Grammaticalization and Lexical Expression of Tropative from a Typological Perspective
Roman Tarasov,
Higher School of Economics, Moscow, Russia
The Fifth Annual International Conference on Languages, Linguistics, Translation and Literature
2-3 February 2021, Ahwaz
For more information, please visit the conference website:
WWW.LLLD.IR
The document discusses different types of hypothetical and logical propositions including:
- Conditional propositions expressed with "if-then" statements.
- Disjunctive propositions expressed with "either-or" statements.
- Conjunctive propositions that express two alternatives cannot be true simultaneously.
- Complex statements that contain logical components like hypothetical and negative propositions.
It also covers propositional logic concepts like negation, material implication, disjunction, conjunction, and material equivalence. Truth tables are provided to define the truth conditions for each logical operator.
It is a nptel course pdf made available here from its official nptel website . Its full credit goes to nptel itself . I am just sharing it here as i thought it would help someone in need of it . It is a course of INTRODUCTION TO ADVANCED COGNITIVE PROCESSES
English 100 error detection & correction for all exams by das sir(09038870684)Tamal Kumar Das
This document provides 65 tips for correcting sentences in English related to subject-verb agreement, uses of participles and infinitives, uses of verbs, uses of adjectives, and uses of adverbs. Some key points include: subject-verb agreement depends on whether the subjects are singular or plural; participles must have a subject of reference; certain verbs like advise are followed by an object and infinitive; adjectives show quantity, number, or degree; and adverbs modify verbs, adjectives, or other adverbs. The document aims to help with grammar corrections needed for exams.
Syllogism by premises from das sir (08961556195)Tamal Kumar Das
The document discusses two types of logical reasoning: deductive and inductive. Deductive reasoning uses premises to reach a logically certain ("necessary") conclusion, while inductive reasoning uses premises to reach a logically possible conclusion. It provides examples of arguments using each type of reasoning and explains how to represent them visually using Venn diagrams. The key difference between the two types of reasoning is whether the conclusion is logically necessary or possible given the premises.
The document discusses logic and propositions. It begins by defining a proposition as a statement that is either true or false. It then provides examples of propositions and non-propositions. The document also discusses arguments and their validity. An argument is valid if the premises guarantee the conclusion. It discusses logical operators like conjunction, disjunction, negation and implication. Truth tables are used to determine the truth values of compound propositions formed using logical operators. Laws of algebra are also discussed for propositional logic.
This book is written by LOIBANGUTI, BM, it is just an online copy provided for free. No part of this book mya be republished. but can be used and stored as a softcopy book, can be shared accordingly.
Grammaticalization and Lexical Expression of Tropative from a Typological Perspective
Roman Tarasov,
Higher School of Economics, Moscow, Russia
The Fifth Annual International Conference on Languages, Linguistics, Translation and Literature
2-3 February 2021, Ahwaz
For more information, please visit the conference website:
WWW.LLLD.IR
The document discusses different types of hypothetical and logical propositions including:
- Conditional propositions expressed with "if-then" statements.
- Disjunctive propositions expressed with "either-or" statements.
- Conjunctive propositions that express two alternatives cannot be true simultaneously.
- Complex statements that contain logical components like hypothetical and negative propositions.
It also covers propositional logic concepts like negation, material implication, disjunction, conjunction, and material equivalence. Truth tables are provided to define the truth conditions for each logical operator.
It is a nptel course pdf made available here from its official nptel website . Its full credit goes to nptel itself . I am just sharing it here as i thought it would help someone in need of it . It is a course of INTRODUCTION TO ADVANCED COGNITIVE PROCESSES
English 100 error detection & correction for all exams by das sir(09038870684)Tamal Kumar Das
This document provides 65 tips for correcting sentences in English related to subject-verb agreement, uses of participles and infinitives, uses of verbs, uses of adjectives, and uses of adverbs. Some key points include: subject-verb agreement depends on whether the subjects are singular or plural; participles must have a subject of reference; certain verbs like advise are followed by an object and infinitive; adjectives show quantity, number, or degree; and adverbs modify verbs, adjectives, or other adverbs. The document aims to help with grammar corrections needed for exams.
Syllogism by premises from das sir (08961556195)Tamal Kumar Das
The document discusses two types of logical reasoning: deductive and inductive. Deductive reasoning uses premises to reach a logically certain ("necessary") conclusion, while inductive reasoning uses premises to reach a logically possible conclusion. It provides examples of arguments using each type of reasoning and explains how to represent them visually using Venn diagrams. The key difference between the two types of reasoning is whether the conclusion is logically necessary or possible given the premises.
The document discusses logic and propositions. It begins by defining a proposition as a statement that is either true or false. It then provides examples of propositions and non-propositions. The document also discusses arguments and their validity. An argument is valid if the premises guarantee the conclusion. It discusses logical operators like conjunction, disjunction, negation and implication. Truth tables are used to determine the truth values of compound propositions formed using logical operators. Laws of algebra are also discussed for propositional logic.
This book is written by LOIBANGUTI, BM, it is just an online copy provided for free. No part of this book mya be republished. but can be used and stored as a softcopy book, can be shared accordingly.
Introduction to logic and prolog - Part 1Sabu Francis
The document provides an introduction to logic and Prolog programming. It discusses:
1) Alan Turing's invention of the modern computer to solve complex problems like decoding encrypted messages. This established the concept of algorithms being carried out through linear instruction processing.
2) Prolog programming focuses solely on logic and removes concerns about procedural elements like instruction pointers. It allows programmers to focus only on the problem's logic.
3) Logic is a tool for reasoning that uses concepts like true, false, if-then statements, and, or, etc. It helps clarify reasoning but cannot validate conclusions on its own if premises are flawed.
