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'''BOETHIUS' TRANSLATION OF THE PERIHERMANEIAS'''
<a href = "#c1">Chapter 1</a>. The spoken word is a symbol of thought.<br>
<a href = "#c1">Chapter 1</a>. The spoken word is a symbol of thought.<br>
<a href = "#c2">Chapter 2</a>. Definition of noun<br>
<a href = "#c2">Chapter 2</a>. Definition of noun<br>
Note that only once does Boethius use the word 'propositio'for what Edghill translates as 'the admission of a premiss'<ref> Cicero invented some of the Latin equivalents for Greek terms, such as <i>propositio</i>, meaning the leading premiss of an argument, which contrasts with <i>assumptio</i> meaning the additional premiss. Kneale (p. 178) claims that 'propositio' was used by Quintilian in the more general sense of 'statement' or 'indicative sentence', in which it was used throughout the middle ages</ref>. However, later writers such is Ockham preferred 'proposition', which is the ancestor of our modern 'proposition'.
Note that only once does Boethius use the word 'propositio'for what Edghill translates as 'the admission of a premiss'<ref> Cicero invented some of the Latin equivalents for Greek terms, such as <i>propositio</i>, meaning the leading premiss of an argument, which contrasts with <i>assumptio</i> meaning the additional premiss. Kneale (p. 178) claims that 'propositio' was used by Quintilian in the more general sense of 'statement' or 'indicative sentence', in which it was used throughout the middle ages</ref>. However, later writers such is Ockham preferred 'proposition', which is the ancestor of our modern 'proposition'.
2. Spoken words are signs of mental modifications (Boethius: <i>notae passionum anima</i> - literally passions or modifications of the soul).
While the signs are not necessarily the same (i.e. if the written or spoken languages are different)
While the signs are not necessarily the same (i.e. if the written or spoken languages are different)
these modifications are the same in all people (<i>eaedem omnibus passiones animae sunt</i>).
these modifications are the same in all people (<i>eaedem omnibus passiones animae sunt</i>).
This later developed into the idea, defended by Ockham and Buridan and others, that spoken propositions,
This later developed into the idea, defended by Ockham and Buridan and others, that spoken propositions,
i.e. sentences, represent mental propositions of which they are the outward signs.
i.e. sentences, represent mental propositions of which they are the outward signs.
3. Universal signs are 'of a nature' to be predicated of many.
3. Universal signs are 'of a nature' to be predicated of many.
The Latin formula was <i>universale quod in pluribus natum est praedicari</i>, repeated by writers of logic textbooks
The Latin formula was <i>universale quod in pluribus natum est praedicari</i>, repeated by writers of logic textbooks
such as Peter of Spain and a hundred others since.
such as Peter of Spain and a hundred others since.
4. An affirmation is a assertion of something about something (<i>affirmatio vero est enuntiatio alicuius de aliquo</i>),
4. An affirmation is a assertion of something about something (<i>affirmatio vero est enuntiatio alicuius de aliquo</i>),
a denial is an assertion of something "from" something (<i>negatio vero enuntiatio alicuius ab aliquo</i>).
a denial is an assertion of something "from" something (<i>negatio vero enuntiatio alicuius ab aliquo</i>).
to deny<sup><a href = "#note3">[3]</a></sup>.
to deny<sup><a href = "#note3">[3]</a></sup>.
5. Every affirmation has an opposite denial, and similarly every denial an opposite affirmation
(<i>omni affirmationi est negatio opposita et omni negationi affirmatio</i>). This was the basis of the well-known
(<i>omni affirmationi est negatio opposita et omni negationi affirmatio</i>). This was the basis of the well-known
'square of opposition' - see below.
'square of opposition' - see below.
6. The distinction between singular and general propositions.
7. The idea of 'wide scope' or 'sentence' negation. Aristotle says that a denial must deny exactly whatthe affirmation affirms,
(<i>idem oportet negare negationem quod affirmavit affirmatio</i>)
(<i>idem oportet negare negationem quod affirmavit affirmatio</i>)
8. In the case of that which is or which has taken place, either the affirmation or the denial is true or false.
8. In the case of that which is or which has taken place, either the affirmation or the denial is true or false.
(<i>In his ergo quae sunt et facta sunt necesse est affirmationem vel negationem veram vel falsam esse</i>).
(<i>In his ergo quae sunt et facta sunt necesse est affirmationem vel negationem veram vel falsam esse</i>).
unavoidably true, and that what will happen in the future will happen by necessity.
unavoidably true, and that what will happen in the future will happen by necessity.
