Assignment 4

according to Aristotelian logic, the square of opposition is a diagramatic way to represent the ways in which the propositions are logically related to each other.

according to aristotle, a catagorical proposition is a proposition which has a subject, & a predicate, where the predicate is either asserted or denied by the subject. aristotle says that these catagorical propositions can be of 4 types:
1 universal affirmative
2 universal negative
3 particular affirmative
4 particular negative
the square of opposition logically relates these 4 types of propositions. according to the aristotelian philosophy, for every affirmative, there must be a negative, & only one of them is true( both can't be true at the same time). it also establishes the relation between the universals and particulars. hence, if a statement is true universally, it must be true in a particular case too.

as per the aristotelian logic system SQUARE OF OPPOSITION is a diagram that represents the four proposition(ARISTOTELIAN propisition)that are logically related or associated with veach other.This system is useful or analysinsg the syllogistic logic.(SYLLOGISTIC LOGIC involves the logical arguement that involves deriving one opposition from two other opposition in a particular format).The four aristotelian opposition are-->
1-->universal affirmative:It says every S is P.
2-->universal negative:It says no S is P
3-->particular affirmative:some S is P
4-->particular negative:some S is not P
In the square of opposition one finds that UNIVERSAL AFFIRMATIVE contradicts PARTICULAR NEGATIVE and UNIVERSAL NEGATIVE contradicts PARTICULAR AFFIRMATIVE.
UNIVERSAL statements are contraries.This means for ex."every man is just "and "no man is just",both the statements are togther not true,either one is true or both are false.
PARTICULAR statements are subcontraries.
  

as per the aristotelian logic system SQUARE OF OPPOSITION is a diagram that represents the four proposition(ARISTOTELIAN propisition)that are logically related or associated with veach other.This system is useful or analysinsg the syllogistic logic.(SYLLOGISTIC LOGIC involves the logical arguement that involves deriving one opposition from two other opposition in a particular format).The four aristotelian opposition are-->
1-->universal affirmative:It says every S is P.
2-->universal negative:It says no S is P
3-->particular affirmative:some S is P
4-->particular negative:some S is not P
In the square of opposition one finds that UNIVERSAL AFFIRMATIVE contradicts PARTICULAR NEGATIVE and UNIVERSAL NEGATIVE contradicts PARTICULAR AFFIRMATIVE.
UNIVERSAL statements are contraries.This means for ex."every man is just "and "no man is just",both the statements are togther not true,either one is true or both are false.
PARTICULAR statements are subcontraries.
  

In the system of Aristotelian logic , the square of opposition is a diagram representing the different ways in which each of the four propositions of the system are logically related ('opposed') to each of the others.
# Aristotle states (in chapters six and seven of the Perihermaneias (Latin De Interpretatione, English 'On Exposition'), that there are certain logical relationships between these four kinds of proposition. He says that to every affirmation there corresponds exactly one negation, and that every affirmation and its negation are 'opposed' such that always one of them must be true, and the other false. A pair of affirmative and negative statements he calls a 'contradiction' (in medieval Latin, contradictio). Examples of contradictories are 'every man is white' and 'not every man is white', 'no man is white' and 'some man is white'.Universal statements are contraries: 'every man is just' and 'no man is just' cannot be true together, although one may be true and the other false, and also both may be false (if at least one man is just, and at least one man is not just).Particular statements are subcontraries. 'Some man is just' and 'some man is not just' cannot be false togethe
# he universal affirmative and the particular affirmative are subalternates, because in Aristotelian semantics 'every A is B' implies 'some A is B'. Note that modern formal interpretations of English sentences interpret 'every A is B' as 'for any x, x is A implies x is B', which does not imply 'some x is A'. This is a matter of semantic interpretation, however, and does not mean, as is sometimes claimed, that Aristotelian logic is 'wrong'.
# The universal affirmative and the particular negative are contradictories. If some A is not B, not every A is B. Conversely, though this is not the case in modern semantics, it was thought that if every A is not B, some A is not B. This interpretation has caused difficulties (see below). While Aristotle's Greek does not represent the particular negative as 'some A is not B', but as 'not every A is B', Boethius in his commentary on the Perihermaneias, renders the particular negative as 'quoddam A non est B', literally 'a certain A is not a B', and in all medieval writing on logic it is customary to represent the particular proposition in this way.

square of opposition is a logical relationship among the four kinds of oppositions. an opposition is a spoken statement,it has two terms-subjects and predicate. the predicate either satisfies the subject or it opposes it. According to a Aristotle these propositionts fall under the following catagories and have a logical relationship-
1.universal affirmative-predicate assserted of the subject
2.universal negative-predicate denied of the subject
3.particular affirmative-predicate partially asserted of the subject
4.particular negative-some predicate denied of subject
universal affirmative & negative contradict each other eg."every man is honest" & "no man is honest"contradict each other.if universal affirmative is true then particular affirmaive must be true,so they are subalternates.similarly universal negative & particular negative are subalternates.universal aff.&particular neg. are contradictories,similarly uni.neg. & part.aff. are contradictories. part.aff. &part.neg. contradict each other

aristotle states that there are certain logic relationships between the four kinds of proposition (universal affirmative,universal negative,particular affirmative,particular negative).according to him every affirmation and its negation are opposed such that always one of them must be true,and other false.in universal statements words like (all,every etc.) are used but in case of particular statements
words like (some etc.) is used,i mean to say it is not applicable for all.............

according to aristotle, a catagorical proposition is a proposition which has a subject, & a predicate, where the predicate is either asserted or denied by the subject. aristotle says that these catagorical propositions can be of 4 types:
1 universal affirmative
2 universal negative
3 particular affirmative
4 particular negative
the square of opposition logically relates these 4 types of propositions. according to the aristotelian philosophy, for every affirmative, there must be a negative, & only one of them is true( both can't be true at the same time). it also establishes the relation between the universals and particulars. hence, if a statement is true universally, it must be true in a particular case too.

the square of opposition is a diagram representing the different ways in which each of the four preposition of the system are logically related to each of the other.
                A_________contraries________E
                . .
                . . . .
      subalterns. . . .subalterns
                . contradictories .
                . . . .
                . . . .
                . .
                I___________________________O
                     subcontraies
*two proposition are contradictories iff they can't both be true and they can't both be false.
*contraries iff they can't both be true but can both be false.
*subcontraries iff they can't both be false but can both be true.
*subaltern of the another it must be true if it's superaltern is true and the superaltern must be false if the subaltern is false.

                    

the square of opposition is a diagram representing the different ways in which each of the four preposition of the system are logically related to each of the other.
                A_________contraries________E
                . .
                . . . .
      subalterns. . . .subalterns
                . contradictories .
                . . . .
                . . . .
                . .
                I___________________________O
                     subcontraies
*two proposition are contradictories iff they can't both be true and they can't both be false.
*contraries iff they can't both be true but can both be false.
*subcontraries iff they can't both be false but can both be true.
*subaltern of the another it must be true if it's superaltern is true and the superaltern must be false if the subaltern is false.

                    

I had given the diagram and names but after saving all got mixed .
sorry.