index of quotations on key words from corcoran, j. 1989. argumentations and logic

8/14/2019 Index of quotations on Key Words from Corcoran, J. 1989. Argumentations and Logic.

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UPDATED: 9 10 05.

Index of quotations on Key Words from

or!oran" #. 19$9. Ar%umentations and &o%i!. Argumentation'" 1()*'.

+u,,-emented it/ additiona- -o%i!a- termino-o%y.

Initially compiled by Andrew Spear

This index was originally constructed by taking the key words listed on page 17 of

Argumentations and Logic and registering significant !uotes pertaining to each key"word from the body of the text under a bold"face key"word heading# $ther entries ha%e

been added o%er the years# &age citations are included immediately after each !uotation#

Sometimes many !uotations are taken from a single page# In such cases the page is cited

at the end of all !uotations from that page' not after each indi%idual !uotation# (ross"references to the literature ha%e also been added# The original article was intended as an

essay and not as a learned treatise' accordingly it has no footnotes' no page"references

and no bibliography#

(omments and suggestions for other !uotation and key"word inclusions are welcome#adspear)acsu#buffalo#edu

www#buffalo#edu*+adspear,$TATI$,- The usual con%ention is to use single !uotes for making names of sentences

and other expressions' for example names of words' phrases' symbols' etc# Thus .$ne

plus two is three/ is a fi%e"word 0nglish sentence and .s!uare/ is a six"letter 0nglishword' both of which were used by oole' but neither of which would ha%e been

recogni2ed by Aristotle# 3ollowing ertrand 4ussell 51903' 6ff# and 1905/1967' 889 and

others' double !uotes are used in naming propositions and other meanings# Thus' $ne

plus two is three is a true proposition known both to oole and to Aristotle and s!uareis a concept also well known to both# In familiar cases' expressions express meanings or

senses and they name entities or things# Thus' the sentence .$ne plus two is three/expresses the proposition $ne plus two is three and the number"word .three/ names thenumber three#

Pro,osition: Some propositions are known to be true and some are known to be false#ut the propositions that are important to us often include hypotheses' propositions which

are neither known to be true nor are known to be false# 17u1# The properties true and

false ha%e as their range of applicability the class of propositions# :u17# Any attempt

to affirm or deny true or false of a non"proposition results in gibberish' incoherence'category error' nonsense# :u1;#

+enten!e: Some sentences express propositions and some do not# :u


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s!uare is a line e!ual to the diagonal of the gi%en s!uare/# &ropositions are what we

belie%e' what we know' what we doubt' what we assume for purposes of reasoning' and

so on# They are the ob>ects of our propositional dispositions and acts# Sentences arewhat we use to con%ey our beliefs' doubts' etc# to others and the sentences are what we

make inscriptions of in order that we can con%ey our beliefs' etc# to people who are not

present at the time we ha%e the desire to do the con%eying# See (ohen",agel 188# xxii"xxiii#

2y,ot/eses: #propositions which are neither known to be true nor known to be false#0%ery hypothesis is either actually true or actually false# ut no hypothesis is either

known to be true or known to be false ? by the person for whom it is a hypothesis#

5179

Ar%umentation 34,ro!ess6: Argumentation is in%ol%ed in settling hypotheses on the

basis of what we already know# @educti%e method and ypothetico"deducti%e method#

51:9

, Argumentation is to the argumentations as deduction is to the deductions#Argumentation is to the indi%idual argumentations as inference is to the indi%idual

inferences and as calculation is to the indi%idual calculations# In one sense the word.argumentation/ is an abstract proper name of a general process and in this sense it is not

a common noun' it takes no article' and it has no plural# In another sense the word

.argumentation/ is a common noun and it is strictly speaking not a name# In the secondsense it takes article 5.an/' .the/9 and it has a plural#

Ar%ument: The expression argument 5more clearly premise"conclusion argument9

indicates the two part system that bounds an argumentation# An argument can beconstructed from an argumentation by deleting the chain of reasoning# Bore explicitly'

an argument is a two pat system composed of a set of propositions called its premise"set

and a single proposition called its conclusion# 0%ery argument bounds infinitely manyargumentations' but no argument is an argumentation# 5


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forth particular information from other information in which it is already contained#

@eduction takes place in time# @eduction is the process of coming to know implication#

A deduction is sufficient for knowledge of %alidity# 5ect is aproposition and its indirect ob>ect is a set of propositions# 589

The common noun .deduction/ is often used %ery nearly in the sense of .cogent

argumentation/# ere we take it to be an exact synonym# 5


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Proof: 0%ery proof is an argumentation that pro%es its conclusion to be true# 0%ery

proposition pro%ed to be true is known to be true by those persons who ha%e pro%ed it tobe true# JThe expressionsK .proof and .pro%ed to be true/ make tacit reference to a

participant or to a community of participants# 5#


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The class of arguments is the range of applicability of %alid and in%alid# 5:9

