The basics that make up an argument

Logic

Logic is a formal science that evaluates arguments. Good arguments are those in which premises really do support the conclusion. The argument can be valid or invalid. Logic doesn’t assign truth values. Correct thought.

• The simplest argument is a statement set (one or more premises and exactly one conclusion). Where the premises (or evidence) provide support for the conclusion.

$Premises \implies Conclusion$.

• Example

  🏫

  All the men are mortal. (Premise Q)
  Plato is a man. (Promise P)
  
  Therefore, Plato is a mortal. (The conclusion indicated by "therefore")

  The argument is not a good one!

  🏫

  Some men are gay.
  Plato is a man.
  
  Therefore, Plato is gay.

  The argument is a bad one!

• The premises set forth reasons or evidence. By elimination, if it is not a conclusion then is a premise.

  • Indicators

    • since

    • as indicated by

    • because

    • for

    • in that

    • may be inferred from

    • as

    • given that

    • seeing that

    • for the reason that

    • in as much as

    • owing to

  • Example

• The conclusion is the statement that the premises are claimed to support.

  • Indicators

    • threfore

    • wherefore

    • thus

    • consequently

    • we may infer

    • so

    • accordingly

    • we may conclude

    • it must be that

    • for this reason

    • entails that

    • hence

    • it follows that

    • implies that

    • as as result

  • Example

• The reader asks questions about arguments that contain no indicators.

  • What try to prove?

  • What statement follows others?

  • What is the main point?

• By logical principles, the conclusion is listed after the premises.

Worked examples

I. List the premises and conclusion of each argument.

• Nivaldo J.Tro, Chemistry: A Molecular Approach,2nd ed.

  $P_1$: Carbon monoxide molecules happen to be just the right size and shape, and happen to have just the right chemical properties, to fit neatly into cavities within hemoglobin molecules in blood that are normally reserved for oxygen molecules.

  $C:$ Carbon monoxide diminishes the oxygen-carrying capacity of blood.

• Avrum Stroll and Richard Popkin, Philosophy and the Human Spirit

  $P_1:$ The good, according to Plato, is that which furthers a person’s real interests.

  $C:$ Men will seek the good when it is known.

• Judge Stephanie Kulp Seymour, United States v. Jones

  $P_1:$ When individuals voluntarily abandon property, they forfeit any expectation of privacy in it that they might have had.

  $C:$ A warrantless search or seizure of abandoned property is not unreasonable under the Fourth Amendment.

• U.S. National Institutes of Health, “Your Guide to Healthy Sleep

  $P_1:$ Studies show that people who are taught mentally challenging tasks do better after a good night’s sleep.

  $P_2$: Other research suggests that sleep is needed for creative problem-solving.

  $P_3:$ We need sleep to think clearly, react quickly, and create memories.

  $C:$ It really does matter if you get enough sleep.

• Walter Mischel and Harriet Mischel, Essentials of Psychology

  $P_1:$ Punishment, when speedy and specific, may suppress undesirable behavior.

  $P_2$: Punishment cannot teach or encourage desirable alternatives.

  $C:$ It is crucial to use positive techniques to model and reinforce appropriate behavior that the person can use in place of the unacceptable response that has to be
  suppressed.
  

• Leon P. Baradat, Political Ideologies, Their Origins and Impact

  $P_1:$ Private property helps people define themselves.

  $P_2:$ Private property frees people from mundane cares of daily subsistence.

  $P_3:$ Private property is finite.

  $C:$ No individual should accumulate so much property that others are prevented from accumulating the necessities of life.

• John W. Hill and Doris K. Kolb, Chemistry for Changing Times, 7th ed.

  $P_1:$ The nations of planet Earth have acquired nuclear weapons with an explosive power equal to more than a million Hiroshima bombs.

  $P_2:$ Studies suggest that explosion of only half these weapons would produce enough soot, smoke, and dust to blanket the Earth, block out the sun, and bring on a nuclear winter that would threaten the survival of the human race.

