introduction to logic: argumentation and interpretation

Introduction to Logic:

Argumentation and Interpretation

Vysoká škola mezinárodních a veřejných vztahů

PhDr. Peter Jan Kosmály, Ph.D.

24. 2. 2016

Introduction to Logic: Argumentation and Interpretation

Annotation

The course offers an overview of topics in logic, communication,

reasoning, interpretation and summary of their practical use in

communication. It provides basic orientation in terminology of

linguistic research and communication, persuasion and

communication strategies, understanding the logic games, exercises

and tasks, and offers the opportunity to learn the reasoning applied

in various situations. The aim is that students not only get familiar

with lectures, but also acquire the means of communication and

argumentation through exercises and online tests.

Topics

1. Brief history of Logic and its place in science

2. Analysis of complex propositions using truth tables

3. The subject-predicate logic – Aristotelian square

4. Definitions and Terminology

5. Polysemy, synonymy, homonymy, antonymy

6. Analysis of faulty arguments

7. Interpretation – rules and approaches

8. Analysis of concrete dialogue

http://mediaanthropology.webnode.cz/kurzy/introduction-to-logic/



Barnes, Richard. Animal Logic Series. California Academy of Sciences, San Francisco, 2008. Online: http://www.richardbarnes.net/#at=0&mi=2&pt=1&pi=10000&s=8&p=0&a=0 Barnes, Richard. Animal Logic Series. Smithssonian Museum, Washington DC, 2005. Online: http://www.richardbarnes.net/#at=0&mi=2&pt=1&pi=10000&s=16&p=0&a=0

Logic of the nature? Logic of the market? Logic of the hunter and the prey? Logic of self-preservation?

Logic of the history?

- logic of archeological excavations and related hypotheses/theories

- T-Rex: monster (hunter) vs. collector

Logic…a Prehistory… August 24, 2010, Online: http://atypicalatheist.files.wordpress.com/2010/08/amnh- tyrannosaurus.jpg



-

- Iguanodon: collector vs. monster (hunter)

Sources: http://images2.wikia.nocookie.net/__cb20120821150244/dinosaurs/images/d/d6/220px- Iguanodon_Crystal_Palace.jpg; http://www.lauriefowler.com/iguanodon-cs.jpg



Logic of the history?

logic of archeological excavations and related hypotheses/theories

Logic of language and communication?

- language and signification - signification and coding - definition and interpretation - decoding and comprehension - feedback

Praha - Nové mlýny, Google Earth, Quoted 18. 1. 2011 Online: http://www.panoramio.com/photo/46737351



Osvobodit nemožno popravit

verb negation verb


Even a comma can save life:

Sources: https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcTEGOlRPrha9XHehDGeA2f9C9e-C8ET5tn0M8mBkKUfzwkcj_H2Yg http://www.write.com/wp-content/uploads/2012/02/collage10.png



Source: http://4.bp.blogspot.com/-TS4FYHiYlGA/VbDjpJ1wS6I/AAAAAAAABRo/iH5RjLthUPo/s1600/j2.png



Source: http://randomoverload.org/wp-content/uploads/2013/02/f153funny-girl-breakfast-use-comma.jpg


Can you think of other examples?

Source: https://media.licdn.com/mpr/mpr/shrinknp_400_400/AAEAAQAAAAAAAAQMAAAAJDkzODc5MTMwLWQwYjYtNGQ0Zi1iZDk1LTZlYmNmOTdhM2IyZQ.jpg http://www.buzzfeed.com/jessicamisener/commas-save-lives#.mmKVA6AW0J

Punctuation gives the sentence a certain sense Logic originates in philosophy and mathematics as the search for the proper / correct - It analyzes and uses argumentation, statement, assumptions/premises and reasoning.


logic mathematics

Logic is to Mathematics as the title to the painting... Linguistics and Mathematics meet in mathematical analysis of language Linguistics and Logic meet e.g. in theory of standard/literary language, didactics of the (foreign or native) language, corpus linguistics, computer languages, neurolinguistic programming, cognitive and neuro sciences...


