(LAW) BLS LLB Sem-1 : Logic Brief Notes

8/10/2019 (LAW) BLS LLB Sem-1 : Logic Brief Notes

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Brief Answers

1) Define Logic. What are traditional and modern definition of logic, and why they whererejected?

All our lives we are giving and accepting reasons. Reasons are the coin we pay for the

belief we hold.-Edith Watson Schipper.

Simply stating logic is an art and science of correct thinking or presenting it in most

simple word,ogic is the study of the !ethods and principles used to distinguish correct

reasoning fro! incorrect reasoning.It took irth y sole and hard work of Aristotle! that ecame the "ery mo#ld of

medie"al tho#ght! it ne"ertheless trained the intellect of adolescent $#rope to reasoning

and s#tlety and constr#cted the terminology of modern science.It is deri"ed from %reek word & logy or logos which means !ethod of every

science of every discipline and every art, as reasonor e'pression of reason in words, that

is, discourse. Looking to its wide ranging alpha and omega and placing specific r#les like

physics or mathematics. (raditional logicians claimed logic as"he science that investigate the general principles of valid thought.

(hey felt logic as systematic en*#iry into principles that helps to disciplines

tho#ght to disting#ish etween correct and incorrect thinking.+#t it over clai!ed and failedas tho#ght is not mere correct or incorrect rather it

includes i!agination drea!ing and day drea!ing, what is not a task of logician, rather it

is task of psychologist. ence it was too widedefinition.(o o"ercome this prolem #ohen and $agelperformed ard#o#s task and de"elop

definition as

"he science of i!plication or of valid inferences %based on such i!plication&+#t here definition went too narrow as implication is only limited #nto ded#cti"e

arg#ment, while logic also incl#des ind#cti"e arg#ments.-nd finally it takes mo#ld, it was een oser"ed that no logician is bound to say

!y content is only true' and else false. ather logician j#st gets an opport#nity to practice

the analysis of arg#ments and constr#ct arg#ments. /n this asis logic was defined as

"he study of the for! of valid argu!ent

(his definition incl#des partic#larly tho#ght related to arg#ment, ded#cti"e aswell as ind#cti"e, ser"ing the p#rpose of logician.

0) Disting#ish etween Ded#cti"e and ind#cti"e.-ns. Ded#ction is &nothing do#tf#l 23rege)

Ind#ction is &to en*#ire what is nat#re of e"idence which ass#res #s of any real e'istence

and matter of fact, eyond the present testimony of o#r senses, or the records of o#rmemory. 2D. #me)

2(raditional logicians also regarded ded#ction and ind#ction as two processes of

reasoning that was, in"erse. -rg#ment is classified into 1) Ded#cti"e and other 0)

ind#cti"e, they can e disting#ish as1) Definitions

Ded#cti"e When the premises of an arg#ment claim to pro"ide s#fficient e"idence for

the concl#sion, the arg#ment is said to e ded#cti"e arg#ment.


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Ind#cti"e It is an inference which claims to pro"ide some e"idence for the concl#sion.

0) $"idence

Ded#cti"e pro"ide s#fficient e"idence for concl#sion.Ind#cti"e does not pro"ide s#fficient e"idence and goes eyond premises.

4) 5roperty

Ded#cti"e is j#dged as "alid or in"alidInd#cti"e is said to e tr#e or false

26any logicians feel ded#cti"e if formally "alid and ind#cti"e is materially "alid)

7) (r#thIn ded#cti"e arg#ment premises implies concl#sion. So, if premises are tr#e concl#sion

m#st e tr#e.

In ind#cti"e arg#ment concl#sion depends #pon the so#ndness and proaility of

e"idence.8) 9ertainty

Ded#cti"e arg#ments are certain. 2its concl#sion is eyond do#t)

Ind#cti"e arg#ments are proale, and therefore +ennett and +aylis call them

&e!pirically probable argu!ent. -nd they can e rejected on disco"ery of contradictoryinstances.

:) Deri"ationDed#cti"e is deri"ed from general to partic#lar 2tho#gh modern logician disagrees with

it).

Ind#cti"e is deri"ed from partic#lar to general. (herefore it is e"en called leap in dark.;) $'ample

Write yo#r own e'ample.

elation of ded#cti"e and ind#cti"e and Law


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similarity, so it will e contin#ed f#rther. ence it is clearly seen trial courts areadapted by inductive procedure.

+#t in -ppellate co#rt, premises is lower co#rts j#dgement and doc#mentation,and concl#sion is merely on that ase, there is no comparision and f#rther resemlance

accepted, it is direct from premise concl#sion is deri"e. So appellate courts are adapted

to deductive arguments.

4) (r#th and "alidity.

-ns. >alidity of arg#ment is sometime conf#sed with tr#th of concl#sion@A.(. +asantani.

(he disc#ssion concerning the nat#re of arg#ment makes one arri"e at the

*#estion of tr#th and "alidity. Defining the tr#th and falsehood in logic 9opi says, it

&characteriBes propositions or statements and may also e said to characteriBe thedeclarati"e sentences in which they are form#lated. Looking to it one may feel that tr#th

and "alidity are generally dependent on each other. +#t, they can e disting#ished as

1) (r#th or falsity depends on fact. 2if it is fact, then it is tr#e and fact is asent then it is

false)alidity depends on form. 2if the relation etween premises and concl#sion are implying

each other, then it is "alid, or else in"alid)0) (o "erify statement to e tr#e or false, one has to analyBe its content or s#ject matter.

(o "erify "alid or in"alid one has to check formal relation.

4) (r#th is property of ind#ctionalidity is property of ded#ction

7) +rief with yo#r own e'ample.

7) Disting#ish etween inference and implication.-ns. 9ohen and


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false when the premises are tr#e. (his means when the premises are tr#e,

the concl#sion m#st also e tr#e.)