The document discusses arguments and how to identify their key components. An argument is defined as a claim supported by reasons or evidence, called premises, that are intended to prove or support a conclusion. Indicator words can help identify premises and conclusions. While arguments often contain these indicators, some do not, so conclusions must be inferred. The document also distinguishes arguments from non-arguments like reports, unsupported assertions, conditional statements, illustrations, and explanations.
Associate Professor Michael Emmison: AIEMCA 2012 Keynote 1ajcmanager
Emmison, M. (2013). "Epistemic engine" versus "role-play method": divergent trajectories in contemporary conversation analysis. Australian Journal of Communication, 40 (2), 5-7.
This document discusses and distinguishes between arguments and non-arguments, and outlines key elements of arguments including premises, conclusions, and common argument structures. It defines an argument as a claim defended with reasons, composed of one or more premises and a conclusion. It also discusses deductive arguments, which aim to prove conclusions with logical necessity from premises, and inductive arguments, which claim conclusions that are probable or likely given the premises. Common patterns of deductive reasoning like categorical syllogisms and elimination arguments are described.
An argument consists of one or more premises intended to support a conclusion. Premises provide evidence or reasons to accept the conclusion. Arguments contain indicators like "therefore" or "so" but these are not always present. Conditionals, reports, unsupported assumptions, illustrations, and explanations are not considered arguments. Arguments differ from explanations in that arguments aim to prove something is the case while explanations provide a causal account for something already accepted as true.
The document discusses critical thinking versus logic, providing examples to illustrate the differences. It argues that critical thinking encourages skepticism and subjective reasoning, while logic assumes the existence of objective truth. It provides guidance for teaching children logic, including understanding the difference between valid and true arguments, and avoiding fallacies. Examples of fallacies like ad hominem attacks are given. The goal is to train children to evaluate arguments for both truth and logical soundness.
Semantics iv proposition and presuppositionBrian Malone
This document summarizes key concepts about propositions and presuppositions from semantics. It defines propositions as statements that can be evaluated as true or false based on certain truth conditions. Even propositions that are not factually true can still be meaningful if they have identifiable truth conditions. Presuppositions refer to implicit assumptions in utterances about shared background knowledge between speakers. The example given presupposes the reader's familiarity with daily COVID-19 briefings from the White House. Analyzing presuppositions provides insights into implicature and how speakers communicate beyond just the literal meaning of words.
Understanding arguments, reasoning and hypothesesMaria Rosala
As researchers working in government, influencing service design, we need to know that our research is methodologically sound, our research findings are grounded in empirical data and our recommendations are logically derived.
'Understanding arguments, reasoning and hypotheses' is the first in a series of 5 short courses, covering introduction courses to various aspects of methodology in research, from the use of grounded theory in discovery research, to hypothesis testing and sampling in more experimental research.
In this course, you'll learn:
About arguments
- what we mean by an argument
- how to identify a valid/invalid argument
- what we mean by premises
- what validity and soundness of arguments mean
About reasoning
- what is deductive reasoning and where do we use it
- what is inductive reasoning and where do we use it
- what is abductive reasoning and where do we use it
About hypotheses
- what is a hypotheses and a null hypothesis
- how do we test them
Week 14 April 28 & 30 - Love and Death Castillo, Chap. 9 .docxmelbruce90096
Week 14: April 28 & 30 - Love and Death
Castillo, Chap. 9 “Sofia, Who Would Never Again Let Her Husband Have the Last Word…”
Chap. 10 “Wherein Sofia Discovers La Loca’s Playmate…”
Chap. 11 “The Marriage of Sofia’s Faithful Daughter to her Cousin”
Chap. 12 “Of the Hideous Crime of Francisco el Penitente…”
1. For all chapters, identify the four levels of analysis: 1) metaphoric/symbolic; 2) literary; 3) sociological; and spiritual.
Chapter 9 “Sofia, Who Would Never Again Let Her Husband Have the Last Word…”
2. In this chapter, Sofia begins a transformation of her own. What is this transformation and what role does Esperanza play?Chapter 10
3. In this chapter, we return to La Loca, reading from her point of view. What do we learn from this, the youngest of Sofi’s daughters?
4. As Fe leaves Sofia’s home we realize she has not come to terms with what she went through when Tom broke off the engagement. What is Fe like now? Has she also changed?
5. What about Esperanza, what news about her? And what about “La Llorona, Chicana international astral-traveler”?
Chapter 11
6. Much happens to Fe in this chapter. Be able to recount all of Fe’s experiences and the relationship to big business, the U.S. government, and the medical profession.Chapter 12
7. What to make of this last chapter in Caridad and Francisco’s lives? What are the recurring themes and metaphors/symbolizes, etc.?
In preparation for the Opposing Viewpoints short paper due in Module Five, you will outline a position (thesis) on a topic of your choosing.
Using the Prewriting Template provided, outline two to three of your reasons for supporting your thesis and then also outline the objection’s position. Please note that the main purpose of this assignment is to formulate the strongest possible objection to your own position before responding to it.
You will be required to use at least four outside (i.e., other than the textbook) sources for this paper, two for each side of the issue. You do not need to do extensive reearch before completing the outline.
Possible topics: Affirmative Action, Abortion, State-Financed Health Care, Flat Tax...or anything you want. It is best to choose a position for which you can find reasonable arguments on both sides.
Click on the title above to turn in your outline.
First Paper (Opposing Viewpoints):
Critical Elements
Distinguished
Proficient
Emerging
Not Evident
Value
Main Elements
Includes almost all of the main elements and requirements and cites ample appropriate support to illustrate each element
(23-25)
Includes most of the main elements and requirements and cites appropriate support to illustrate each element
(20-22)
Includes some of the main elements and requirements
(18-19)
Does not include any of the main elements and requirements
(0-17)
25
Inquiry and Analysis
Explores multiple reasons and offers in-depth analysis of evidence to make informed conclusions about the issue
(18-20)
Explores so.
