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/
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
-
- 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
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
Osvobodit nemožno popravit
verb negation verb
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
Even a comma can save life:
Source: http://4.bp.blogspot.com/-TS4FYHiYlGA/VbDjpJ1wS6I/AAAAAAAABRo/iH5RjLthUPo/s1600/j2.png
Introduction to Logic: Argumentation and Interpretation
Even a comma can save life:
Source: http://randomoverload.org/wp-content/uploads/2013/02/f153funny-girl-breakfast-use-comma.jpg
Introduction to Logic: Argumentation and Interpretation
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.
Introduction to Logic: Argumentation and Interpretation
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...
Introduction to Logic: Argumentation and Interpretation
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“.
Introduction to Logic: Argumentation and Interpretation
Introduction to Logic: Argumentation and Interpretation
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.
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
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
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
Logic and learning
Learning new things: I. – II. – III. – IV.
Awareness, development, improvement: IV. – III. – II. – III. – IV.
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
- 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)
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
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)
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
1. Classical – Greek – logic
the book Posterior Analytics – application of formal logic, conditions of the scientific knowledge
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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.
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
1. Classical – Greek – logic
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
1. Classical – Greek – 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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
1. Classical – Greek – logic
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
1. Classical – Greek – logic
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)
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
1. Classical – Greek – logic
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
1. Classical – Greek – logic
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:
Introduction to Logic: Argumentation and Interpretation
1. Brief history of Logic and its place in science
1. Classical – Greek – logic
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
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)
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
https://en.wikipedia.org/wiki/Syllogism
Gottfried Wilhelm Leibniz (1646 Leipzig – 1716 Hannover)
calculus: the statements are treated like arithmetic equations
monads: unique substances
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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.
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
3. modern logic
4. contemporary logic
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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...)
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
Introduction to Logic: Argumentation and Interpretation
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.
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
Introduction to Logic: Argumentation and Interpretation
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.
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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
Introduction to Logic: Argumentation and Interpretation
Brief history of Logic and its place in science
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:
Top Related