Logic is a system for analyse of the language Logic is interested in argumentation and reasoning

Google definition: Logic: ...reasoning conducted or assessed according to strict principles of validity. synonyma: reasoning, line of reasoning, rationale, argument, argumentation ...a system or set of principles underlying the arrangements of elements in a computer or electronic device so as to perform a specified task. Example: The computer program code logic is executed by the processing circuitry and is configured to generate an output signal. Wikipedia definition: Logic is the branch of philosophy concerned with the use and study of valid reasoning... Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning.

I. If Argentina joins the Alliance, then Brasil and Chile will boycott the Alliance.

II. If Brasil or Chile will boycott the Alliance, it won´t be effective.

III. If Argentina joins the Alliance, it won´t be effective.

Advertisement – promotion claim:

Everyone applies charges. Everyone raises the prices,

everything becomes more expensive... We are different!

Following the argumentation you await either gradation, or conflict –

that´s why the claim sound so „proper“.



Logic can be learned. We use and control logic subconsciously...

Assumptions, reasoning, argumentation are phenomena that we

encounter every day (semiotic pollution is 1500 logos daily).

We use rhetoric, strategy, psychology and interpretation every day in

decoding and encoding communication and acquisition of social and

epistemic competence.

Logic deals with universal causal relationships aand is a tool

for many disciplines and everyday interpersonal communication ...

Among other things, is part of discipline´s philosophy and didactics –

as a set of rules (the system) of the given scientific field.


Types of logic

Syllogistic (Aristotelian) logic – analysis of the judgements into

propositions consisting of two terms that are related by one of a fixed

number of relations, and the expression of inferences by means of

syllogisms that consist of two propositions sharing a common term as

premise, and a conclusion that is a proposition involving the two

unrelated terms from the premises.

Exapmle:

All men are mortals.

All Socrates are men.

All Socrates are mortals.

Source: https://en.wikipedia.org/wiki/Logic


Types of logic

Propositional logic (sentential logic) – is the branch of

mathematical logic concerned with the study of propositions

(whether they are true or false) that are formed by other

propositions with the use of logical connectives, and how their

value depends on the truth value of their components.

Exapmle:

Premise 1: If it's raining then it's cloudy.

Premise 2: It's raining.

Conclusion: It's cloudy.

Source: https://en.wikipedia.org/wiki/Propositional_calculus


Types of logic

Predicate logic – is a system distinguished from other systems in

that its formulae contain variables which can be quantified. Two

common quantifiers are the existential ∃ ("there exists") and

universal ∀ ("for all") quantifiers. Predicate logics also include

logics mixing modal operators and quantifiers.

Exapmle:

For every a, if a is a philosopher, then a is a scholar

for every unary relation (or set) P of individuals, and every

individual x, either x is in P or it is not:

Source: https://en.wikipedia.org/wiki/Predicate_logic


Types of logic

Modal logic – is a type of formal logic primarily developed in the

1960s that extends classical propositional and predicate logic to

include operators expressing modality. Modals—words that express

modalities—qualify a statement. modal operators are usually

written □ for Necessarily and ◇ for Possibly.

Exapmle:

It is possible that it will rain today if and only if it is not necessary

that it will not rain today; and it is necessary that it will rain today if

and only if it is not possible that it will not rain today.

Source: https://en.wikipedia.org/wiki/Modal_logic


Types of logic

Informal reasoning – A branch of logic whose task is to develop non-

formal standards, criteria, procedures for the analysis,

interpretation, evaluation, criticism and construction of

argumentation (J. Anthony Blair). Since the 1980s, informal logic has

been partnered and even equated with critical thinking.

Exapmle of a Conductive argument:

(1) I will take the job in Chicago, because (2) people are nice there,

(3) the pay is good, (4) the infrastructure is good there, (5) I have

already friends there, (6) the working hours are not too long, and (7)

the public transport system is great. Source: https://en.wikipedia.org/wiki/Informal_logic, https://faculty.unlv.edu/ledwig/chapter12.html


Types of logic

Mathematical logic – is a subfield of mathematics exploring the

applications of formal logic to mathematics. It bears close

connections to metamathematics, the foundations of mathematics,

and theoretical computer science.[1] The unifying themes in

mathematical logic include the study of the expressive power of

formal systems and the deductive power of formal proof systems.