$'amples

8) Differentiate etween form and s#ject matter or content?

-ns. Logic deals with forms of "alid arg#ment, so form has primary importance in logicthen s#ject matter, it can e disting#ished as follows

Definition

3orm means str#ct#re of arg#ment. In other words way in which the concl#sion is

deri"ed from premises.

S#ject matter are sentences and its words that make arg#ment, it is facts of

arg#ments

6eaning

3orm gi"es general idea of how concl#sion can e deri"ed from the premises

S#ject matter helps #s to #nderstand what each arg#ment wants to say.

3orm itself makes sense or it can e said sense of arg#ment is gi"en y form

S#ject matter gets it sense y getting a partic#lar form, it does not make sense

alone

$ffects on change of arg#ments

(he form remains same tho#gh arg#ment changes 2there are few form only in

which arg#ment can e made

S#ject matter changes from arg#ment to arg#ment.

(esting

3orm can e said as "alid or in"alid

S#ject matter can e said tr#e or false

$'istence

3orm does not ha"e physical e'istence, it is recogniBe y way premises areconnected with each other and to concl#sion

It has physical e'istence and recogniBed y words #sed in it

$'amples

-ll men are mortal Socrates is man

(herefore Socrates is mortal

In it form is -C +, +C 9 ! so -C9 or say ded#cti"e

In it words like Socrates , is , mortal etc are s#ject matter

:) 5roposition and sentences

5roposition and sentence is closely related as a 5roposition is e'pressed in theform of a sentence. +#t it is not same as a sentence. (he same 5roposition may e

e'pressed y different sentences.

$g I am an Indian.

-o"e three sentences are from three different lang#ages, yet they con"ey thesame 5roposition. (his is eca#se 5roposition is what a sentence states, and not the words

in which the statement is made.


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We know a 5roposition is either tr#e or false. +#t tr#th and falsity arises only with

regard to what declarati"e or indicati"e sentences say. (herefore, all sentences do not

e'press propositions.$g 1). (hief E

0). What (hief wo#ld tr#st a thief ?

(r#th or falsity of ao"e sentences not possile to determine so these sentences donot e'press propositions. So, we can say that, e"ery sentence does not e'press a

5roposition. +#t e"ery 5roposition is in the form of a sentence.

:. Distinction etween %rammatical sentence and 5roposition.

-ns. In common mans lang#age proposition is e*#al to sentence. +#t technically

speaking proposition is &sentence that is either tr#e or false. So, it is clear that all

propositions can e said sentence, #t all sentences are not proposition.%rammatical sentences can e disting#ished y proposition in following way

%rammatical sentences are of fo#r types a) Imperati"e, ) Interrogati"e, c)

e'clamatory and d) asserti"e or indicati"e, while proposition is only asserti"e or

indicati"e type sentence. -s lang#age changes sentence is grammatically said to e different, while on

change of lang#age makes no difference in proposition

%rammatical sense of s#ject predicate #nderstanding is different from logical

one! also in grammatical sentence s#jectpredicate can change its position, #t in

proposition first s#ject and then predicate

%rammatical sentence has two di"isions only "iB., s#ject and predicate, while

proposition has one more part "iB. cop#la 2and has "ery important f#nction)

%rammatical sentence can ha"e m#ltiple s#ject as &time and tide waits for no

ody #t proposition has only one s#ject, and if there are two s#jects of

propositions there m#st e two and not one proposition

%rammatical sentence can e in past, present or f#t#re tense, #t logical

proposition m#st e in present tense only

%rammatical sentence can e with or witho#t any *#antity or *#ality, #t

proposition m#st ha"e one *#antity and one *#ality

%rammatical sentence can e tr#e today and false tomorrow, #t propositions

tr#th and falsity m#st e #ni"ersal i.e. if it is tr#e then it m#st e tr#e in all time andall places

Lastly grammatical sentence can e e'pressed incompletely, while proposition has

to e complete and definite to maintain its condition of tr#e or false of#ni"ersality. 3or e'ample

Sentence &India has congress go"ernment. 2it can e tr#e now, #t in past it was false, soit is not proposition in real sense) to e proposition it m#st eIndia has congress go"ernment on 14thof -#g#st 0FF:.

- sentence has a physical e'istence, when spoken it is so#nd wa"es. When written

other hand, a 5roposition is what a sentence says. (he 5roposition has no physical

e'istence.

(he logical form of a 5roposition depends #pon the statement that a 5roposition

e'presses. /n the other hand, grammatical form of a sentence is determined y


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"ario#s considerations. Some of them ha"e nothing to do with gi"ing information.

$g $'pression, GHnited we stand, di"ided we fallG, emphasiBes the fact that #nity

is strength and dis#nity is weakness.

;) 9onstit#ent and component

-ns. (ho#gh 5roposition is the asic #nit of logic, it can e analysed into its elements.

owe"er, the elements into which a 5roposition is analysed ha"e no e'istence apart fromthe 5roposition. (hese are called constit#ents. So, constit#ents can e defined as Gthe

$lements into which a 5roposition can e analysed are called its constit#entsG.

$.g. Seeta is ea#tif#l girl

In ao"e 5roposition, Seeta is ea#tif#l are constit#ents of gi"en proposition.

- constit#ent is any element of a 5roposition! it can e s#ject, oject or cop#la.

In e"ery 5roposition there is one element which comines the other elements.

(his comining element is called as 9omponent.

$g In 5roposition, -6 L/$D SI(-, L/$D is comining element, i.e.,

9omponent. So, witho#t comining element, there wo#ld e no 5roposition.

Difference etween component and constit#ents

1. - component is #ni"ersal, while the constit#ents it comines can e partic#lars.

