Explanation : summing up



Explanation  (^)

The building bricks of Explanation are:

  • Statement(s)
  • Argument(s)


The main requirement for being accepted as building bricks of Explanation is that they are not corrupted by Fallacy.



Statements  (^)



Statements  (^)


Statements are Messages asserting/expressing  Data - Facts - Concepts.


Statements can be classified according to:


Form Categorical Statements

Conditional Statements


Content Empirical Statements

Theoretical Statements

Categorical statements  (^)


  • Affirmative Universal : all S are Q. (Subset or Identity)

  • Affirmative Particular : some S are Q. (Overlapping or Superset)

  • Negative Universal : no S are Q. (Disjointed)

  • Negative Particular : some S are not Q. (Overlapping or Superset)

Conditional statements  (^)


  • Positive : if X  then Y
  • Negative : if not X then not Y
  • Bi-conditional : if and only if X then Y (necessary and sufficient condition)

Empirical statements  (^)


Empirical statements are statements concerning matters of fact.

Example : T. S. Kuhn wrote "The Structure of Scientific Revolutions"


Universal Empirical Statements can be falsified by one negative instance.

Example : Universal Empirical Statement : "All swans are white" (Falsified by the existence of just one non-white swan)

Theoretical statements  (^)


Theoretical statements are statements concerning relations of concepts.

They appear as hypotheses, empirical generalizations, theories.

Example : "The history of all hitherto existing society is the history of class struggle" (Karl Marx and Friedrich Engels)


A theoretical statement cannot be falsified by a negative instance but can be weakened by several negative instances up to a point where it is no longer useful or acceptable.

Linked statements  (^)

Statements usually appear linked to each other.

In this case they can be:

  • Compatible : they can all be true at the same time.
    Example : (1) Some books are useful   (2) Some books are not useful

  • Contradictory : they cannot all be true at the same time.
    Example : (1) All books are useful  (2) Some books are not useful

  • Contrary : they cannot all be true at the same time but they could all be false.
    Example : (1) All books are useful  (2) No book is useful


A series of linked Statements makes an Argument.



Arguments  (^)



Arguments  (^)

Arguments are the product of reasoning.

Common types of Reasoning are in the form of:

  • Induction  (Inductive Arguments)

  • Deduction (Deductive Arguments)



Induction  (^)



Induction  (^)

An Induction is an Inductive Argument based on incomplete information that leads to a probabilistic conclusion.

Modes of Induction

The conclusion of an Inductive Argument can be reached through:

  • Generalization

  • Analogy

Generalization  (^)


A Generalization is the conceptual extension, to a population, of factors and features that are present in a sample.


A reliable Generalization is characterized by the following requirements:

representativeness of the sample the sample takes into account the variety of subjects/objects present in the population (quality)


adequate size of the sample the magnitude of the sample bears some relation to the magnitude of the population under examination (quantity)


randomness in the selection of the sample's entities each entity of the sample has equal chance of being selected


ample margin of error allowed the greater the margin of error, the more reliable the generalization

Compare, for example:

a) "it seems that more than half of the pupils are ..." (soft statement, ample margin of error)

b) "eighty-three per cent of the pupils are ..." (very confident statement, very narrow margin of error)

Analogy  (^)


An Analogy is the extension to a population of factors and features that are present in another similar population so that what applies to one applies also to the other.


  • Check number and strength of relevant similarities   (low/weak similarities - low/weak analogies)

  • Check number and strength of relevant differences  (low/weak differences - high/strong analogies)

  • Allow for a certain margin of error  (make soft statements stressing the fact that we are dealing with analogies, i.e. similar entities, and not homologies, i.e. same entities)



Deduction  (^)



Deduction  (^)

A Deduction is a Deductive Argument, based on general assumptions, leading to specific conclusions.

The general assumptions are in the form of Postulates from which the Deductive Argument derives and on which it relies.

Postulate  (^)


A Postulate is an assumption on which a Deductive Argument is based.


Postulates should possess the following requirements :

  • Simplicity : a postulate should be simple to grasp in order to be widely acceptable and accepted

  • Consistency: a postulate should be consistent (compatible) with other related assumptions

  • Fertility: a postulate should bear fruit in terms of knowledge and knowledge engineering



Fallacies  (^)



Fallacies  (^)


Fallacies are faults in Research that emerge during Explaining, also as a result of pitfalls in Experiencing and Exploring.


 Fallacies can be classified into:

  • Material Fallacies

  • Psychological Fallacies

  • Logical Fallacies



Material fallacies  (^)



Material fallacies  (^)

Material Fallacies are errors in the factual content of a statement.