Integers and rationals can be expressed in first-order logic using only the less than relation <. The difference between integers and rationals can also be expressed in first-order logic. Specifically, integers have the property that between any two integers, there is no other integer, while this is not true for rationals - between any two rationals there is always another rational.
The document provides guidance on how to structure an effective essay. It discusses the key components of an introduction, body paragraphs, and conclusion. For the introduction, it recommends including a neutral sentence, context sentence, argument sentence, and summary sentence. For body paragraphs, it advises using the PREC structure - point, reason, example, and concluding sentence. Finally, it suggests that the conclusion should restate the argument, outline how it was demonstrated, include a thoughtful analysis, and end with a strong concluding statement. The document also includes examples and tips for writing introductions, body paragraphs, and conclusions according to this structure.
1Week 3 Section 1.4 Predicates and Quantifiers As.docxjoyjonna282
1
Week 3: Section 1.4 Predicates and Quantifiers
Assume that the universe of discourse is all the people who are participating in
this course. Also, let us assume that we know each person in the course. Consider the
following statement: “She/he is over 6 feet tall”. This statement is not a proposition
since we cannot say that it either true or false until we replace the variable (she/he) by a
person’s name. The statement “She/he is over 6 feet tall” may be denoted by the symbol
P(n) where n stands for the variable and P, the predicate, “is over six feet tall”. The
symbol P (or lower case p) is used because once the variable is replaced (by a person’s
name in this case) the above statement becomes a proposition.
For example, if we know that Jim is over 6 feet tall, the statement “Jim is over six
feet tall” is a (true) proposition. The truth set of a predicate is all values in the domain
that make it a true statement. Another example, consider the statement, “for all real
numbers x, x2 –5x + 6 = (x - 2) (x – 3)”. We could let Q(x) stand for x2 –5x + 6 = (x - 2)
(x – 3). Also, we note that the truth values of Q(x) are indeed all real numbers.
Quantifiers:
There are two quantifiers used in mathematics: “for all” and “there exists”. The
symbol used “for all” is an upside down A, namely, . The symbol used for “there
exists” is a backwards E, namely, . We realize that the standard, every day usage of the
English language does not necessarily coincide with the Mathematical usage of English,
so we have to clarify what we mean by the two quantifiers.
For all For every For each For any
There exists at least one There exists There is Some
The table indicates that the mathematical meaning of the universal quantifier, for
all, coincides with our everyday usage of this term. However, the mathematical meaning
of the existential quantifier does not. When we use the word “some” in everyday
language we ordinarily mean two or more; yet, in mathematics the word “some” means at
least one, which is true when there is exactly one.
The Negation of the “For all “Quantifier:
Consider the statement “All people in this course are over 6 feet tall.” Assume it
is false (I am not over six feet tall). How do we prove it is false? All we have to do is to
point to one person to prove the statement is false. That is, all we need to do is give one
counterexample. We need only show that there exists at least one person in this class
who is not over 6 feet tall. Here is a more formal procedure.
Example 1:
Let P(n)stand for “people in this course are over 6 feet tall”, then the sentence
“All people in this course are over 6 feet tall” can be written as: “ n P(n)”. The negative,
“ ( n P(n))”, is equivalent to: “ n( P(n))”. So, in English the negative is, “There is
(there is at least one/ there exists/ some) a person in this room who is not over 6 feet tall.”
2
Example 2:
How w ...
6
Elementary Symbolic Logic
Heinz-Dieter Falkenstein
Against logic there is no armor
like ignorance.
—Laurence Peter
mos66065_06_c06_137-168.indd 137 3/31/11 1:25 PM
CHAPTER 6Section 6.1 The Logic of Sentences
Now that we have looked at inductive arguments, deductive arguments, and the com-ponents—premises and conclusions—that make them up, we can turn to making our
understanding of deductive reasoning more precise. We do so by introducing a few sym-
bols for sentences and for the kinds of terms—such as and and or—that connect sentences,
and we use these symbols to look at the structure of both sentences and arguments. For
the most part, we look at material we have already examined; here we just use symbols to
make the various structures involved a bit more explicit. Arguments often get sidetracked
because of the information presented, and although that information is important, we can
avoid being sidetracked in this way by focusing on the structure of the arguments. Sym-
bols are helpful in keeping the focus on such structures.
What We Will Be Exploring
• We will look at how symbols can be applied to sentences, and then to arguments.
• We will examine the notion of a truth function and the kinds of specific logical properties sentences
possess.
• We will see how truth tables can be used to evaluate certain kinds of sentences, as well as testing
deductive arguments for validity.
• We will use basic symbolic logic to examine some earlier material and see how it can be made more
precise.
6.1 The Logic of Sentences
We begin by seeing how to apply symbols—sentence letters—to sentences, first using basic sentences and then using sentences constructed out of these basic sentences.
Assertoric Sentences and Sentence Letters
Earlier we looked at various strings of words: some were questions, some were commands,
and some were assertions. Here are some examples of the kinds of sentences we examined
earlier, as well some new, compound sentences, which assert more than one claim:
1. Cheddar cheese is better than American cheese.
2. The window is broken.
3. Turn left at the next light.
4. Art is a great dancer.
5. Art is very popular.
6. Art is very popular and he is a great dancer.
7. Art is very popular because he is a great dancer.
8. John and Mary got married.
9. John and Mary had a baby.
10. John and Mary got married and had a baby.
11. John and Mary had a baby and got married.
12. Can you hear that music?
Can you determine which of these make assertions or state some kind of claim? You’ll
find that most of the sentences on this list do. Sentence 3, however, is an imperative, and
mos66065_06_c06_137-168.indd 138 3/31/11 1:25 PM
CHAPTER 6Section 6.1 The Logic of Sentences
sentence 12 is a question; we are not able to evalu-
ate those sentences, because they do not put forth
claims that can be evaluated as true or false; that
is, they are not assertoric sentences. In the type of
logic we dis.