  $C:$ Radioactive fallout isn’t the only concern in the aftermath of nuclear explosions.

• J. John Palen, Social Problems

  $P_1:$ Antipoverty programs provide jobs for middle-class professionals in social work, penology, and public
  health.
  

  $C:$ Workers’ future advancement is tied to the continued growth of bureaucracies dependent on the existence of poverty

II. In most instances, the main conclusion must be rephrased to
capture the author's full intent. Write out what you interpret the main conclusion to be.

• Michael McDonnell, letter to the editor

  $C:$ University administrators are not as interested in amateur athletes themselves as in money.

• Robert S. Griffith, “Conservative College Press

  Neoconservatives are given by financial success as intellectual stimuli.

Identify an argument

1. If no evidence is given to prove that such statements are true, then there is no argument.

2. If they don't support or imply anything, there is no argument. If this passage contains an argument, then these are the premises and that is the conclusion.

3. If a passage develops a topic but doesn't prove that topic, then there is no argument.

4. Keep an eye out for premise and conclusion indicator words.

5. The presence of an inferential relationship between the statements.

Typical kinds of nonarguments

• Noninferential passages

• Expository passages

• Warning

• Piece of advice

• Report

• Statement of belief or opinion

• Illustrations. Expressions and Examples intend to show what something means or how it is done.

• Explanations. Every explanation is composed of two components: the explanandum and explanans.

• Conditional statements. A single conditional statement is not an argument. A conditional statement may serve as either the premise or the conclusion (or both) of an argument. The inferential content of a conditional statement may be expressed to form an argument.

Worked examples

I. Determine which of the following passages are arguments and their conclusion, if it is not, determine the kind of nonargument.

• The turkey vulture is called by that name because its red featherless head resembles the head of a wild turkey.

  Nonargument; explanation.

• A mammal is a vertebrate animal that nurses its offspring. Thus, cats and dogs are mammals, as are sheep, monkeys, rabbits, and bears.

  Nonargument; illustration.

• If stem-cell research is restricted, then future cures will not materialize. If future cures do not materialize, then people will die prematurely. Therefore, if stem-cell research is restricted, then people will die prematurely.

  It’s a hypothetical syllogism argument and its conclusion is “if stem-cell research is restricted, then people will die prematurely”.

• Five college students who were accused of sneaking into the Cincinnati Zoo and trying to ride the camels pleaded no contest to criminal trespass yesterday. The students scaled a fence to get into the zoo and then climbed another fence to get into the camel pit before security officials caught them, zoo officials said. (Newspaper clipping)

  Nonargument; report.

• Any unit of length, when cubed, becomes a unit of volume. Thus, the cubic meter, cubic centimeter, and cubic millimeter are all units of volume. (Nivaldo J. Tro, Chemistry: A Molecular Approach, 2nd ed.)

  Nonargument; illustration.

• Bear one thing in mind before you begin to write your paper: Famous literary works, especially works regarded as classics, have been thoroughly studied to the point where prevailing opinion on them has assumed the character of orthodoxy. (J. R. McCuen and A. C. Winkler, Readings for Writers, 4th ed.)

  Nonargument; piece of advice.

• For organisms at the sea surface, sinking into deep water usually means death. Plant cells cannot photosynthesize in the dark depths. Fishes and other animals that descend lose contact with the main surface food supply and themselves become food for strange deep-living predators. (David H. Milne, Marine Life and the Sea)

  Argument and its conclusion is “For organisms at the sea surface, sinking into deep water usually means death”.

• Atoms are the basic building blocks of all matter. They can combine to form molecules, whose properties are generally very different from those of the constituent atoms. Table salt, for example, a simple chemical compound formed from chlorine and sodium, resembles neither the poisonous gas nor the highly reactive metal. (Frank J. Blatt, Principles of Physics, 2nd ed.)

