
Intentional fallacy
Invalid proof
Lump of labor fallacy (also called the fallacy of labor scarcity)
Meaningless statement
Middle ground (also called argumentum ad temperantiam)
Misleading vividness
Naturalistic fallacy
Negative proof
Non sequitur including:
Affirming the consequent
Denying the antecedent
No true Scotsman
Package deal fallacy
Pathetic fallacy
Perfect solution fallacy
Poisoning the well
Proof by verbosity
Questionable cause (also called non causa pro causa) including:
Correlation implies causation (also called cum hoc ergo propter hoc)
Fallacy of the single cause
Joint effect
Post hoc (also called post hoc ergo propter hoc)
Regression fallacy
Texas sharpshooter fallacy
Wrong direction
Red herring (also called irrelevant conclusion)
Reification (also called hypostatization)
Relativist fallacy (also called subjectivist fallacy)
Retrospective determinism (it happened so it was bound to)
Shifting the Burden of proof
Slippery slope
Special pleading
Straw man
Style over substance fallacy
Syllogistic fallacies, including:
Affirming a disjunct
Affirmative conclusion from a negative premise
Existential fallacy
Fallacy of exclusive premises
Fallacy of four terms (also called quaternio terminorum)
Fallacy of the undistributed middle
Illicit major
Illicit minor

(Tabacco Comments: With all these opportunities, is it any wonder that George W. Bush and his comrades have confused and befuddled the American public. I guarantee that if you assiduously study these argument “fallacies”, you will never again be 2 steps behind your offspring or the Bush administration.

And, yes I sometimes use fallacious techniques to confuse the unwary. I most certainly argue ad hominem when it comes to GWB and his administration. But since they always lie anyway, even though my methods may be suspect, my conclusions are always valid with regard to the kakistocrats running our government - there, I did it! "Appeal to Ridicule", among others.)


Metaphor: A metaphor resembles a form of syllogism called affirming the consequent, which is a logical fallacy:

Grass (B) dies (A).
Men (C's) die (A).
Men (C's) are grass (B).

A Barbara syllogism involves grammar and logical types; it has a subject (e.g. Socrates) and a predicate (mortal). Affirming the Consequent, the basis of metaphor, is grammatically symmetrical: it equates two predicates. This form of syllogism is logically invalid.

Paradox: A paradox is an apparently true statement or group of statements that seems to lead to a contradiction or to a situation that defies intuition. Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true (or, cannot all be true together). The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has often led to significant advances in science, philosophy and mathematics.


Robert Boyle 's self-flowing flask
fills itself in this diagram, but
perpetual motion machines do not exist.

The word paradox is often used interchangeably with contradiction; but where a contradiction by definition cannot be true, many paradoxes do allow of resolution, though many remain unresolved or only contentiously resolved. Still more casually, the term is sometimes used for situations that are merely surprising (albeit in a distinctly "logical" manner). This is also the usage in economics, where a paradox is an unintuitive outcome of economic theory.

Perception: Perception is the process of acquiring, interpreting, selecting, and organizing sensory information.

Precognition: Precognition is a form of extra-sensory perception, which allows a "percipient" to perceive information about future places or events before they happen (as opposed to merely predicting them based on deductive reasoning and current knowledge). A related term, presentiment is used to refer to information about future events which may not present itself in conscious form but rather in the form of emotions or feelings at the autonomic level. These terms are considered by some to be special cases of the more general term clairvoyance.
Wikipedia, Online Encyclopedia

Remember, we can’t all be Sherlock Holmes. But if you’ve read this far, you may as well finish by perusing Part II, which is the ultimate purpose of this dissertation. After all, how bad would it be to be Columbo!

June 4, 2009: Tabacco has yet to create Part II, but I will get to work on it hopefully!

Tabacco: I consider myself both a funnel and a filter. I funnel information, not readily available on the Mass Media, which is ignored and/or suppressed. I filter out the irrelevancies and trivialities to save both the time and effort of my Readers and bring consternation to the enemies of Truth & Fairness! When you read Tabacco, if you don’t learn something NEW, I’ve wasted your time.

Tabacco is not a blogger, who thinks; I am a Thinker, who blogs.

In 1981's 'Body Heat', Kathleen Turner said, "Knowledge is power".

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