The document discusses the "pyramid principle" for effectively structuring written communications. It advocates organizing information in a hierarchical pyramid structure, with the main point or conclusion at the top, supported by increasingly detailed explanations below. This structure mirrors how the human mind naturally processes and recalls information. The pyramid principle helps ensure a logical flow of ideas and provides only the level of detail needed for each part of the communication.
The document discusses the "pyramid principle" for effectively structuring written documents. It argues documents should be organized in a pyramid structure, with the main point or conclusion at the top, supported by increasingly detailed explanations below. This structure mirrors how the human mind naturally imposes order and groups related ideas. The pyramid structure forces the writer to only present information to the reader as needed. Within this structure, each level of the pyramid should contain summaries of the ideas from the level below.
This document summarizes and critiques three articles published in the first issue of Critique, the undergraduate philosophy journal of Durham University.
The editor's preface welcomes readers to the newly launched journal and highlights its goal of publishing outstanding undergraduate work. It references a quote by Stanley Cavell cautioning that philosophers often view each other's work as "fundamentally wrong." The preface expresses hope that the journal can serve as praise and demonstrate the value of philosophical inquiry.
The first article analyzes whether the question "Why is there something rather than nothing?" is a meaningful question and possibly answerable. It argues the question is meaningful as it is not senseless, dispensable, or insoluble. It then
The document discusses the key differences between deductive and inductive arguments. It notes that when evaluating an argument, one should consider whether the premises are true and whether the premises provide good reasons to accept the conclusion. For chapter 3, it will only focus on the latter. It provides examples of deductive and inductive arguments. It also outlines different ways to determine whether an argument is deductive or inductive, such as looking for indicator words, applying tests of strict necessity and charity, and identifying if the argument follows a commonly used pattern of deductive or inductive reasoning.
Through this we will be able to understand the fallacies of vagueness clearly with the help of examples. It shares some useful examples. the definitions and points are very clear here.
The document discusses the components of an argument, including the thesis/conclusion and premises/evidence. It provides examples of how to describe facts versus inferences and how to analyze arguments by identifying assumptions, locating the conclusion, evaluating the strength of evidence/premises, and putting arguments in standard form. Transition words are also discussed.
1.1Arguments, Premises, and ConclusionsHow Logical Are You·.docxbraycarissa250
1.1Arguments, Premises, and Conclusions
How Logical Are You?
· After a momentary absence, you return to your table in the library only to find your smartphone is missing. It was there just minutes earlier. You suspect the student sitting next to you took it. After all, she has a guilty look. Also, there is a bulge in her backpack about the size of your phone, and one of the pouches has a loose strap. Then you hear a “ring” come from the backpack—and it’s the same ringtone that you use on your phone. Which of these pieces of evidence best supports your suspicion?
Answer
The best evidence is undoubtedly the “ring” you hear coming from her backpack, which is the same ringtone as the one on your phone. The weakest evidence is probably the “guilty look.” After all, what, exactly, is a guilty look? The bulge in the backpack and the loose strap are of medium value. The loose strap supports the hypothesis that something was quickly inserted into the backpack. In this section of the chapter you will learn that evidentiary statements form the premises of arguments.
Logic may be defined as the organized body of knowledge, or science, that evaluates arguments. All of us encounter arguments in our day-to-day experience. We read them in books and newspapers, hear them on television, and formulate them when communicating with friends and associates. The aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own. Among the benefits to be expected from the study of logic is an increase in confidence that we are making sense when we criticize the arguments of others and when we advance arguments of our own.
An argument, in its simplest form, is a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). Every argument may be placed in either of two basic groups: those in which the premises really do support the conclusion and those in which they do not, even though they are claimed to. The former are said to be good arguments (at least to that extent), the latter bad arguments. The purpose of logic, as the science that evaluates arguments, is thus to develop methods and techniques that allow us to distinguish good arguments from bad.
As is apparent from the given definition, the term argument has a very specific meaning in logic. It does not mean, for example, a mere verbal fight, as one might have with one’s parent, spouse, or friend. Let us examine the features of this definition in greater detail. First of all, an argument is a group of statements. A statement is a sentence that is either true or false—in other words, typically a declarative sentence or a sentence component that could stand as a declarative sentence. The following sentences are statements:
Chocolate truffles are loaded with calories.
Melatonin helps relieve jet lag.
Political can.
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Associate Professor Michael Emmison: AIEMCA 2012 Keynote 1ajcmanager
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As researchers working in government, influencing service design, we need to know that our research is methodologically sound, our research findings are grounded in empirical data and our recommendations are logically derived.
'Understanding arguments, reasoning and hypotheses' is the first in a series of 5 short courses, covering introduction courses to various aspects of methodology in research, from the use of grounded theory in discovery research, to hypothesis testing and sampling in more experimental research.
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Week 14 April 28 & 30 - Love and Death Castillo, Chap. 9 .docxmelbruce90096
Week 14: April 28 & 30 - Love and Death
Castillo, Chap. 9 “Sofia, Who Would Never Again Let Her Husband Have the Last Word…”
Chap. 10 “Wherein Sofia Discovers La Loca’s Playmate…”
Chap. 11 “The Marriage of Sofia’s Faithful Daughter to her Cousin”
Chap. 12 “Of the Hideous Crime of Francisco el Penitente…”
1. For all chapters, identify the four levels of analysis: 1) metaphoric/symbolic; 2) literary; 3) sociological; and spiritual.
Chapter 9 “Sofia, Who Would Never Again Let Her Husband Have the Last Word…”
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3. In this chapter, we return to La Loca, reading from her point of view. What do we learn from this, the youngest of Sofi’s daughters?
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7. What to make of this last chapter in Caridad and Francisco’s lives? What are the recurring themes and metaphors/symbolizes, etc.?
In preparation for the Opposing Viewpoints short paper due in Module Five, you will outline a position (thesis) on a topic of your choosing.