== The Square of Opposition ==
The idea that there are certain logical relationships between the four kinds of Aristotelian proposition,
The idea that there are certain logical relationships between the four kinds of Aristotelian proposition, when they have the same subject and predicate, is developed in chapters [[#c6|>six]] and [[#c7"|seven]]. It became the basis of a diagram originating with Boethius and used by medieval logicians to classify these possible logical relations. The four propositions - the universal affirmative ('every man is just'), the universal negative ('no man is just'), the particular affirmative ('some man is just') and the particular negative ('some man is not just') - are placed in the four corners of a square, and the relations represented as lines drawn between them.
when they have the same subject and predicate, is developed in chapters
It became the basis of a diagram originating with Boethius and used by medieval logicians to classify
these possible logical relations. The four propositions - the universal affirmative ('every man is just'),
the universal negative ('no man is just'),
the particular affirmative ('some man is just') and the particular negative ('some man is not just') -
are placed in the four corners of a square, and the relations represented as lines drawn between them.
Pairs of propositions are called <i>contradictories</i> (contradictoriae) when they cannot at the same time both be true or both be false, <i>contraries</i> (contrariae) when both cannot at the same time be true, <i>subcontraries</i> (subcontrariae) when both cannot at the same time be false, and <i>subalternates</i> (subalternae) when the truth of the one proposition implies the truth of the other, but not conversely. The corresponding relations are known as contradiction (contradictio), contrariety (contrarietas), subcontrariety (subcontrarietas) and subalternation (subalternatio).
<i>contraries</i> (contrariae) when both cannot at the same time be true, <i>subcontraries</i> (subcontrariae) when both cannot at the same time be false,
and <i>subalternates</i> (subalternae) when the truth of the one proposition implies the truth of the other, but not conversely.
The corresponding relations are known as contradiction (contradictio), contrariety (contrarietas), subcontrariety (subcontrarietas) and subalternation (subalternatio).
Thus
Thus
* 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 one at least man is not just, and at least one man is not just).
and also both may be false (if one at least man is not 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 together
* The universal affirmative and the particular affirmative are subalternates, because in Aristotelian semantics 'every A is B' implies 'some A is B'. This fact has caused endless controversy since the middle of the nineteenth century, following the development of modern semantics where there is no such implication. Similarly the universal negative and the particular negative are subalternates since, again, 'no A is B' was thought to imply 'some A is not B'.
'every A is B' implies 'some A is B'. This fact has caused endless controversy since the middle of the nineteenth century,
following the development of modern semantics where there is no such implication. Similarly the universal negative
and the particular negative are subalternates since, again, 'no A is B' was thought to imply 'some A is not B'.
* The universal affirmative and the particular negative are contradictories. Clearly if some A is not B,
not every A is B. Conversely, though this is not intuitive for modern semantics, it was thought that if every A is not B,
not every A is B. Conversely, though this is not intuitive for modern semantics, it was thought that if every A is not B,
some A is not B. This interpretation has also caused much controversy. Note that Aristotle's Greek does not
some A is not B. This interpretation has also caused much controversy. Note that Aristotle's Greek does not
follows him. However, in Boethius commentary on the Perihermaneias,
follows him. However, in Boethius commentary on the Perihermaneias,
he renders the particular negative as 'quidam A non est B', literally 'a certain A is not a B',
he renders the particular negative as 'quidam A non est B', literally 'a certain A is not a B',
which under any ordinary reading of the Latin (see Lewis and Short, e.g.) is existential, implying the existence of
which under any ordinary reading of the Latin (see Lewis and Short, e.g.) is existential, implying the existence of a particular A which is not a B. Terence Parsons has suggested ([http://plato.stanford.edu/entries/square here]) that the Latin 'quidam A non est B' does not have existential import, but this seems implausible, given that it means that a certain, or a particular A, is not B.
a particular A which is not a B. Terence Parsons has suggested (<a href = "http://plato.stanford.edu/entries/square">here</a>)
that the Latin 'quidam A non est B' does not have existential import, but this seems implausible,
given that it means that a certain, or a particular A, is not B.
<blockquote>
<blockquote>
<table border="0" cellpadding="0" cellspacing="0" summary="">
<table border="0" cellpadding="0" cellspacing="0" summary="">
== Hyperlinks ==
Another advantage of using Boethius' Latin is that medieval commentators on Aristotle refer to this translation, or very similar translations, in making references.
Another advantage of using Boethius' Latin is that medieval commentators on Aristotle refer to this translation, or very similar translations, in making references.
we have the much easier way of using the hyperlink to take us there. No heavy books, no leafing through pages of indecipherable contractions. Progress indeed.
we have the much easier way of using the hyperlink to take us there. No heavy books, no leafing through pages of indecipherable contractions. Progress indeed.
I am developing a set of pages in the Logic Museum consisting of medieval commentaries (such as by Aquinas, Abelard and Boethius himself) on the Perihermaneias.
(such as by Aquinas, Abelard and Boethius himself) on the Perihermaneias.
== References ==
Kneale, W. & M., <i>The Development of Logic</i>, Oxford, 1971
Kneale, W. & M., <i>The Development of Logic</i>, Oxford, 1971