(his is the reason, constit#ents and component comines may e changed, yet the

5roposition wo#ld e meaningf#l.

$g We will change indi"id#als comined y the component lo"ed and still 5roposition

will e meaningf#l.

6other lo"ed 9hildren

1. 6ajn# lo"ed Laila.In these, the component 2comining element) lo"ed cannot e replaced y an indi"id#al.

(h#s, we may say that a partic#lar can occ#r as a constit#ent, #t it cannot e a

component.

0. $"ery 5roposition is ao#t certain content 2s#ject matter). -nd constit#ents indicatethe content of a 5roposition. Since the contents of propositions differ, their constit#ents

too differ. owe"er, e"en tho#gh propositions differ in their constit#ents, they may ha"e

the same form.

$.g. 1. am is honest

0. ah#l is tall

4. aman is cle"er

-ll these ao"e propositions assert that an indi"id#al possess a *#ality. (h#s, theao"e propositions ha"e different constit#ents, the relation etween the constit#ents is the

same.

4. (he form of a 5roposition depends #pon the way the constit#ents are comined. (hat

is to say, form of a 5roposition depends #pon the component. owe"er, a component is


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not to e identified with the words thro#gh which it is e'pressed. (he following

propositions ha"e different component, tho#gh in all of them the component is e'pressed

y the same word GisG.

1. =ohn is intelligent

0. Son#


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1) ypothetical 5roposition*t is one which presents a condition together with so!e

conse+uences which follows fro! it. In other words it is if-then sentence. 3or

e.g. If ram scores K8 in logic, then he will e awarded scholarship

It does not refer to any act#al instance! it only states on f#lfillment of condition,

res#lt will follow.

In hypothetical proposition there are two propositions,antecedent i.e. which states

the condition and conse+uent which e'presses conse*#ence. So, hypothetical

proposition is like*f antecedent then conse+uent

0) Disj#ncti"e proposition *t is one which states alternatives. In other words it is

&either , or sentence. 3or e.g. $ither ram will go to D#ai or ongkong. $ach

part of condition e'pressed here that is part efore or and after or is called

disj#nct.

In this e'ample proposition is m#t#ally e'cl#si"e, #t there are some proposition

like &eyan will pass in logic or $nglish. Infact he can pass in oth the s#jects.

So, Aeynes calls it none'cl#si"e proposition, whereas, atleast one disj#nct has to

e tr#e 2and it means if oth are tr#e then also there is no prolem

4) 9ategorical proposition *t either affir!s or denies a predicate of the sub(ect

absolutely. (here is no condition and it is single, simple and n#clear sentence. If

any sentence occ#rs with and then according to traditional logician, they are two

proposition and m#st e segregated to gi"e logical form.

(here is a pec#liarity in this proposition as it states ao#t assertion of predicate relation

with s#ject, it m#st state *#antity and *#ality of the proposition as well. So, logician

states that e"ery proposition has one *#antity and one *#ality. Whereas

a) #antity It means reference of n#mer of s#ject! rather it is to indi"id#al, complete

classMgro#p or part of the gro#p. ence there are three types of *#antity

Hni"ersal It refers to whole class. 3or e.g. N -ll 6aharashtrian are Indian

5artic#lar It refers not only some, #t e"erything that comes #nder 1 to

KK.KK. 3or e.g. N Some st#dent are smarts.

Sing#lar It asserts ao#t one single indi"id#al y #sing proper name or

designation or pointing him o#t. 3or e.g. Logic 5rofessor of D.O. 5atil


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Law 9ollege is orator. +#t logicians classify it #nder #ni"ersal proposition

and states only two type

) #ality It indicates that whether predicate is affirmed or denied y s#ject. In other

words s#ject has any relation with predicate or not is indicated y *#ality. (here are two

type of *#ality

-ffirmati"e It means s#ject has relation with predicate. 3or e.g. &Some

roses are red. It indicates some roses e'ists that has *#ality of redness.


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K) %i"e in details opposition of proposition and disting#ish etween mediate and

immediate inferences? /r gi"e acco#nt of 9ontradiction, contrary, s#contrary and s#

altern.

-ns. Immediate and 6ediate Inferences

(raditionally, ded#cti"e inferences ha"e een classified into immediate and mediate

In an immediate inference we proceed from one gi"en proposition 2the premise) to

another proposition 2the concl#sion) witho#t re*#iring anything f#rther for drawing the

concl#sion. In other words one can say that in immediate inference one proposition is

s#fficient from drawing the concl#sion.

In mediate inference concl#sion is drawn from two or more proposition taken together.

6ediate inferences are generally di"ided into

Syllogism

ed#ction

Immediate inferences are generally di"ided into

/pposition of proposition

$d#cations

/pposition of proposition (he term /pposition is #sed for the relation etween two

propositions ha"ing the same s#ject and the same predicate, #t differing either in

*#antity or in *#ality or in oth.

(he traditional logicians applied the doctrine of opposition of propositions to the fo#r

kinds of categorical proposition.

(aking &- &$ &I &/ propositions in comination, fo#r kinds of oppositions are possile.

(hese are

1) Contradictory Opposition 9ontradictory opposition is the relation

etween two propositions which differ oth in *#antity and *#ality 2keeping

s#ject and predicate same). It is the relation etween &- and &/ proposition.e.g. L.3.-. N -ll men are mortal is contradictory to

L. 3. /. N Some men are not mortal

Same relation is showed y propositions &$ and &I as

e.g. L.3.$ N


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0) Contrary OppositionN 9ontrary opposition is the relation etween

two #ni"ersal propositions differing in *#ality 2keeping s#ject and predicate

same). It is the relation etween &- and &$ propositions.

e.g. L.3.- N -ll flowers are white is contrary to

L.3. $. N


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(he relations of oppositions are the asis of some elementary inferences i.e. gi"en

tr#th or falsity of any propositions, we can see which of the opposed propositions

will e tr#e which is false and which is do#tf#l.