Using the Prewriting Template provided, outline two to three of your reasons for supporting your thesis and then also outline the objection’s position. Please note that the main purpose of this assignment is to formulate the strongest possible objection to your own position before responding to it.
You will be required to use at least four outside (i.e., other than the textbook) sources for this paper, two for each side of the issue. You do not need to do extensive reearch before completing the outline.
Possible topics: Affirmative Action, Abortion, State-Financed Health Care, Flat Tax...or anything you want. It is best to choose a position for which you can find reasonable arguments on both sides.
Click on the title above to turn in your outline.
First Paper (Opposing Viewpoints):
Critical Elements
Distinguished
Proficient
Emerging
Not Evident
Value
Main Elements
Includes almost all of the main elements and requirements and cites ample appropriate support to illustrate each element
(23-25)
Includes most of the main elements and requirements and cites appropriate support to illustrate each element
(20-22)
Includes some of the main elements and requirements
(18-19)
Does not include any of the main elements and requirements
(0-17)
25
Inquiry and Analysis
Explores multiple reasons and offers in-depth analysis of evidence to make informed conclusions about the issue
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Explores so.
Integers and rationals can be expressed in first-order logic using only the less than relation <. The difference between integers and rationals can also be expressed in first-order logic. Specifically, integers have the property that between any two integers, there is no other integer, while this is not true for rationals - between any two rationals there is always another rational.
The document provides guidance on how to structure an effective essay. It discusses the key components of an introduction, body paragraphs, and conclusion. For the introduction, it recommends including a neutral sentence, context sentence, argument sentence, and summary sentence. For body paragraphs, it advises using the PREC structure - point, reason, example, and concluding sentence. Finally, it suggests that the conclusion should restate the argument, outline how it was demonstrated, include a thoughtful analysis, and end with a strong concluding statement. The document also includes examples and tips for writing introductions, body paragraphs, and conclusions according to this structure.
1Week 3 Section 1.4 Predicates and Quantifiers As.docxjoyjonna282
1
Week 3: Section 1.4 Predicates and Quantifiers
Assume that the universe of discourse is all the people who are participating in
this course. Also, let us assume that we know each person in the course. Consider the
following statement: “She/he is over 6 feet tall”. This statement is not a proposition
since we cannot say that it either true or false until we replace the variable (she/he) by a
person’s name. The statement “She/he is over 6 feet tall” may be denoted by the symbol
P(n) where n stands for the variable and P, the predicate, “is over six feet tall”. The
symbol P (or lower case p) is used because once the variable is replaced (by a person’s
name in this case) the above statement becomes a proposition.
For example, if we know that Jim is over 6 feet tall, the statement “Jim is over six
feet tall” is a (true) proposition. The truth set of a predicate is all values in the domain
that make it a true statement. Another example, consider the statement, “for all real
numbers x, x2 –5x + 6 = (x - 2) (x – 3)”. We could let Q(x) stand for x2 –5x + 6 = (x - 2)
(x – 3). Also, we note that the truth values of Q(x) are indeed all real numbers.
Quantifiers:
There are two quantifiers used in mathematics: “for all” and “there exists”. The
symbol used “for all” is an upside down A, namely, . The symbol used for “there
exists” is a backwards E, namely, . We realize that the standard, every day usage of the
English language does not necessarily coincide with the Mathematical usage of English,
so we have to clarify what we mean by the two quantifiers.
For all For every For each For any
There exists at least one There exists There is Some
The table indicates that the mathematical meaning of the universal quantifier, for
all, coincides with our everyday usage of this term. However, the mathematical meaning
of the existential quantifier does not. When we use the word “some” in everyday
language we ordinarily mean two or more; yet, in mathematics the word “some” means at
least one, which is true when there is exactly one.
The Negation of the “For all “Quantifier:
Consider the statement “All people in this course are over 6 feet tall.” Assume it
is false (I am not over six feet tall). How do we prove it is false? All we have to do is to
point to one person to prove the statement is false. That is, all we need to do is give one
counterexample. We need only show that there exists at least one person in this class
who is not over 6 feet tall. Here is a more formal procedure.
Example 1:
Let P(n)stand for “people in this course are over 6 feet tall”, then the sentence
“All people in this course are over 6 feet tall” can be written as: “ n P(n)”. The negative,
“ ( n P(n))”, is equivalent to: “ n( P(n))”. So, in English the negative is, “There is
(there is at least one/ there exists/ some) a person in this room who is not over 6 feet tall.”
2
Example 2:
How w ...
6
Elementary Symbolic Logic
Heinz-Dieter Falkenstein
Against logic there is no armor
like ignorance.
—Laurence Peter
mos66065_06_c06_137-168.indd 137 3/31/11 1:25 PM
CHAPTER 6Section 6.1 The Logic of Sentences
Now that we have looked at inductive arguments, deductive arguments, and the com-ponents—premises and conclusions—that make them up, we can turn to making our
understanding of deductive reasoning more precise. We do so by introducing a few sym-
bols for sentences and for the kinds of terms—such as and and or—that connect sentences,
and we use these symbols to look at the structure of both sentences and arguments. For
the most part, we look at material we have already examined; here we just use symbols to
make the various structures involved a bit more explicit. Arguments often get sidetracked
because of the information presented, and although that information is important, we can
avoid being sidetracked in this way by focusing on the structure of the arguments. Sym-
bols are helpful in keeping the focus on such structures.
What We Will Be Exploring
• We will look at how symbols can be applied to sentences, and then to arguments.
• We will examine the notion of a truth function and the kinds of specific logical properties sentences
possess.
• We will see how truth tables can be used to evaluate certain kinds of sentences, as well as testing
deductive arguments for validity.
• We will use basic symbolic logic to examine some earlier material and see how it can be made more
precise.