Errors are committed when:

  • presenting wrong evidence

  • denying sound evidence

Material Fallacies originates from pitfalls in:

  • Observation

  • Induction



Material Fallacies : pitfalls in observation  (^)



Material Fallacies : pitfalls in observation  (^)

Material Fallacies in Observation could originate from deficiencies such as:

  • Refusing to check the evidence

  • Presenting wrong evidence

  • Denying sound evidence

Refusing to check the evidence  (^)

Galileo Galilei and his opponents:

"One of the schoolmen to whom Galileo offered his telescope to view the newly discovered moons of Jupiter declined to look, being convinced that none could possibly be seen because no mention of them could be found in Aristotle's treatise on astronomy"

(from : Irving M. Copi,  Logic,  p. 467)

Presenting wrong evidence  (^)

Charles II and the Royal Society:

"On the occasion of the creation of the Royal Society the king (Charles II) dined with its members and, towards the close of the evening, admitted ... that among such learned men he now hoped for a solution to a question which had long perplexed him. The case he thus stated :

'Suppose two pails of water were fixed in two different scales that were equally poised, and which weighed equally alike, and that two live bream, or small fish, were put into either of these pails, he wanted to know the reason why the pail, with such addition, should not weigh more than the other pail which stood against it.' Every one was ready to set at quiet the royal curiosity; but it appeared that every one was giving a different opinion. One, at length, offered so ridiculous a solution, that another of the members could not refrain from a loud laugh; when the King, turning to him, insisted, that he should give his sentiments as well as the rest. This he did without hesitation, and told His Majesty, in plain terms, that he denied the fact! On which the King, in high mirth, exclaimed 'Odds fish, brother, you are in the right!'."

(from :  C. L. Hamblin,  Fallacies, pp. 38-39)

Denying sound evidence  (^)

Charles Silvester de Ford and the flatness of the earth:

"To me truth is precious ... I should rather be right and stand alone than to run with the multitude and be wrong. ... The holding of the views herein set forth has already won for me the scorn and contempt and ridicule of some of my fellowmen. I am looked upon as being odd, strange, peculiar... But truth is truth and though all the world rejects it and turns against me, I will cling to truth still."

"These sentences are from the preface of a booklet, published in 1931, by Charles Silvester de Ford, of Fairfield, Washington, in which he proves the earth is flat."

(from :  Martin Gardner,  Fads and Fallacies,  pp. 12-13)



Material fallacies : pitfalls in induction  (^)



Material fallacy : pitfalls in induction  (^)

A Fallacy in Induction could originate from :

  • Faulty Generalization

  • Faulty Analogy

Faulty Generalization  (^)

  • Hasty Generalization : jumping to conclusion from insufficient evidence. (e.g. too small sample, unrepresentative sample, etc.)

    Recommendation : Make "soft" statements; check thoroughly the quality and quantity of the evidence

  • Division : what holds true for all members of a class taken together does not necessarily hold true for each one taken on his own

    (Example : "That football team is the best this year in its League" does not mean that each player of the team is the best of the League this year in his respective role)

  • Composition : what holds true for each member of a class standing alone does not necessarily hold true for all members taken together

    (Example : "Each building represents a superb piece of architecture" does not necessarily imply that the total scheme results in a superb piece of urban planning)

  • Faulty  Causal Generalization : common causation assumed as exclusive causation

     Example :  Flat tyre  -  cause : puncture (right)

                       Flat tyre  -  cause : puncture (right)

                       Flat tyre  -  cause : puncture (right)

                      Flat tyre  -  cause : puncture (wrong) ;  leaky valve (right)

     Advice : Look for new/different/possible explanations, beyond common explanation

  • Faulty Causal Connection : Spatial/Temporal Connection assumed as Causal Connection (e.g. post hoc ergo propter hoc)

    (Example :  The cock crows when the sun rises - temporal connection and not causal connection)

    Advice : Look for plausible/relevant/essential connections as possible causes

Faulty Analogy  (^)

  • False Analogy : things associated present significant substantial differences but some formal similarities leading to erroneous conclusions

    (Example : The analogy of an orange with a round ball, leading to erroneous conclusion if taken beyond the field of geometrical figures)

  • Excessive Analogy : things associated present significant similarities but are not alike in every respect as an excessive analogy would pretend

    (Example : The analogy of a social body with a physical body)



Psychological fallacies  (^)



Psychological fallacies  (^)

Psychological Fallacies are faults of diversion and distraction committed through the form/style/mode of expressing a statement.

The common aspects of all psychological fallacies is the putting aside of the main points of a matter in order to focus on trivial, non-pertinent aspects.

The main Psychological Fallacies are:

  • Improper Appeal to Authority

  • Improper Appeal to Majority

  • Abuse and Ridicule

  • Loaded Question

  • Problem Banalization

Improper Appeal to Authority  (^)

A fallacious Appeal to Authority is a way of blocking a discussion about a contentious subject by invoking some authority considered as beyond dispute.


"I am not disposed to approve the practice traditionally ascribed to the Pythagoreans, who, when questioned as to the grounds of any assertion that they advanced in debate, are said to have been accustomed to reply, 'He himself said so [Ipse dixit]' ... 'he himself' being Pythagoras."

(Marcus Tullius Cicero,  De Natura Deorum)


Reliance on authority must be :

  • topically specified : restricted to the field in which the person is an authority

  • temporally qualified : up to the time the person is still an authority

  • tempered by criticism : questioned and disputed when unanswered problems arise.