1) (wo contradictory propositions can neither e tr#e together nor false together.

If one is tr#e, the other will e false and if one is false other has to e tr#e.

0) (wo contraries can ne"er e tr#e together, #t they may oth e false.

4) S# 9ontraries can not e false together, #t they may oth e tr#e.

7) It is the relation etween #ni"ersal and partic#lar proposition so if #ni"ersal is

tr#e partic#lar will e tr#e #t when partic#lar is tr#e #ni"ersal can tr#e.

Similarly, when #ni"ersal is false, partic#lar can e false, and partic#lar is

false, #ni"ersal has to e false

Opposition of *ingular %roposition

Aeynes points o#t that in case of sing#lar proposition, we can not g eyond single

denial, so opposition etween sing#lar propositions is to e called contradictory

opposition.

1F) %i"e acco#nt of fail#re of traditional logic? What are the reasons for fail#re of

traditional classification of proposition? 9ompare etween traditional and modern

classification?

-ns. &time and tide waits for no men, e"ery moment there is progress, in this tide logic

is no e'ception. 3rom -ristotelian logic to modern logic i.e. symolic or mathematical

logic it is re"ol#tion. Oet, it cannot e said that two are #nconnected and m#t#ally

e'cl#si"e. (he symolic logic makes #se of hea"y technical symols and minim#m #se

of lang#age is de"elopment of traditional logic. asson and /#onnor' >that modern

symolic logic is a de"elopment of concepts and techni*#es which were implicit in the

work of -ristotle@. Let #s mark distinct point of modern logic as stated y #.*. ewis,

there are three points

a) (he #se of ideogram 2i.e. signs like ' or?) or signs which directly stands for concepts,

instead of phonogram 2or written words &m#ltiplication or &*#estion marks) which

directly stands for so#nd and indirectly for concepts.

) (he ded#cti"e method. +y positing the tr#th of certain elementary statements we can

deri"e indefinite r#les,


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c) (he #se of "ariale ha"ing a definite range of significance.

Distinction can e ro#ght o#t as follows

1) Definition

-ristotle finds logic as tool to pro"e his theories, so finds it as &science which in"estigates

general principles of tho#ght! while modern logician cite word tho#ght as too "ag#e, and

simplifies it as &logic is form of "alid arg#ment.

0) 3orm

If we take close per#sal of oth logic, then it will e fo#nd that oth depends on form and

oth elie"es in tr#th or falsity y "irt#e of its form! #t traditional elie"es in tr#th n

falsity of proposition n stress on form as partic#lar way of writing the proposition called

as -,$,I,/! while modern logicians ad"ances as logic has concern with "alidity, so if we

ded#ce it into symols as mathematics does then also analysis will e possile and easy

to generaliBe. So they ga"e technical symols.

4) 9lassification of propositions

(raditional logician simple classify proposition into simple and compo#nd, while

modern logician e'tends as simple, compo#nd and general.

(raditional finds simple as categorical i.e. sub(ect-predicate type, while modern

finds these are only *#antity representing proposition, and classify them #nder

general i.e. *#antification. -t same time modern logicians elie"e simpleproposition as n#clear statements, and term them assub(ectless' sub(ect-predicate

%individual&' class-!e!bership and Relational. 9ompo#nd for tradition are

conditional and that to hypothetical and dis(unctiveonly, while modern enhances

as negation' con(unction' dis(unctive' i!plication %what is hypothetical for

traditional&' and i-conditional.

7) 5arts of proposition

(raditional logicians oser"e three parts of propositions, "iB., s#ject, predicate and

cop#la! and modern logician says it to e constit#ent and component. Whereas

constit#ent is same as s#jectpredicate 2tho#gh it indicate something more then

s#ject and predicate), and component is cop#la.

8) (ense


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(raditional logician elie"es in present tense and specially recommends that cop#la m#st

e present tense "er &to e so &is or are is mandatory to add. While modern accept all

tense.

:) Symols

In traditional logic there are only 7 symols "iB. -,$, I, /! while modern logic gi"e

technically gi"e symols to each type of sentence as for conj#nction &. 2dot), or

disj#ncti"e &" 2wedge) etc, eside it for sing#lar sentence like &am is wise it issymoliBed as &Wr, and for *#antity special signs are #sed as for #ni"ersal &' and

e'istential &'.

;) 5redication(raditional logician finds f#nction of cop#la as e'pressing relation of s#ject with

predicate is of class incl#sion or e'cl#sion, while in modern logic cop#la i.e. component

&is comine constit#ent in three waysa) 3or class incl#sion or e'cl#sion

) (o indicate memershipc) (o indicate predication as attri#te to indi"id#al or class.

J) #antification(raditional logicians say &all as #ni"ersal and symoliBe as &- or so, #t in modern it is

directly gi"en symol as of #ni"ersal and e'istential and of implication and conj#nction

respecti"ely.K) Way of 5roof

In traditional form it was j#dged on ase of ded#cti"e or ind#cti"e type, while in modern

logic special ded#cti"e r#les and tr#th tales are de"ice that help #s to deri"e "aliditye"en for long stanBas and proof.

ailure of Traditional classification

2as it is mentioned in earlier there is hardly any difference) #t yet traditional logic hasmany drawack as1. Short come in analyses

(raditional logician analyses only asserti"e proposition as proposition and also

strictly ask to consider proposition as &P*#antity signQ S#ject Pcop#laQ 5redicate nforces e"en compo#nd proposition to red#ce to s#ch form. +#t in reality there are

many sentences and e'pression in different ways and when red#ce loses its

weightage.0. 5roposition classification

(hey disting#ish compo#nd as only hypothetical or disj#ncti"e proposition and miss

o#t conj#nction or iconditional and so.