Mathematical logic is often divided into the fields of set theory,

model theory, recursion theory, and proof theory.

Source: https://en.wikipedia.org/wiki/Mathematical_logic


Types of logic

Philosophical logic – deals with formal descriptions of ordinary, non-

specialist ("natural") language... Philosophical logic is essentially a

continuation of the traditional discipline called "logic" before the

invention of mathematical logic. Philosophical logic has a much

greater concern with the connection between natural language and

logic. As a result, philosophical logicians have contributed a great

deal to the development of non-standard logics (e.g. free logics,

tense logics) as well as various extensions of classical logic (e.g.

modal logics) and non-standard semantics for such logics (e.g.

Kripke's supervaluationism in the semantics of logic). Source: https://en.wikipedia.org/wiki/Logic


Types of logic

Computational logic – is the use of logic to perform or reason about

computation. It bears a similar relationship to computer science and

engineering as mathematical logic bears to mathematics and as

philosophical logic bears to philosophy. It is synonymous with "logic in

computer science".

Non-classical logics (sometimes alternative logics) – are formal systems

that differ in a significant way from standard logical systems such as

propositional and predicate logic. Examples of non-classical logics:

Many-valued logic, Fuzzy logic, Linear logic, Modal logic, Paraconsistent

logic, Relevance logic, etc. Sources: https://en.wikipedia.org/wiki/Computational_logic https://en.wikipedia.org/wiki/Non-classical_logic

Logic and learning

I. I do not know that I can not / do not know something.

- I do not have the knowledge or ability to use something

II. I know that I can not / do not know something.

- I do have the knowledge, but do not have the ability to use something

III. I know that I can / do know something.

- Focus on activities and use of skills, lack of automatic behavior

IV. I do not know that I can / do know something.

- Habitual behaviors, subconscious skills



Logic and learning

Learning new things: I. – II. – III. – IV.

Awareness, development, improvement: IV. – III. – II. – III. – IV.



- from habit through the unconscious to the conscious level

(defining terms and concepts), exploration, and the

subsequent automatization into the logical thinking.

4 basic historical periods:

1. ancient (classical) logic

(Aristotle, Stoics)

2. medieval logic

(scholastic)

3. modern logic

(Leibniz)

4. contemporary logic (Frege)



Source of the image: http://upload.wikimedia.org/wikipedia/commons/thumb/4/49/Aristoteles_Logica_1570_Biblioteca_Huelva.jpg/220px-Aristoteles_Logica_1570_Biblioteca_Huelva.jpg

1. Classical – Greek – logic

h t t

p : /

/ c s .

w i k

i p e d

i a . o

r g / w

i k i /

A r i

s t o

t e l é

s

http://cs.wikipedia.org/wiki/Boëthius


Brief history of Logic and its place in science

Preparatory period: Sophists, Presocratic philosophers, Socrates & Plato, unwritten rules of logic, until the publication of Ariistotle´s TOPICS. Aristotelian – Stoic period: 4th and 3rd century BC, produces the "formal logic" Period of commentators: processing and developing previous ideas, Boethius: last philosopher of antiquity, the first medieval (Consolatio philosophiae – Consolation of Philosophy – Útěcha z filosofie)



Pre-Socratic/Aristotelian Logic

Heraclitus Heraclitus (c. 535 – c. 475 BC) was the first place where the word logos was given special attention in ancient Greek philosophy, Parmenides held that all is one and nothing changes; Heraclitus held everything changes. He is known for his paradoxes. Heraclitus was famous for his insistence on ever-present change as being the fundamental essence of the universe, as stated in the famous saying, "No man ever steps in the same river twice" (panta rhei)

Aristotle (384–322 BC)

logic as a tool for science, Organon writings;

the book Category – science of terms

the book On expression (on interpretation) – science of statements

the book Prior Analytics – science of argument, syllogisms

the book Topics – analysis of dialectical arguments

the book Sophistic Refutations – on false arguments

h t t

p : /

/ c s .

w i k

i p e

d i a

. o r g

/ w i k

i / A

r i s t

o t e

l é s




the book Posterior Analytics – application of formal logic, conditions of the scientific knowledge



Pre-Socratic/Aristotelian Logic

Heraclitus Contraries and paradoxes: Sea is the purest and most polluted water: for fish drinkable and healthy, for men undrinkable and harmful. As the same thing in us are living and dead, waking and sleeping, young and old. For these things having changed around are those, and those in turn having changed around are these. For souls it is death to become water, for water death to become earth, but from earth water is born, and from water soul.