Im,-i!ation: In order for a conclusion to be a logical conse!uence of a premise set it isnecessary and sufficient for the information of the premise set to include that of the

conclusion' in other words' for there to be no information in the conclusion beyond that

already in the premise set# In order for a conclusion to be a logical conse!uence of apremise set it is necessary and sufficient that it be logically impossible for the premises to

all be true with the conclusion false# In order for a conclusion to be a logical

conse!uence of a premise set it is necessary and sufficient that were the premises all truethen necessarily the conclusion would be true' in other words' that were the conclusion

false then necessarily at least one premise would be false# Those who ha%e grasped

the concept do not need any characteri2ation# The problem of characteri2ing .logical

conse!uence' despite insightful attempts by (arnap' Tarski' and uine' is still open#,o true proposition implies e%en one false proposition# 0%ery true proposition is

implied by infinitely many false propositions# 0%ery false proposition is implied by

infinitely many false propositions# 0%ery false proposition implies infinitely many true

propositions# 0%ery proposition implying its own negation is false# 0%ery propositionimplied by its own negation is true# 0%ery proposition implying a certain proposition and

also implying the negation of that certain proposition is false# 0%ery proposition impliedby a certain proposition and also by the negation of that certain proposition is true# 0%ery

proposition implies itself# It is of course not the case that e%ery true proposition

implies e%ery other true proposition# ,or is it the case that e%ery false propositionimplies e%ery true proposition# ,or is it he case that e%ery false proposition implies

e%ery other false proposition# 5=9

The relation"%erb .implies/ is tense"less# Its sub>ect is a set of propositions and its

ob>ect is a proposition# 589

o%ent: A chain of reasoning is said to be cogent per se if the conclusion that it reachesis actually shown to follow from the premises that it uses# 5


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A chain of reasoning is said to be cogent in context of an argumentation if it is cogent per

se and its conclusion and premises are respecti%ely the conclusion and among the

premises of the argumentation#

(ogency"in"context is not a property of chains of reasoning' but it is a relation of a

chain"of"reasoning to' in effect' an argument# Thus it is incoherent to say that a gi%en($4 is cogent in context when no argumental context has been indicated# (ogency"in"

context is an epistemic' sub>ecti%e' or participant"relati%e relation' basically' of ($4s

to premise"conclusion arguments# If Jan argumentation/sK chain of reasoning is fallacious in context then either it is

fallacious per se 5and hence in%ol%es a gap or logical error in the narrow sense9 or else it

smuggles a premise or it reaches a wrong conclusion# An argumentation whose chain

of reasoning is cogent in context is itself said to be cogent and an argumentation whosechain of reasoning is not cogent in context is said to be fallacious# (ogent in context'

cogent per se'# apply to discourses' or chains of reasoning' whereas cogent and

fallacious' simpliciter' apply to argumentations# 5ectual knowledge or knowledge ofob>ects 5entities' concepts' propositions' argumentations9' operational knowledge or

known"how to perform %arious tasks' and propositional knowledge or knowledge that

propositions are true or false# It is already clear that cogency of a deri%ation re!uires all

three and that it pi%ots on operational knowledge# (ogent per se' cogent incontext' fallacious per se and fallacious in context all apply exclusi%ely to chains of

reasoning# (ogent and fallacious simpliciter apply exclusi%ely to argumentations#

An argumentation is cogent or fallacious according as its chain of reasoning is cogent incontext or fallacious in context# 5:9

There is no way to de%elop a coherent philosophy of logic without careful attention to

coherent discourse# 589

As mentioned abo%e' the expression .cogent in context/ is used in connection with an

argumentation for a relation between its chain"of"reasoning and its bounding argument#

Imagine two cogent argumentations' one arithmetic and the other geometric# In each case

the ($4 is cogent in contextNbut the contexts are different# ,ow imagine two newargumentations obtained by interchanging the two ($4s# ,ow' the two ($4s are not

cogent in context ? because the context changed# The two new argumentations are both

fallacious- at the %ery least they in%ol%e wrong"conclusion or ignoratio elenchi#

E--i,sis" E--i,ti!a-:


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Deri;ation: Let us use the word derivationto indicate a chain of reasoning that is

cogent per se' i# e# that shows' makes clear' makes e%ident the fact that its final

conclusion is a logical conse!uence of the propositions it uses as premises# 5;9# Thusin this sense a deri%ation is not a syntactic entity composed of characters arranged a

certain way#

7a--a!ious: In some cases' the chain of reasoning is fallacious per se' for example' by

%irtue of logical errors# In some cases' the chain of reasoning is fallacious in context5sc# $f the argumentation at issue9' for example by %irtue of using premises not among

the premise of the argumentation or by %irtue of reaching a conclusion other than the

conclusion of the argumentation# fallacy of premise smuggling fallacy of wrong

conclusion 5


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&ro%ability is a criterion of truth and dispro%ability is a criterion of falsity#

@educibility is a criterion of %alidity and refutability is a criterion of in%alidity# 59

3or further discussion see "o#en and $agel 193%/1962/1993& 'vii# 0%ery premiseof a proof has been %erified by e%ery person for whom the proof is conclusi%e#

Oerification is broader than demonstration# In normal 0nglish' .pro%e/ has a broad and a

narrow sense' like .animal/# In the broad sense' e%ery human is an animal# In the narrowsense' no human is an animal# In the broad sense of .pro%e/' e%ery proposition that has

been %erified has been pro%ed# In the narrow sense' a person/s ultimate premises were

necessarily %erified' but except in rare cases they were not pro%ed# ,othing pre%ents aperson from non"demonstrati%e %erification of a proposition already demonstrated# And'

of course' nothing pre%ents a person from demonstrating a proposition already non"

demonstrati%ely %erified

T0,TATIO0 ILI$C4A&P

Alexander of Aphrodisias c#


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index of quotations on key words from corcoran, j. 1989. argumentations and logic

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