6.1 The Logic of Sentences
We begin by seeing how to apply symbols—sentence letters—to sentences, first using basic sentences and then using sentences constructed out of these basic sentences.
Assertoric Sentences and Sentence Letters
Earlier we looked at various strings of words: some were questions, some were commands,
and some were assertions. Here are some examples of the kinds of sentences we examined
earlier, as well some new, compound sentences, which assert more than one claim:
1. Cheddar cheese is better than American cheese.
2. The window is broken.
3. Turn left at the next light.
4. Art is a great dancer.
5. Art is very popular.
6. Art is very popular and he is a great dancer.
7. Art is very popular because he is a great dancer.
8. John and Mary got married.
9. John and Mary had a baby.
10. John and Mary got married and had a baby.
11. John and Mary had a baby and got married.
12. Can you hear that music?
Can you determine which of these make assertions or state some kind of claim? You’ll
find that most of the sentences on this list do. Sentence 3, however, is an imperative, and
mos66065_06_c06_137-168.indd 138 3/31/11 1:25 PM
CHAPTER 6Section 6.1 The Logic of Sentences
sentence 12 is a question; we are not able to evalu-
ate those sentences, because they do not put forth
claims that can be evaluated as true or false; that
is, they are not assertoric sentences. In the type of
logic we dis.
The document discusses the "pyramid principle" for effectively structuring written communications. It advocates organizing information in a hierarchical pyramid structure, with the main point or conclusion at the top, supported by increasingly detailed explanations below. This structure mirrors how the human mind naturally processes and recalls information. The pyramid principle helps ensure a logical flow of ideas and provides only the level of detail needed for each part of the communication.
The document discusses the "pyramid principle" for effectively structuring written documents. It argues documents should be organized in a pyramid structure, with the main point or conclusion at the top, supported by increasingly detailed explanations below. This structure mirrors how the human mind naturally imposes order and groups related ideas. The pyramid structure forces the writer to only present information to the reader as needed. Within this structure, each level of the pyramid should contain summaries of the ideas from the level below.
This document summarizes and critiques three articles published in the first issue of Critique, the undergraduate philosophy journal of Durham University.
The editor's preface welcomes readers to the newly launched journal and highlights its goal of publishing outstanding undergraduate work. It references a quote by Stanley Cavell cautioning that philosophers often view each other's work as "fundamentally wrong." The preface expresses hope that the journal can serve as praise and demonstrate the value of philosophical inquiry.
The first article analyzes whether the question "Why is there something rather than nothing?" is a meaningful question and possibly answerable. It argues the question is meaningful as it is not senseless, dispensable, or insoluble. It then
The document discusses the key differences between deductive and inductive arguments. It notes that when evaluating an argument, one should consider whether the premises are true and whether the premises provide good reasons to accept the conclusion. For chapter 3, it will only focus on the latter. It provides examples of deductive and inductive arguments. It also outlines different ways to determine whether an argument is deductive or inductive, such as looking for indicator words, applying tests of strict necessity and charity, and identifying if the argument follows a commonly used pattern of deductive or inductive reasoning.
Through this we will be able to understand the fallacies of vagueness clearly with the help of examples. It shares some useful examples. the definitions and points are very clear here.
The document discusses the components of an argument, including the thesis/conclusion and premises/evidence. It provides examples of how to describe facts versus inferences and how to analyze arguments by identifying assumptions, locating the conclusion, evaluating the strength of evidence/premises, and putting arguments in standard form. Transition words are also discussed.
1.1Arguments, Premises, and ConclusionsHow Logical Are You·.docxbraycarissa250
1.1Arguments, Premises, and Conclusions
How Logical Are You?
· After a momentary absence, you return to your table in the library only to find your smartphone is missing. It was there just minutes earlier. You suspect the student sitting next to you took it. After all, she has a guilty look. Also, there is a bulge in her backpack about the size of your phone, and one of the pouches has a loose strap. Then you hear a “ring” come from the backpack—and it’s the same ringtone that you use on your phone. Which of these pieces of evidence best supports your suspicion?
Answer
The best evidence is undoubtedly the “ring” you hear coming from her backpack, which is the same ringtone as the one on your phone. The weakest evidence is probably the “guilty look.” After all, what, exactly, is a guilty look? The bulge in the backpack and the loose strap are of medium value. The loose strap supports the hypothesis that something was quickly inserted into the backpack. In this section of the chapter you will learn that evidentiary statements form the premises of arguments.
Logic may be defined as the organized body of knowledge, or science, that evaluates arguments. All of us encounter arguments in our day-to-day experience. We read them in books and newspapers, hear them on television, and formulate them when communicating with friends and associates. The aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own. Among the benefits to be expected from the study of logic is an increase in confidence that we are making sense when we criticize the arguments of others and when we advance arguments of our own.
An argument, in its simplest form, is a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). Every argument may be placed in either of two basic groups: those in which the premises really do support the conclusion and those in which they do not, even though they are claimed to. The former are said to be good arguments (at least to that extent), the latter bad arguments. The purpose of logic, as the science that evaluates arguments, is thus to develop methods and techniques that allow us to distinguish good arguments from bad.
As is apparent from the given definition, the term argument has a very specific meaning in logic. It does not mean, for example, a mere verbal fight, as one might have with one’s parent, spouse, or friend. Let us examine the features of this definition in greater detail. First of all, an argument is a group of statements. A statement is a sentence that is either true or false—in other words, typically a declarative sentence or a sentence component that could stand as a declarative sentence. The following sentences are statements:
Chocolate truffles are loaded with calories.
Melatonin helps relieve jet lag.
Political can.
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Syllogism by premises from das sir (08961556195)
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SYLLOGISM STUDY NOTES BY DAS SIR,KOLKATA (08961556195)
Broadly, you need to understand two types of arguments. We have already come to see what arguments look like. Now it is time to comprehend some ‘categories’ of arguments.