Contraries in general Binary oppositions Contrary and contradictory – distinctive oppositions Complementary oppositions: yin and yang Contradictory oppositions: black/white, good/evil Oppositions with/without symptoms: teacher (he/she) – masculine/feminine Partial oppositions: house – window

has examined in statements:

quality aspect (positive and negative: does, does not ...)

quantity aspect (general and partial: everyone, anyone, no one ...)

affirmo (I claim, lat.) – neggo (I deny, lat.)

The sentence consists of the subject (S) and the predicate (P)

Singular sentences: Sokrates is rational. Universal sentences: Every human is rational. Particularm sentences: Some people are rational.

Subject Predicate




Aristotle (384–322 BC)

Most of Aristotle’s logic was concerned with certain kinds of propositions that can be analyzed as consisting of (1) usually a quantifier (“every,” “some,” or the universal negative quantifier “no”), (2) a subject, (3) a copula, (4) perhaps a negation (“not”), (5) a predicate.

Universal affirmative: “Every β is an α.” Universal negative: “Every β is not an α,” or equivalently “No β is an α.” Particular affirmative: “Some β is an α.” Particular negative: “Some β is not an α.” Indefinite affirmative: “β is an α.” Indefinite negative: “β is not an α.” Singular affirmative: “x is an α,” where “x” refers to only one individual Singular negative: “x is not an α,” with “x” as before.

Source: http://www.britannica.com/topic/history-of-logic




Aristotelian Square of opposition

affirmo (I claim, lat.) – neggo (I deny, lat.), subject (S) a predicate (P)

All S are P (+) Universal affirmative

No S is P (-) Universal negative

S a P

S e P

Some S are P (+) Particular affirmative

Some S are not P (-) Particular negative S i P S o P




Aristotelian Square of opposition – relations between statements

Každý (+) contrary Nikdo (-)

S a P S e P

subaltern contradictory subaltern

Někdo (+) subcontrary Někdo (-)

S i P S o P




1. Contradictory statements: either, or (neither, nor)

All are ≡ is not true that some are not (SaP ≡ ¬ SoP; SeP ≡ ¬ SiP)

Examples: every man is white – not every man is white, no man is – some...is...

2. Contrary statements: the negation of the second results from the first All are – is not true that no one is not (SaP =› ¬ SeP; SeP =› ¬ SaP)

Example: every man is white – no man is white

3. Subcontrary statements: both can be true

some swans are black, some swans are not black (¬ SiP =› SoP; ¬ SoP =› SiP)

4. Subaltern statements: subordinated, are always true Example: every man is white is true therefore some man is white‚ is true (SaP =› SiP; SeP =› SoP; ¬ SiP =› ¬ SaP; ¬ SoP =› ¬ SeP)



Aristotelian Square of opposition – relations between statements

Stoics:

founder of the Megarian school was Euclid of Megara

founder of the Stoics school was Zeno from Kitia

logic as a part of philosophy (together with physics and ethics)

within logic there was studied:

Theory of knowledge (the criterion of truth)

Semantics and grammar – language and mind

Logic in the strict sense (the formal correctness of syllogisms)

http://cs.wikipedia.org/wiki/Zénón_z_Kitia http://cs.wikipedia.org/wiki/Eukleidés_z_Megary







Aristotle distinguished singular terms such as Socrates and general terms such as Greeks. Aristotle further distinguished: (a) terms that could be the subject of predication, and (b) terms that could be predicated of others by the use of the copula ("is a"). In Aristotle's view singular terms were of type (a) and general terms of type (b). Thus Men can be predicated of Socrates but Socrates cannot be predicated of anything. Therefore, for a term to be interchangeable—to be either in the subject or predicate position of a proposition in a syllogism—the terms must be general terms, or categorical terms as they came to be called. Consequently, the propositions of a syllogism should be categorical propositions (both terms general) and syllogisms that employ only categorical terms came to be called categorical syllogisms. https://en.wikipedia.org/wiki/Syllogism