4. Symolic shortcomewhile stating symol for any statement with &all is symoliBe as &- or so. -nd it fails

to show sign of *#antity and relation etween s#ject and predicate

7. 5artial precision(raditional people fails to recogniBe importance of partial in its f#llest sense they

consider it j#st as partial class incl#sion or e'cl#sion, #t in fact in modern sense it

gets it "al#e y stating & e'istential denotes atleast once


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8. S#ject

In traditional s#jectless has no e'istence, e"en proposition like &no one is immortal

has any stand in tradition(his is the reason where traditional logic fails.

11) %i"e modern classification of proposition? %i"e rief on SimpleMcompo#ndproposition?

-ns. We ha"e seen traditional classification as simple and compo#nd proposition. We

see it is modern Logic.

Simple proposition we may define

Simple proposition are one which does not contain any other proposition as its

component.

e.g. 1) (aj 6ahal is ea#tif#l

0) ekha was actress.

-o"e statements are simple propositions. - simple proposition cannot e

analysed into it other proposition i.e. constit#ents of simple proposition are not

proposition.

(he simple proposition makes an assertion ao#t an indi"id#al 2or indi"id#als)

(here are fo#r kinds of simple propositions are as

-) S#jectless propositions

+) S#ject N predicate propositions

9) elational propositions.

D) 9lass N memership propositions.

1) S#jectless 5ropositions N (his is the first and simplest kind of simple proposition in

which statement is not f#lly e'pressed y thinker. %enerally s#jectless propositions are

either e'clamatory or impersonal propositions.

It rains

In ao"e e'amples first proposition is an e'clamatory proposition as it gi"es

information ao#t fire.

(he second s#jectless proposition is impersonal proposition which has

grammatical s#ject #t not logical s#ject.


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0) S#ject 5redicate propositions - s#ject 5redicate proposition states that an

indi"id#al possesses a *#ality or an attri#te. -s indi"id#al is sing#lar term, s#ject of

this kind of proposition is sing#lar.

e.g. 1) Shi"aji was a king

0) -hijit is a singer

4) Soloman was wise.

-ll ao"e propositions assert an attri#te ao#t as indi"id#al. (he form of s#ject

predicate proposition is symolically represented as S5 is it &S stands for s#ject and &5

stands for the predicate which is an attri#te.

4) elational 5ropositions - relational proposition asserts a relation etween two or

more constit#ents. (he constit#ents etween which a relation is asserted are called terms

of relation. (hese terms of relation can not e called s#ject and predicate. -ll of them

are s#jects of relation which can e minim#m two

e.g. am lo"ed Sita.

In it two s#jects are &am and Sita and their relation is shown y lo"ed.

In relational propositions the relation proceeds from something to something else.

(his is called sense or direction of relation. (he term from which the relation proceeds is

called referent. (he term to which the relation proceeds is called relation. /ne can

indicate the sense or direction of relation may e indicated y an arrow. e.g.

defeated

ama awana

Same proposition can e e'pressed y #sing symols as &a will e

for referent and &arrow for relation and &D will e for showing. (he relation of defeated.

In it &a and &" are small letters and &D will e capital letter.

(he symoliBation will e

a D " stands for &a"ana and &D stands for Defeated.

(he direction or sense of relation is indicated y the order in which the small

letters &' &y etc. &o &" etc. occ#r. (he letter which occ#rs first is referent and that which

comes ne't is the relation.

7) 9lass N memership proposition - class memership proposition asserts that as

indi"id#al is a memer of &a class


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e.g. -mitah is a hero.

Son#


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0) 9onj#ncti"e propositions

4) Disj#ncti"e propositions

7) Implicati"e propositions.

8) $*#i"alent propositions.

1)


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(he components of a conj#ncti"e proposition are called conj#ncts.

5ropositional connecti"e conj#ncti"e propositions is & . 2dot)

e.g. amesh is intelligent and hardworking

(his proposition will e symoliBed as

I.

in which &I stands for amesh is intelligent and & stands for amesh is hardworking.

- conj#ncti"e proposition is tr#e if and only if oth the conj#ncts are tr#e e"en if

one of the conj#ncts is false, it is false.

4) Disj#ncti"e proposition a disj#ncti"e proposition is compo#nd proposition in which

the word either or comines two propositions.

(he components of disj#ncti"e propositions are called disj#ncts 2or alternati"es)

Disj#nction may e #sed in two senses

1) Incl#si"e sense 2weak) N when oth

(he disj#ncts can e tr#e disj#nction is said to e #sed in incl#si"e sense.

e.g. Son#


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In an implicati"e proposition the component proposition etween the word &if

and the worked &then is called the antecedent 2or implicans) and the component

proposition which follows the word &then is called the conse*#ent 2or the implicate)

e.g. If he is g#ilty then he will e p#nished.

In ao"e e'ample he is g#ilty is antecedent and he will e p#nished is conse*#ent.

5repositional connecti"e for implicate proposition is &s 2horse shoe)

e.g. If he is g#ilty then he will e p#nished will e symoliBed as

O 5

Where &O stands for he is g#ilty and &p stands if he will e p#nished.

-n implicati"e proposition is false if and one if. (he antecedent is tr#e and the

conse*#ent is false.

8) $*#i"alent 2or iconditional) propositions-n e*#i"alent proposition is a compo#nd proposition in which two component

propositions materially imply each others.

(he prepositional connecti"e material e*#i"alence is symoliBed as & 2triple ar) or

2two headed arrow).

e.g. If and only if an animal is mammal then it reastfeeds its yo#ng ones.

