Logic: Deductive and Inductive

Name: Logic: Deductive and Inductive
Author: Read, Carveth

Read, Carveth

Logic

There is no contrapositive of I., because the obverse of I. is in the
form of O., and we have seen that O. cannot be converted. O., however,
has a contrapositive (_Some not-P is S_); and this is sometimes given
instead of the converse, and called the 'converse by negation.'

Contraposition needs no justification by the Laws of Thought, as it is
nothing but a compounding of conversion with obversion, both of which
processes have already been justified. I give a table opposite of the
other ways of compounding these primary modes of Immediate Inference.

                     A                I               E                 O
--------------------------------------------------------------------------------

          1 All A is B       Some A is B       No A is B        Some A is not B

--------------------------------------------------------------------------------

Obverse   2 No A is b        Some A is not b   All A is b       Some A is b

--------------------------------------------------------------------------------

Converse  3 Some B is A      Some B is A       No B is A

--------------------------------------------------------------------------------

Obverse
of        4 Some B is not a  Some B is not a   All B is a
Converse

--------------------------------------------------------------------------------

Contra-
positive  5 No b is A                          Some b is A      Some b is A

--------------------------------------------------------------------------------

Obverse
of        6 All b is a                         Some b is not a  Some b is not a
Contrapos

--------------------------------------------------------------------------------

Converse
of
Obverse   7                                    Some a is B
of
Converse

--------------------------------------------------------------------------------

Obverse
of
Converse
of        8                                    Some a is not b
Obverse
of
Converse

--------------------------------------------------------------------------------

Converse
of
Obverse   9 Some a is b
of
Contrapos

--------------------------------------------------------------------------------

Obverse
of
Converse
of       10 Some a is not B
Obverse
of
Contrapos

--------------------------------------------------------------------------------

In this table _a_ and _b_ stand for _not-A_ and _not-B_ and had better
be read thus: for _No A is b, No A is not-B_; for _All b is a_ (col. 6),
_All not-B is not-A_; and so on.

Public-domain text, read in full here on John Shaqi.

Opening the text

Logic: Deductive and InductiveRead, Carveth

Philosophy

Logic: Deductive and Inductive

Read, Carveth

Logic

There is no contrapositive of I., because the obverse of I. is in the
form of O., and we have seen that O. cannot be converted. O., however,
has a contrapositive (_Some not-P is S_); and this is sometimes given
instead of the converse, and called the 'converse by negation.'

Contraposition needs no justification by the Laws of Thought, as it is
nothing but a compounding of conversion with obversion, both of which
processes have already been justified. I give a table opposite of the
other ways of compounding these primary modes of Immediate Inference.

                     A                I               E                 O
--------------------------------------------------------------------------------

          1 All A is B       Some A is B       No A is B        Some A is not B

--------------------------------------------------------------------------------

Obverse   2 No A is b        Some A is not b   All A is b       Some A is b

--------------------------------------------------------------------------------

Converse  3 Some B is A      Some B is A       No B is A

--------------------------------------------------------------------------------

Obverse
of        4 Some B is not a  Some B is not a   All B is a
Converse

--------------------------------------------------------------------------------

Contra-
positive  5 No b is A                          Some b is A      Some b is A

--------------------------------------------------------------------------------

Obverse
of        6 All b is a                         Some b is not a  Some b is not a
Contrapos

--------------------------------------------------------------------------------

Converse
of
Obverse   7                                    Some a is B
of
Converse

--------------------------------------------------------------------------------

Obverse
of
Converse
of        8                                    Some a is not b
Obverse
of
Converse

--------------------------------------------------------------------------------

Converse
of
Obverse   9 Some a is b
of
Contrapos

--------------------------------------------------------------------------------

Obverse
of
Converse
of       10 Some a is not B
Obverse
of
Contrapos

--------------------------------------------------------------------------------

In this table _a_ and _b_ stand for _not-A_ and _not-B_ and had better
be read thus: for _No A is b, No A is not-B_; for _All b is a_ (col. 6),
_All not-B is not-A_; and so on.

Public-domain text, read in full here on John Shaqi.

Logic: Deductive and Inductive

Logic: Deductive and Inductive

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