Megarian-stoic period:




The hypothetical syllogism: statements appearing in the syllogism may be composed of other statements, basic is the statement

(At least one premise is a compound statement; if, then, either or, and, not)

Categorical syllogism: according to Aristotle it consists of two premises and a conclusion (simple statements), form depends on the internal structure, on terms and their quantity and quality

(subject-predicate statements; each, some, none, no, it is)

2. Medieval logic

I. Period of Logica antiqua: 6th century AC untill the 13th century Reception of the 2 introductory writings from the Organon (terms, statements), Dialectica from Peter Abelard is the major work

II. Period of Logica modernorum: 13th to 14th century, overcoming Aristotle's logic, concerning the properties of terms, consequences, liabilities, paradoxes



University studies of trivium (grammar, rhetorics, and logic) followed by quadrivium (arithmetic, geometry, music, and astronomy)

scholastic theory of the term (decomposition to: statements and terms), term without context = terms denoting and terms not denoting (conjunctions, particles, etc.)

2. Medieval logic



Peter Abelard wrote commentaries on Aristotle's work on logic. Among other things, Abelard wrote on the role of the copula in categorical propositions ("all" or "none"), the effects of placing the negation sign in different positions, modal notions such as "possible," and conditional propositions (if___ then … ). During the medieval period mnemonic names were created for the valid moods of the syllogism that had been discussed in Aristotle's Prior Analytics. Two of those moods were BARBARA, in which the three propositions of the syllogism consist entirely of universal affirmatives, and CELARENT, in which one premise is a universal negative, the other a universal affirmative, and the conclusion is a universal negative. Medieval logicians also investigated modal logic.

2. Medieval logic



Figure 1 Figure 2 Figure 3 Figure 4

Barbara Cesare Datisi Calemes

Celarent Camestres Disamis Dimatis

Darii Festino Ferison Fresison

Ferio Baroco Bocardo Calemos

Barbari Cesaro Felapton Fesapo

Celaront Camestros Darapti Bamalip

The vast majority of the 256 possible forms of syllogism are invalid (the conclusion does not follow logically from the premises). Even those logically valid are sometimes considered to commit the existential fallacy, meaning they are invalid if they mention an empty category.

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

Examples Barbara (AAA-1)[edit] All men are mortal. (MaP) All Greeks are men. (SaM) All Greeks are mortal. (SaP) Celarent (EAE-1) Similar: Cesare (EAE-2) No reptiles have fur. (MeP) All snakes are reptiles. (SaM) No snakes have fur. (SeP) M:reptile S:snake P:fur




Examples Darii (AII-1) Similar: Datisi (AII-3) All rabbits have fur. (MaP) Some pets are rabbits. (SiM) Some pets have fur. (SiP) M:rabbit S:pet P:fur




Examples Ferio (EIO-1) Similar: Festino (EIO-2), Ferison (EIO-3), Fresison (EIO-4) No homework is fun. (MeP) Some reading is homework. (SiM) Some reading is not fun. (SoP) M:homework S:reading P:fun




Examples Baroco (AOO-2) All informative things are useful. (PaM) Some websites are not useful. (SoM) Some websites are not informative. (SoP) M:informative S:website P:useful




Examples Bocardo (OAO-3) Some cats have no tails. (MoP) All cats are mammals. (MaS) Some mammals have no tails. (SoP) M:cat S:mammal P:tail




Examples Barbari (AAI-1) All men are mortal. (MaP) All Greeks are men. (SaM) Some Greeks are mortal. (SiP) M:man S:Greek P:mortal




Examples Celaront (EAO-1) Similar: Cesaro (EAO-2) No reptiles have fur. (MeP) All snakes are reptiles. (SaM) Some snakes have no fur. (SoP) M:reptile S:snake P:fur




Examples Camestros (AEO-2) Similar: Calemos (AEO-4) All horses have hooves. (PaM) No humans have hooves. (SeM) Some humans are not horses. (SoP) M:hooves (kopyta) S:human P:horse