  Argument and its conclusion is “can combine to form molecules, whose properties are generally very different from those of the constituent atoms ”

• It is usually easy to decide whether or not something is alive. This is because
  living things share many common attributes, such as the capacity to extract
  energy from nutrients to drive their various functions, the power to actively
  respond to changes in their environment, and the ability to grow, to differentiate, and to reproduce. (Donald Voet and Judith G. Voet, Biochemistry, 2nd ed.)
  

  Nonargument; explanation.

• A person never becomes truly self-reliant. Even though he deals effectively
  with things, he is necessarily dependent upon those who have taught him to
  do so. They have selected the things he is dependent upon and determined the
  kinds and degrees of dependencies. (B. F. Skinner, Beyond Freedom and Dignity)
  

  Argument and its conclusion is “a person never becomes truly self-reliant.”

• In areas where rats are a problem, it is very difficult to exterminate them with
  bait poison. That’s because some rats eat enough poison to die but others eat
  only enough to become sick and then learn to avoid that particular poison
  taste in the future. (Rod Plotnik, Introduction to Psychology, 4th ed.)
  

  This passage can be either an argument or an explanation. Conclusion: “In areas where rats are a problem, it is very difficult to exterminate them with bait poison”

• Nations are made in two ways, by the slow working of history or the galvanic
  force of ideas. Most nations are made the former way, emerging slowly from
  the mist of the past, gradually coalescing within concentric circles of shared
  sympathies, with an accretion of consensual institutions. But a few nations are
  formed and defined by the citizens’ assent to a shared philosophy. (George Will, “Lithuania and South Carolina”)
  

  Nonargument. Loosely associated statements.

Notes.

Aristotle is the father of logic.

https://www.youtube.com/watch?v=gMpxNrs53yE&ab_channel=MarceloVásconezCarrasco

Deduction, Induction

Evaluate a deductive or inductive argument consists of two steps:

• Evaluate the link between premises and conclusion

• Evaluate the truth of the premises

Deductive argument forms

The conclusion follows necessarily from the premises.

• An argument based on mathematics except for arguments that depended on statistics and probability.

Despite the name, mathematical induction is a deductive argument too.

• An argument from the definition.

• A disjunctive syllogism.

• A hypothetical syllogism.

• A syllogism.

Inductive argument forms

The conclusion follows probably from the premises.

• A prediction

• Argument from analogy

• A generalization

• An argument based on signs

• Argument from authority.

• A causal inference

Validity, Truth, Soundness, Strength, Cogency

Validity is the relationship between premises and conclusion, do premises support the conclusion?

Deductive Argument

Deductive arguments are valid, invalid, sound, and unsound.

In a valid deductive argument is impossible to be false given that the premises are true and it’s determined by the argument’s form. So, any deductive argument having true premises and a false conclusion is invalid.

A sound argument is a deductive argument that is valid and has all true premises. Otherwise is called an unsound argument.

Having a superfluous false premise doesn’t change the soundness.

1. Principio de Identidad

2. Principio de NO contradicción. ??Principle of explosion??

3. Principio de Tercero Excluido

4. Principio de la Razón Suficiente.

https://en.wikipedia.org/wiki/Classical_logic

Inductive Argument

It depends on the uniformity of nature - a mathematical induction depends on natural numbers that are uniform by the Well-Ordering property.

Inductive arguments are strong, weak, cogent or uncogent.

Strong: The conclusion follows the premises.

Abductive arguments. Retroductive reasoning.

Proof methods

Counterexample method

Axiom vs Law

Einstein paper. https://einsteinpapers.press.princeton.edu/vol7-trans/124

Material conditional

Paradoxes of material implication

Language: Meaning and Definition

Varieties of meaning

Language has virtually unlimited functions but, in logic particularly, it conveys information or evokes feelings. The first function, chiefly logic concerned, uses cognitive meaning terms including “legal”, “most often”, “Georgia”, and so; the second one uses emotive meaning terms including “cruel”, “inhuman”, “hapless”, and so forth, statements of this sort very often have both. Since emotive meaning is not mainly concerned with logic, we differentiate the cognitive meaning from the emotive meaning which is a value claim, that is, a claim that something is good, better, or more important than some other thing. We treat these claims as separate statements and as usual, they require evidence to support them. Thus, many writers and speakers use emotive meaning to obscure value claims so the receivers are inclined to swallow them without any evidence.