Analyse this, (P1= Premise 1, P2= Premise 2, C= Conclusion)
P1 – All men are buffoons.
P2 – Ravi (poor chap) is a man.
C – Ravi is a buffoon.
This kind of argumentation is known as deductive reasoning. Here, the conclusion arrived at, is a logical ‘necessity’, which you will find me referring to henceforth as an LN. The structure of the deductive argumentation is simple. We picked a set, gave it a characteristic (P1), picked an element from the set (P2), and with certainty, arrived at the conclusion that the element shall show the same characteristic.
P.S. I hope you understand that my sympathies with Ravi have nothing to do with the argument.
Now, the second type,
P1 – Ravi is an engineer.
P2 – Ravi is a fool.
C – All engineers are fools.
While many of you may express surprise, nay, even disdain for such argumentation, it is still deemed a valid form of argumentation. So much so, that we would not have had the evolutionary history if mankind had refused to allow room for such argumentation. Appalled? Do not be. All knowledge has been attained and transferred through this form of reasoning for thousands of years now in the evolution of ‘life’. This form of argumentation is known as ‘Inductive logic’.Here, the conclusion arrived at is not an LN but a logical ‘possibility’ (LP). The conclusion that we derived here ‘may or may not’ be true. And hence we call it an LP.
I hope you understand the structural difference between the two types of reasoning. Inductive reasoning suggests that if some (read ‘one’) elements of a set show a characteristic, others will too. In fact, you SHALL find yourself arguing many a time with exactly the same structure. Stereotypes, such as ‘women cannot drive’, ‘engineers are an intelligent species’, ‘politicians are corrupt’,‘people with work experience have a better chance of getting into a B-School’etc. are born of the same category of argumentation. While it is easy to refute such an argument as having a conclusion that you do NOT agree with, do understand that it MAY just be true! It is just that we do not possess information about the rest of the elements of the set and hence cannot say for certainty whether the conclusion will be correct or incorrect.
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Also, do not be emotional with the variables- ‘engineers’, ‘fools’, ‘men’ etc. They are just representative and should be deemed as X’s and Y’s.
All said and done, when you are attempting a question, you must always try to look for a‘logical necessity’ as an answer, not a ‘logical possibility’. We mark LP as an answer only if the answer choices do not HAVE a necessity answer choice in the first place.
One more thing before we move on to the next topic. DO NOT include anything external to the premises in the conclusion. For example, if
P1 – All women are intelligent.
P2 – Sita is a woman.
C – Sita is an intelligent woman.
This is specious reasoning. Our P1 does not state ‘intelligent women’, but simply ‘intelligent’.
Takeaways
In questions, we are looking for LN’s, not LP’s. We shall mark LP as an answer choice only in the absence of an LN.
Do not take the variables of the questions to heart, treat them as X’s and Y’s.
Do not add anything external to the premises in the conclusion.
There are four basic premises to understand in syllogisms.
a) All X are/is Y.
b) No X are/is Y.
c) Some X are/is Y.
d) Some X are/is not Y.
Let us deal with each in totality.
a) All X is/are Y.
This statement comes under the ‘universal positive’ category. But that is elementary and not worth keeping in mind. What you really need to understand in this statement is that the usage of ‘is/are’ is not important; whatever verb appears here will be independent of interpretation. The simple translation of this statement is that all the elements of set X will also be elements of set Y.
Another important thing to note is that, even if the statement does not have the prefix‘all’, (e.g. x is y) it will have the same interpretation.
Let us also try and understand this with Venn diagrams.
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The second diagram shows a possibility that exists, in that the two sets X and Y are overlapping.
While solving questions, you should use the first diagram. And, as I have stated earlier, do not get emotionally involved in trying to picturise the verb. The trick is-find out the verb, then recognise the ‘doer’ of the verb (i.e. the ‘subject’ of the sentence) and put the subject in the inner circle, while the object occupies the outer circle.
For example,
All men are blue.
Here, the verb is ‘are’, and the subject ‘all men’. Hence the set of‘men’ will be represented by the inner circle, and the set of ‘blue’ by the outer circle.
Sometimes, if one becomes paranoid about being able to picturise stuff, things can get tricky. For example, if the statement were “monkeys have brains”,one would be tempted to draw the outer circle to represent the monkeys. Do NOT be tricked by the verb. Follow the same rule that I have mentioned earlier. The verb here is “have”, the doer of which is “monkeys”. Hence, make the inner circle to represent monkeys and the outer to represent brains.
On a parting note, do remember
The presence or absence of the prefix “all” does not matter. The statement shall still be treated as mentioned above. Hence “all X is Y”, is the same as “X is Y”.
Put the subject of the sentence in the ‘inner’ circle.
For solving a question, use the first diagram. The second diagram is a possibility to be kept in mind for solving CR/ RC questions.
b) No X is/are Y.
This is a rather simpler statement to understand. It means that no elements of set X are elements of set Y. Simply put, the elements of the two have nothing in common. These can be easily represented as disjoint sets, i.e. two circles, not touching each other anywhere.
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However, there are some other important things to learn here. Please understand that this premise (which, incidentally, comes under the ‘universal negative’ category) has some misrepresentations as well. Many people try to represent the opposite of ‘all X is Y’ as ‘all X is NOT y’. Now, this is fallacious, since such a negation becomes dubious to interpret and hence ambiguous. Premises in logic cannot afford to be ambiguous, since it is they who set the stage for the conclusion to follow. You just have to try different emphasis points in this kind of negation to understand what I mean.
All engineers are not fools. (Implies that no engineer is a fool)
All engineers are not fools. (Implies that only some of them are. J)
Since it is semantics at play here, such a negation is considered illogical.
Similarly, a negation of the nature “Not all X are Y” has comparable problems, and hence is not deemed a valid negation of “All X are Y”.
Final takeaways
·The negative of “All X is Y” is“No X is Y”.