Examples Felapton (EAO-3) Similar: Fesapo (EAO-4) No flowers are animals. (MeP) All flowers are plants. (MaS) Some plants are not animals. (SoP) M:flower S:plant P:animal




Examples Darapti (AAI-3) All squares are rectangles. (MaP) All squares are rhombuses. (MaS) Some rhombuses are rectangles. (SiP) M:square (čtverec) S:rhomb (kosočtverec) P:rectangle (obdélnik)




Gottfried Wilhelm Leibniz (1646 Leipzig – 1716 Hannover)

calculus: the statements are treated like arithmetic equations

monads: unique substances



3. modern logic

Humanism emphasizes the aesthetic of language instead of formal development of psychology, rhetoric, theory of knowledge ... The core of classical logic that in addition to formal questions addresses issues of knowledge and psychology is formed.

the proof by contradiction (reductio ad absurdum): if the premise is false and it is applied the exclusion of third (tertium non datur, ambiguity), statement must be true... e.g. a set of interesting and uninteresting numbers – if we choose the most interesting from the set of uninteresting, we have proven, that such numbers don´t exist

4 laws for the proof of syllogisms:

I. If V, then V (V=V or A=A) – tautology The human is human. Sokrates is Sokrates.

II. If (A is B) and (B is C), then (A is C) – classical syllogism If each falcon is a bird and each bird flies, then every falcon flies.

III. If V, then non(non V) and (A=non(non A)) – double negation If a man is mortal, then man is not immortal.

IV. If (A is B), ten (non B is non A) – proof by contracdiction If every tree is green, then being not green is being not a tree.



3. modern logic

4. contemporary logic



In the 19th century the mathematical logic appears as the tool for thinking in mathematics, as founders and pioneers of modern logic are considered George Boole (1815, England–1864 Ireland), Augustus De

Morgan (1806, India–1871 London), and from the Czech environment Bernard Bolzano (1781 Prague–1848 Prague). Friedrich Ludwig Gottlob Frege (1848, Wismar–1925 Bad Kleinen) invented the concept writing (1879 Begriffsschrift...), the way of expressing the mathematical proofs by using symbols (eg. the

implication, negation, condition, universal quantification, existential qualifier, equivalence...). He tried to transfer the concept of function from mathematics analogically (number-number relationship), non-qualifiable scope of the term (house...)



S a P

S e P




Analyze these statements

40 per cent Germans would pay for a better access to information! According to Czechs, the job have to be secured by the state. Not everyone wants Paroubek for the prime minister. Many prefer social security instead of higher salaries. Clinton and Trump met the role of favorites at Tuesday´s primaries.



S a P

S e P




Analyze these statements

Mr. Babiš became the entrepreneur of the year. The schools do not have to worry about inclusion. A part of the population disagrees with the arrival of refugees. A problem with bullying at one school does not mean bullying at every school. This year´s nominations were not suprprising.



Modern logical analysis

The componet analysis Assuption of the generativist linguistics All (speech) can be divided into (hierarchical) categories Components: categorial, sub-categorial, identification, individual Semantics: tells us about (contextual) meaning (význam), sense (smysl) „parrent“ is: + human, living being – categorial + sex (masculine, feminine) – sub-categorial + father, mother



The componet analysis Semantics in verbs of motion

run

(běžet)

walk

(jít)

dance

(tancovat)

crawl

(lézt)

Hop

(skákat)

Jump

(skočit)

Skip

(přeskočit)

At least

one limb is

in contact

with the

surface/no

limb is in

contact

‒ + ± + ‒ ‒ ‒

Contact

alternation 1-2-1-2 1-2-1-2

Differently

but

rhythmicall

y

1-3-2-4 1-1-1

or 2-2-2 irrelevant 1-1-2-2

Number of

limbs 2 2 2 4 1 2 2

https://cs.wikipedia.org/wiki/Komponentová_analýza_významu

Thank you for your attention!

PhDr. Peter Jan Kosmály, PhD.

In case of a need, don´t hesitate to contact me:

[email protected]

introduction to logic: argumentation and interpretation

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