Cognitive meaning can be defective in two cases affecting the entire statement:

• A vague expression is one that is impossible to determine whether it applies or not such that it allows a continuous range of interpretations and its meaning is hazy. For example, vague words are “cold”, “wordy”, and “sweet”. Precision depends on the situation's demands.

• An ambiguous expression is one that is interpreted in different ways having one clear meaning in a context such that it allows a discrete range of interpretations. For example, ambiguous words are “light”, “critical”, and “bank”. Precision depends on the situation's demands.

Disputes

Verbal disputes are argument conflicts caused by vagueness and ambiguity between individuals. Unless it is clarified, disputes are never resolved. So they arise over the meaning of language.

Factual disputes arise over facts and their interpretation.

The Intension and Extension of terms

In the previous section, you saw that some argument problems arise about vague or ambiguous terms, and even though logic is the evaluation of arguments, those arguments are cleared up by supplying a definition. So, the study of meaning is closely related to logic.

Where is the argument vagueness or ambiguousness?

The basic units of language are words, but your chiefly concern in order to clear up arguments is a term, no general words.

Terms are not verbs, adverbs, adjectives, prepositions, conjunctions, and non syntactic arrangements of words.

Even though some words are meaning adjectives and nouns, being a noun, pronoun, proper name, common name, and descriptive phrase is a sufficient condition for being a term.

Increasing extension, decreasing intention

Increasing intention when each term increases attributes than the previous one.

Example:

Programming language, compiled language, oriented-object compiled language, C++.

Increasing extension when each term increases members of the class than the previous one.

Example:

C++, oriented-object compiled language, compiled language, programming language.

How does a term connote a set of attributes?

There are at least two interpretations: an objective approach and a subjective approach. The objective approach holds that a term connotes essential class member attributes. Conversely, our conventional subjective approach holds that a term connotes common attributes in mentally competent people. It's also called conventional connotation. In this approach, connotation and denotation typically remain the same from person to person, but meanwhile, the connotation is stable in time, denotation is not.

Notes

https://www.paultaylor.eu/stable/prot.pdf writes about sense and reference.

https://plato.stanford.edu/entries/definitions/

How do you make a definition?

Purpose of definition

Plato’s view. It expounds on the meaning of their eternal essences.

Most modern logician’s view. It sets out the meaning of a word called definiendum by assignation other words called definiens.

Fallacies

What is a fallacy?

Fallacy, sometimes called non sequitur, is a bad argument that appears a good one.

Varieties of fallacies

• A formal fallacy is a deductive argument that fails to form a well-form deductive argument such as categorical syllogism, modus tollens, and so forth.

• An informal fallacy is whatever argument that mistakes the content.

Informal fallacies

Arguer's goal is to achieve that the reader/listener accepts the conclusion, in fallacies, it's more important than making good arguments. We’re going to enumerate the kind of premises that cause informal fallacies.

Fallacies of relevance

Fallacies of weak induction

Worked examples

Identify the fallacies.

• If a car breaks down on the freeway, a passing mechanic is not obligated to render emergency road service. For similar reasons, if a person suffers a heart attack on the street, a passing physician is not obligated to render emergency medical assistance.

  X: A car breaks down on the freeway

  Y: A person suffers a heart attack on the street

  Formalization.

  Entity X has a emergency road, a person who solves it right away is called passing mechanic, and who is not obligated to render emergency road service.

  Entity Y has an emergency medical, and a person who solves it right away is called passing physician.

  Therefore, entity Y probably has a person who is not obligated to render emergency medical assistance.

  It’s a weak fallacy because a mechanical emergency is not mandatory by law, but a medical emergency in some countries is. Good Samaritan law.