It will e symolised as

m y or m y in which &6 stands for an animal is mammal and &O stands for it

reastfeeds its yo#ng ones.

-n e*#i"alent

5roposition is tr#e if oth the components ha"e the same tr#th "al#e.

%eneral 5ropositions

-part from simple and compo#nd propositions, modern logic, recogniBes general

propositions so a general proposition can e defined as a proposition that makes an

assertion o#t a class or classes. (hese propositions show connection etween two

properties.

(hese propositions consider properties 2characteristics) apart from the indi"id#althings which ha"e these properties. (hat is why the proposition 2-) &-ll fairies are

ea#tif#l wo#ld e tr#e e"en if there were no fairies.

/n the other hand, the proposition 2I) &some singers are actors asserts that there

e'ists at least one indi"id#al who possess the property of eing a singer and eing an


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actor from this we can know #ni"ersal proposition does not imply e'istence #t a

partic#lar proposition does.

Distinction etween general proposition and class memership proposition

In a class memership proposition an indi"id#al is asserted to e a

memer of a certain class. (his shows, one of the constit#ents of a classmemership

proposition is an indi"id#al, while. (he other constit#ent is of a class.

/n the other hand all constit#ents of a general proposition are classes.

%eneral propositions assert relation etween two classes and they are ao#t properties

and not ao#t the indi"id#als which possess these properties.

Distinction etween general proposition from simple and compo#nd proposition.

Simple propositions contain a partic#lar as a constit#ent i.e. one of

the constit#ents of a simple proposition is an indi"id#al.

e.g. 1) ah#l is smart

0) Shi"aji defeated -fBal Ahan

%eneral propositions contain #ni"ersal as its constit#ents.

e.g. all Indians are helpf#l.

In ao"e proposition Indians and helpf#l are #ni"ersals.

9ompo#nd propositions are farmed y comining other propositions

while general proposition is a single statement and it cannot e analysed into

propositions.

10) What is p#rpose of definition?

Definitions are re*#ired for making comm#nication possile as well as clear. (hese

f#nctions can e analysis into fi"e p#rpose of definition.

(hese are

1) (o increase "oca#lary +y e'plaining the meaning of new words, definition

increases "oca#lary one way of "arifying the meaning of a word is y #sing it.

+#t sometimes the conte't does not rarify the meaning. In s#ch case, the meaning

has to e delierately e'plained delierate e'planation of meaning in"ol"es

definition e.g. lady e'plains her friend that she is on her family way. If e'pression


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family way the lady has to define it. (hey will define it as family way means she

is pregnant.

(he ao"e e'ample shows that definition of new words increase "oca#lary.

0) (o eliminate amig#ity In e"ery day many words which are many a time

e*#i"ocal, amig#o#s or "ag#e.

-n e*#i"ocal word is one which can e interpreted in two or more ways #s#ally,

this ca#ses no tro#le. +y this there meaning ecome clear from the conte't.

e.g. (he word &at is e*#i"ocal.

Its one meaning is &animal and the other meaning is &an instr#ment y which

game of cricket is played. So When I say &Sachins at weights more than

Sa#ra"s then e"eryone will #nderstand what I am referring to th#s, in the case of

e*#i"ocal words no diffic#lty arises.

(here are, words whose meaning does not ecome clear from the conte't s#ch

words are said to e amig#o#s.

$.g. Ind#stry sho#ld e enco#raged. In ao"e e'ample, we are not s#re whether

&ind#stry means &hard work or &ind#strial organiBation. (his is d#e to amig#ity

of the word &ind#stry.

In s#ch cases, definition plays "ital roles as is ser"es the p#rpose of eliminating

amig#ity.

4) (o red#ce "ag#eness of words - word is "ag#e when the type of things to which

is applies is not definite which many a time leads to differences of opinion.

Definitions help in resol"ing differences y red#cing the "ag#eness

e.g. cashew sho#ld e considered what a fr#it or a "egetale?

(his conf#sion can e resol"ed y resol"ing "ag#eness of terms.

7) (o e'plain word theoretically (his is especially applicale to the world of science

or disco"ery where they come in to#ch with new words and they not only need special

definition, #t also some technical e'planation. It is also, re*#ired in field of law to

interpret stat#te. 3or e.g. &roery is defined y the &3ederal +#rea# of In"estigation as

>the taking, or attempted taking, of anything of "al#e from one person y another, in

which the offender #ses force or the threat of "iolence@.


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8) (o infl#ence attit#de Lastly, #t not least, it is "ery important aspect, certain words

when define it resol"es the conflicts, and ring peace. It occ#rs j#st eca#se the attit#de

of person is changed towards the meaning of the term. Definition that prod#ces effect to

infl#ence attit#de is called pers#asi"e definition.

14) What are different types of definition? Show its relation with law?

Definition is the e'planation of the meaning of a word phrase or symol 2i.e. non "ertical

symol)

What is defined may e the name of concept or class, or it may e a symol.

Definitions consist of two parts. (hese are

1) What is defined is called definiend#m

0) (he words in which it is defined, is called definiens.

e.g. +achelor means #nmarried man.

In ao"e e'ample &achelor is definiend#m and nmarried man is definien.

When definition is gi"en the definiend#m is placed to the left, and definien to the

right. (he definition sho#ld e stated th#s, R means O.

ere &R is the definiend#m, &O is define and the word &means indicates that the

statement is a definition.

elati"ity of definition Definition is relati"e i.e. it can change from person to person.

(he release, the same word may ha"e to e defined differently for different persons.

e.g. (he definition of soft drink as &a caronated non to'icating e"erage is

appropriate and good definition #t a common man wick fend it c#lt to #nderstand.

So the word which is easy for scientist to #nderstand may not e lean to common

man.