·Can be represented by disjoint sets.
·“All X are not Y” / “Not all X are Y” are invalid premises.
c) Some X are/ is Y.
Unlike the universals we have been looking at so far, where it was either an all or none case, thereby justifying the usage of the word ‘universal’, we now shift our focus to ‘particular’ premises. These premises have prefixes that look like-some, many, a lot of, most et al. Understand that these words have little representative or absolute value, until pitted against their respective ‘whole’numbers. Hence our comprehension of the same will have to be careful.
Let us then agree to interpret these two statements by concurring that
·If some X are Y, then some Y must definitely be X.
·The interpretation of the prefix “some, many etc.” will be “AT LEAST ONE”.
·If some X are Y, it does not imply that some X are then definitely NOT Y.
The first interpretation is fairly simple to understand. If some elements of set X are also elements of set Y, those same elements are both X and Y. Hence some elements of Y automatically become elements of set X.
The second point, when elaborated, means that in logic, the prefix ‘some’ in itself means nothing except “at least one”. Even if the prefix is ‘a lot, many, most, several’ etc. our interpretation of the same shall remain ‘at least one’.
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Now, for the third point, some logic books state that if the premise states ‘some X are y’,then it definitely means that some X are NOT Y. This is bad reasoning. Just as we saw in inductive reasoning erstwhile, if some elements of a set doshow a certain trait, then we cannot for certainty say EITHER that the rest will notshow the same trait OR that they will. Hence, to conclude from ‘Some X are Y’, as a necessity, that ‘Some X are not Y’, is simply not correct. And henceforth you and I shall not indulge in such fallacies.
Time for a Venn interpretation.
The first diagram that I have presented below is what we shall use for solving questions. The rest are just indicative of ‘possibilities’ that may exist, and with which we must familiarise ourselves, for they will help us understand things better when we finally arrive at long CR questions.
In this diagram the shaded portion represents the area in which our ‘at least one X’ and ‘at least one Y’ lie. This is the diagram we shall use for solving questions.
Here, the portion of X that coincides with the portion of Y is our area of concern. Also, please understand that one line of argument may state that here ‘‘aren’t all Y’s, X’s too?’’ To this, a logical response is that our premise concerns itself with some of the X’s being Y’s, not Y’s being X’s. In the process, if all Y’s turn out to be X’s, it is just a possibility, and of course not our primary concern. We had started with trying to prove that at least one X ought to be Y, and the diagram does justice to that. (Remember, we are dealing with all the possibilities here.)
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Here again, one might point out that all of the X’s are Y’s. However, by now, you and I understand that we had set out to prove that at least one X should be Y, and in the process if all X’s DO happen to be Y’s, so be it. Our one X is still safely within Set Y, and our diagram, yet again, does full justice to that.
Well, if you understood the previous diagram, you would find it easy enough to understand that this too is a possibility that exists. And again, our one X is still ensconced firmly within Set Y.
Synopsis
·If some X are Y, then some Y must definitely be X.
·The interpretation of the prefix “some, many etc.” will be “AT LEAST ONE”.
·If some X are Y, it does not imply that some X are then definitely NOT Y.
·For solving a question, we shall use the first diagram.
d) Some X are/is not Y.
This statement has several interpretations across the globe. But we shall treat it as a logically inconsistent premise. Although the statement “Some X are not Y” CAN hold true as a conclusion, it falls flat as a premise. (Hope you remember the distinction between ‘premises’ and ‘conclusion’ well enough by now!!)
For instance, let us try with
P1 – Some boys are not mature.
Immediately with this premise you will have to go with three possible diagrams simultaneously, i.e.
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P2 – Some mature are fools/ All matures are fools/ No mature is a fool.
You understand that any of these three premises will have different impacts on the three possible diagrams that we have made. With such a scenario we shall NOT be able to arrive at a sustainable conclusion at the third stage. In syllogisms, as you must have noticed earlier, we do arrive at a conclusion at the third stage. Hence, this statement, we shall treat as an ‘illogical’ premise.
However, this statement DOES have validity as a conclusion.
For instance,
P1 – Some buckets are trees.
P2 – No tree is a fool
Now, in all of the three possible diagrams you can see that as an LN conclusion, we can safely say that,
Some buckets are not fools. (i.e. the buckets that lie in intersection with trees.)
Takeaways
Some X are/is not Y is a logically inconsistent premise
Some X are/is not Y has an absolutely logical existence as a conclusion.
Finally,
Only X are/is Y.
This is the only remaining premise we need to get hold of, so far as syllogisms are concerned.
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To begin with, if you encounter a statement such as “Only X are Y”, quickly convert it into“All Y are X”. The diagram should be simple now- Y inside, X outside. For solving a question, this much of dope should be enough.
For the sceptics, however, an explanation is just what the doctor ordered!
So here we go! Let us see if the formula works or not.
P1 – Only boys wear trousers.
If this be our premise, isn’t it easy to figure out that the moment I see someone wearing a pair of trousers, without even looking further, I should be safely able to conclude that the person is a ‘boy’? What I mean is that since the premise explicitly states that only boys can wear trousers, then nobody else can wear them. Therefore if someone is wearing trousers, the person OUGHT to be a boy, else our premise falls. Hence, is it not easy to figure out that ‘All trousers can be worn by boys only’? Well, you’ve got it now!
If, “only boys wear trousers”, then “all trousers are worn by boys”! Simple!
Takeaway
Convert “only X are Y” to “All Y are X”, and then work with what you have learnt from the “all” prefix statements, i.e. make Y the inner circle and X the outer circle.
One final word - While solving questions in syllogisms, do remember that the conclusion should be derived usingboth of the previous two premises, and not one premise alone. For example,
1. All babies are black.
2. My baby is cute.
Conclusion-My baby is black.
This is incorrect since the conclusion can be derived using the first premise itself.