Fallacies of presumption, ambiguity, and illicit transference

Fallacies in ordinary language

Notes

A full list is on https://en.wikipedia.org/wiki/List_of_fallacies

https://yourlogicalfallacyis.com/

Analogical Reasoning

Analogical Argument form

Entity A has attributes a, b, c, …, and z.

Entity B has attributes a, b, c, ….

Therefore, entity B probably has attribute z also.

Entity A and entity B are called analogues, where the primary analogue is the first one, and the secondary analogue is the last one.

Procedure.

1) Identify the attributes.

2) Determine if is a causal or systematic relation to the attribute z between a,b, and c, …

Rogers P. Hall (1989). Computational approaches to analogical reasoning: A comparative analysis. , 39(1), 39–120. doi:10.1016/0004-3702(89)90003-9

FitzGerald, M. (2018, October 26). Unit 6: Reasoning by Analogy. Youtube. Retrieved from https://www.youtube.com/watch?v=KerNKoJYd6k&ab_channel=MichaelFitzGerald

Set of principles to evaluate most analogy arguments

• Relevance of similarities.

• A number of similarities.

• Nature and degree of disanalogy.

• A number of primary analogues.

• Diversity among the primary analogues.

• Specificity of the conclusion

Stanford. (2009, September 10). Analogy as the Core of Cognition. Youtube. Retrieved from https://www.youtube.com/watch?v=n8m7lFQ3njk&ab_channel=Stanford

Miller Analogies Test

SAT

https://elearning.shisu.edu.cn/pluginfile.php/36509/mod_resource/content/1/ANALOGIES.pdf

Algorithm

Given an analogy in the form

______ : X :: Y : Z

with options a,b,c,d.

our algorithm must return the missing analogue.

1. find some encode(Y)=Z, such as encode(X)=x, x in options.   
2. find some sequence(Y)=Z, such as encode(X)=x, x in options.   
3. 

We assign greater values conceptual values than encodings. Functions are in our knowledge base.

Notes

https://plato.stanford.edu/entries/definitions/

Reason

“The only definition of rationality that I’ve found that is practically, empirically, and mathematically rigorous is the following: what is rational is that which allows for survival. Unlike modern theories by psychosophasters, it maps to the classical way of thinking. Anything that hinders one’s survival at an individual, collective, tribal, or general level is, to me, irrational.”
Nassim Nicholas Taleb, Skin in the Game: Hidden Asymmetries in Daily Life

What is Truth?

Like beauty, “truth” sometimes depends on the eye of the beholder, and it should not be surprising that what constitutes proof differs among fields. For example,

• in the judicial system, legal truth is decided by a jury based on the allowable evidence presented at trial.

• In the business world, authoritative truth is specified by a trusted person or organization, or maybe just your boss.

• In statistics, probable truth is established by statistical analysis of sample data.

• In fields such as physics or biology, scientific truth is confirmed by experiments.

  Actually, only scientific falsehood can be demonstrated by an experiment—when the experiment fails to behave as predicted. No amount of experimentation can confirm that the next experiment won't fail. No truth, rather theories that accurately predict past, and anticipated future.

Eric Lehman, F Thomson Leighton, and Albert R Meyer. Mathematics for Computer Science. revised Wednesday 6th June 2018, 13:43. MIT

Fallacies

https://en.wikipedia.org/wiki/List_of_fallacies

Categories

• Quantity
  • Unity. A particular statement that makes a claim about one and exactly one member of a class.
  • Plurality. A particular statement that makes a claim about some of the members of a class.
  • Totality. A general statement that makes a claim about all the members of a class.

• Quality
  • Reality
  • Negation
  • Limitation

• Relation
  • Inherence and Subsistence (substance and accident)
  • Causality and Dependence (cause and effect)
  • Community (reciprocity)

• Modality
  • Possibility
  • Existence
  • Necessity

TODO

Is syllogism an inference rule? (2022, October 01). Retrieved from https://philosophy.stackexchange.com/questions/46653/is-syllogism-an-inference-rule