(his is the recon, the need of definition arises, to make, #nderstand the #nknown

word and the p#rpose of defining ser"ed only if the gi"en definition is clear to the

recei"er of definition.

Distinction etween eal and


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1) eal Definition - definition which notifications to state the nat#re of a thing

is called real definition. (his is "iew was p#t forth y traditional logicians.

0)


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Limitations

1) -n oject has many *#alities. +y ostensi"e definition one is not s#re of which

*#ality has een pointed o#t e.g. If one wants do define word &dog ostensi"e

ly. 3rom the gest#re it may not e clear whether the word means colo#r or

ody str#ct#re of the animal

0) We cannot define things ostensi"ely which are not real e.g. ghost fairy etc.

4) Scientific concepts are not possile to define ostensi"e e.g. gra"itation.

0) $'tensi"e definition $'tensi"e definition e'plains shows a word is to e

applied and it consists in gi"ing e'amples of the definiend#m. S#ch, e'amples,

can e gi"en in two ways.

$'amples of indi"id#al ojects, 2incl#ded in the class) to which the word applies

e.g. +omay, 6adras.

$'amples of s#itclasses to which the word applies angles 2ornaments) one can

gi"e a satisfactory e'tensi"e definition when the definiend#m applies to limited

n#mer of ojects.

1) +i"eral definition N +i"eral definition is the e'planation of the meaning of,

one word y another word or of one phrase y another phrase when they

ho#se the same meaning.

e.g. "alo#r means co#rage

In ao"e e'ample, word "elo#r and co#rage ha"e same meaning so one word can

e #sed to e'plain the other.

+i"eral definition of a phrase will consist in e'plaining its meaning y another

phrase.

e.g. (o think etter of the matter means to gi"e it f#rther consideration.

In ao"e e'ample defines has the same meaning as the definiend#m.

7) Definition per gen#s et differentia 9ertain words are names of classes.

6emers of a class ha"e certain *#alities in common. When a definition states

this, this definition is called analytical definition. (he most commonly #sed

definition in this regard is definition.

(here are two more definition ased on #sage of term, this are


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8. Stip#lati"e definition

:. Le'ical definition

8. Stip#lati"e definition "he definition that arises fro! deliberate assign!ent of a

!eaning is properly called stipulative. It is needed if any no"el term is formed or

tentati"e e'planation is gi"en or poet #ses its lierty to e'press any term or many a time it

can e #sed as code to pass secret messages. It is referred as no!inal definition or verbal

definition.

$.g. &+lack +ea#ty in general it may mean &ea#tif#l girl with sharp feat#re, #t with

dark skin, yet in reality it is stip#lated y poet Wordsworth as &lack horsess

It is stip#lati"e till it ecomes pop#lar, or gets it place in dictionary. (hen it ecomes

&le'ical.

:. Le'ical definition It is said to e pop#lar or dictionary meaning or #tmost reported

meaning. *t does not give definiendu! a !eaning' it hitherto lacked but reports a

!eaning of the definiendu! already has. It is referred many a time as &real. When any

term that can e stip#lati"e and ecomes pop#lar, it ecomes le'ical. (his normally occ#r

with scientific term, or newly deri"ed term. 3or e'ample

&moile this word was #sed earlier for mo"ing, then when instr#ment of comm#nication

was de"ice that was #sed to comm#nicate e"en while mo"ing was term &moile and now

e"eryone is familiar with word &moile.

+eside this one more additional definition can e gi"en, that is,

;. 5rcising definition It is definition that red#ces "ag#eness of the term. -s stip#lati"e

and le'ical ser"es to red#ce amig#ity, while this definition is to red#ce "ag#eness. It

means that terms which has orderline meaning that means, s#ch a meaning that it can e

interpreted as per the indi"id#al intends! for s#ch case some limits or appropriate

meaning sho#ld e fi'ed, to a"oid the conflict in #nderstanding. It is concept#al

instr#ment of wide and powerf#l #se.

In appellate co#rts, for e'ample, are oliged to draw concept#al lines, making

some common terms more precise, they commonly gi"e reasons for the refinements

introd#ce.


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In"estigation as >the taking, or attempted taking, of anything of "al#e from one person

y another, in which the offender #ses force or the threat of "iolence@.

17) What are r#les of traditional definition?

-ns. (raditional logician elie"es that there can e no other definition else then &5er

gen#s et differentia. (hey not only elie"e it to e &the definition, #t also prescries

some strict r#le for defining it and they are as follows

1)A definition should state the essential attributes of the species-

In other words it m#st not e too narrow or too road.

3or e.g. If in today scenario, if we consider scientists definition of planets and then state

that there are nine planets then it is too wide

/r if we say &man as animal 2only) then it is too narrow definition

In reality definition m#st state the essential feat#re completely and a"oid e'tra feat#res,

red#ndant feat#re or some accidental i.e. that *#ality r feat#re it is some time seen in

oser"ed thing.

0)*t !ust not be synony!s or circular in definition-

-ny definition if it has same meaning or twisted meaning, and gi"en in circ#lar way its

p#rpose itself fails. 3or e.g.

Synonyms +achelor is #nmarried person

9irc#lar N (his person is m#rderer eca#se he has weapon

-nd he has weapon so he is m#rderer.

4)A definition !ust not be figurative or obscure-

-ny definition m#st not gi"e comple' or perple'ed meaning otherwise indi"id#al will not

get it meaning and term will e "ag#e for e.g.

3ig#rati"e &$n"elop is coffin of letter

/sc#re &anesthesia is sophoric

7)A definition !ust not be negative where it can be affir!ative-

Definition m#st state what it means rather then what it cannot e. If we j#st say that what

it cannot e, one may not e ale to deri"e the perfect meaning. Same case occ#rred in

defining %od in edas. -ccording to edas definition %od is &not like h#man, not like

tree, not like demon, not like air T then lastly *#estion comes then god is like what?