Improper Appeal to Majority  (^)

The Appeal to Majority is a way of answering a contentious question by putting forward and accepting without reserve (critical questioning) the opinion of the majority


Premisses :    The choice is between A, B, C

                      Eighty per cent of people have chosen A

Conclusion :  A is the right choice because so many people cannot be wrong


In the course of history there have been many cases where the majority of people were wrong as to their interests in the long run (e.g. Nazi Germany, Fascist Italy). The force of the large number does not count by itself unless it is underpinned by other, more relevant aspects.

Abuse and Ridicule  (^)

Abuse and ridicule are ways of diverting and distracting the attention from the pertinent matter to trivial or irrelevant aspects as a pretext for lightly/surreptitiously dismissing the entire matter.

Example  (Abuse)

The Nazi condemned the theory of relativity because Einstein, its originator, was a Jew

Example  (Ridicule)

Bishop Wilberforce, in order to pour scorn on the theory of evolution (without seriously discussing it), asked Thomas Huxley if it is was through his grandfather or his grandmother that he claimed to descend from a monkey

Loaded Question  (^)

A Loaded Question is one that implicitly

  • freezes the situation (e.g. Have you stopped beating your wife ?)

  • points to the answer (e.g. Surely you are for X, aren't you ?)

  • unduly restricts choices (e.g. Are you for black or for white ?)


A Loaded Question uses words in an emotional way that distort the answer in the direction wanted by the person who poses the question.


  • Formulate the question without introducing hidden or unsubstantiated assumptions

  • Do not use question tags

  • Leave the field of a complex question open to several answers

Problem Banalization  (^)

Problem Banalization (excessive simplification) is the faulty reduction of a problem to a black/white alternative even if the problem is a complex one and requires several options to be considered.


The running of an economy depends either on the increase or on the decrease of the amount of money in circulation.


Do not formulate the problem in a way leading to the (unnecessary) restriction of choices.



Logical fallacies  (^)



Logical fallacies  (^)

Logical Fallacies refer to flaws in reasoning that originate when the Statements are not properly connected.

A Logical Fallacy makes an Argument invalid.


The main Logical Fallacies are:

  • Irrelevant Reasons

  • Circularity

  • Inconsistency

  • Faulty Conditional Reasoning

Irrelevant Reasons  (^)

In the Fallacy of Irrelevant Reasons (non sequitur) the premisses presented are not pertinent or not substantial enough to support the conclusion.

Example (non pertinent premisses)

Premiss : I have just spent £30 in ten minutes in the supermarket.

Conclusion : This inflation has got out of hand

Example (non substantial premisses)

Premiss : First two games, first two victories

Conclusion : I'm sure we are going to win the tournament

Circularity  (^)

In the Fallacy of Circularity (begging the question)

a) the conclusion restates the premisses using different words but without explaining anything

b) the conclusion is used to uphold the premisses instead of the premisses being capable of supporting the conclusion

Example (the conclusion restates the premisses)

"Why does opium cause sleep ?"

"Because of its soporific power."

(Molière, Le Malade Imaginaire)

Example (the conclusion upholds the premisses)

"In a motion picture featuring the famous French comedian Sacha Guitry some thieves are arguing over division of seven pearls worth a king's ransom. One of them hands two to the man on his right, then two to the man on his left. 'I - he says - will keep three.' The man on his right says, 'How come you keep three?' 'Because I am the leader.' 'Oh. But how come you are the leader?' 'Because I have more pearls.'"

(from Irving M. Copi,  Introduction to Logic,  p. 117)

Inconsistency  (^)

The Fallacy of Inconsistency arises when an argument is based on premisses that cannot all be true (or not all at the same time).


Premiss a) Economic growth is good for the prosperity of people

Premiss b) Economic growth is bad for the state of the environment

Premiss c) The prosperity of people is based on economic growth

Premiss d) The prosperity of people is based on the state of the environment

These four statements taken together as premisses of an argument lead to an inconsistent conclusion.

Faulty Conditional Reasoning  (^)

Faulty conditional reasoning refers to the Fallacies of Affirming the Consequent or Denying the Antecedent.

They originate from confusing the simple

- if X then Y (sufficient condition)

with the more circumscribed

- if and only if X then Y (necessary and sufficient condition)

Example (affirming the consequent)

Premisses:    If it rains the grass becomes wet

                   The grass is wet

Conclusion : So it rained

(Conclusion logically invalid: somebody could have watered the grass)

Example (denying the antecedent)

Premisses :   If that architect has designed this building he is a great architect.

                   That architect has not designed this building

Conclusion : So that architect is not a great architect

(Conclusion logically invalid: he could have designed other remarkable buildings and so be a great architect).



Explanation : summing up  (^)

An Explanation based on factual truth and valid argumentation produces results (e.g. Arguments) with reference to Problem Finding.

There is then a need for a proper vehicle in order to circulate those findings.

This is the task of Exposition.