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18) Define &simple en#meration. $'plain the main feat#res and "al#e of either &simple

en#meration. -nd also, gi"e its application in Law.

*imple #numerationis a generali0ation that is supported by positive instances and nocontrary instances that has been observed.

Si!ple Enu!eration1

6ain feat#res of Simple en#merationi. Uniform (or uncontradicted) experience: Simple enumeration isbased on the belief that what is true of observed is consideredto be true of unobserved.For example, we see few elephants tobe grey, and state that all elephants are grey. And we continueour belief of elephants to be grey until we get anycontradictory experience! li"e stating elephant can be white (orany other colour). #y such opposite experience only we can saythat all elephant cannot be grey. So! very essential feature isuncontradicted experience.

ii. #elief in uniformity of nature: $ne can give any statement forall! only by considering that what is true uptill now will continue

ahead also. And one can believe so! only due to belief inuniformity in nature. Since! nature shows the pattern ofuniformity! which give us the idea of uniformity ahead.

iii. %egree of probability: Simple enumeration is based on theobservation! as much more number of samples observed! morethe de&nite'ness of the conclusion. n other word more strongbelief in conclusion! and lesser the experience less con&dence inthe conclusion! and more the chance of contradictory result.

iv. o scienti&c analysis: Simple enumeration never meansscienti&c analysis! it purely depend on external observation. Aswe never try to see why elephant is grey* s there any organ orchemical or any molecule in elephant which presents elephant

colour grey* +ather we ,ust see the external colour to be greythat is common in many and conclude that all elephant aregrey.

al#e of Simple en#merationi. -ider experience: alue of simple enumeration can only be e/ective

on the wider experience as by such experience we can assure the factto remain same ahead.

ii. +esemblance: -hile observing one need to chec" the resemblance ofobservation with what we need to conclude. As observing colour inelephant is possible! but if we say crying of owl is bad omen! thenthere is no relation between crying of owl and bad or good omen.

-pplication of Simple en#meration in Law

Simple en#meration has immense "al#e in the oser"ation and generaliBation in science,#t e*#ally it carries "al#e in law. -s all the cases in co#rt stand on the ase of e"idences,

as m#ch more the e"idence and their statement, so do we elie"e in the strength of case,

and get the j#dgement accordingly. It is one of the essential elements in =eomatrics.1:) Define &-nalogy. $'plain the main feat#res and "al#e of either &analogy.

Analogyis defined as an argu!ent fro! particular rese!blance to further rese!blance.

6ain feat#res of -nalogy


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i. +elevant resemblance: 0omparison has its e/ect if the comparedfactor has relevance with conclusion. 1or example if we compare twoboys having same locality! same culture! same birthday! same schooland same friend circle. So! if one &nds that &rst boy is smart! it doesnot ma"e second boy intelligent. As the factors what we werecomparing has no relvance with intelligence.

ii. 0ommon characterisitics must be su2cient and di/erence ignorable:-hen one compare earth with moon wherein both have light! water!soil and environment which give us su2cient reason to believe thatthere can be life on the moon. #ut! if we compare it with mercury asboth are planet! both have light of sun and both are round. So! theremust be life on mercury than one can immediately reali3e that we aremissing important di/erence about environment in which life cansurvive and heavy heat on mercury in which it is not possible for anylife to survive. 4ence! comparision must have su2cient reason tobelieve conclusion and di/erence must never be important.

iii. $ne must not conclude more than necessary: -hen we comparebetween the 5 boys as having same locality! same culture! same

birthday! same school! same friend circle and have same 6 and 76.4ence! one got 89! so 5ndmust also get 89 only. 4erein we areaccepting more than re;uired and our conclusion will lead to error. Soone must conclude the minimum.

al#e of -nalogy

i. (otal positi"e analogy -ll characteristics known as well as #nknown in whom

two 2or more) things resemle are the total positi"e analogy.

ii. Anown positi"e analogy (he known etween two things are the known positi"eanalogy.

iii. (otal negati"e analogy -ll the characteristics 2known as well as #nknown) in

which things differ constit#te the total negati"e analogy.i". Anown negati"e analogy(he known differences etween two things constit#te

the known negati"e analogy.(o determine the "al#e of analogy, tho#gh these fo#r concepts are #sed #t for #s

it is not possile to know all the resemlances, e"en not all differences. We can

know only some of them. So while j#dging the proaility of an arg#ment fromanalogy, we ha"e to depend #pon the known positi"e analogy and the known

negati"e analogy. (h#s,When the known positi"e analogy 2resemlances) consists

of important properties, the concl#sion of analogy has a high degree ofproaility.

(hat is to say to deri"e at concl#sion, when we consider important properties of

two things which resemle with each other, then the analogy has high degree ofproailities In case of analogy of earth and mars, resemlances are atmospherewater.

-pplication of -nalogy in Law

-nalogy has immense importance in law in following two ways


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i. 9irc#mstantial e"idence In law of co#rt especially in case of crime when one

does not ha"e eyewitness than in s#ch case j#dgement is taken and gi"en on the

ase of the circ#mstances. In e"idence act circ#mstantial e"idence has got specialcla#se that is on the ase of gi"en facts one can concl#de that in similar condition

one can commit a partic#lar kind of crime, and if same condition has een

pre"alent in present case than y circ#mstantial e"idence person can econsidered g#ilty.

ii. 5recedent 5recedent is the pre"io#sly decided pi"ot case. /n finding that present

case is similar to the precedent 2i.e. earlier case) then j#dgement what is

applicale that time is also applicale in present case also.

ence, the analogy is important in oth the ao"e cases.

f) $'plain any two of the following concept

(LAW) BLS LLB Sem-1 : Logic Brief Notes

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