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1 - 1 Homonyms share a name but differ in definition, like "man" and "picture."

1 - 2 Some things are complex (e.g., "man runs"), others incomplex (e.g., "man").

1 - 3 Predicates of a subject share characteristics; differences exist among unrelated genera.

1 - 4 Things signify substance, quantity, quality, relation, where, when, position, possession, action, or passion.

1 - 5 Substance is primary (e.g., "man") or secondary (e.g., "animal"), neither predicated of nor inherent in another subject.

1 - 6 Quantity is discrete (e.g., "number") or continuous (e.g., "line"), with or without relative position.

1 - 7 Relatives are defined by reference to something else, like "double" to "half."

1 - 8 Quality includes habit, disposition, natural capacities, passive qualities, and form, defining things' characteristics.

1 - 9 Action and passion admit contrariety, and the more and the less, and include positions like sitting or standing.

1 - 10 Opposites include relative, contrary, privation and habit, and affirmation and negation.

1 - 11 Good is opposed to evil, with contraries often sharing a genus or being in contrary genera.

1 - 12 Priority is in time, non-reciprocation of existence, order, or excellence.

1 - 13 Simultaneity is temporal, natural, or by division, with genera always prior to species.

1 - 14 Motion includes generation, corruption, increase, diminution, alteration, and change of place.

1 - 15 "To have" denotes possession, relation, or characteristics, like size, garments, or a spouse.

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2 - 1 First, we must define the terms 'noun' and 'verb', followed by 'denial' and 'affirmation', and then 'proposition' and 'sentence.' Spoken words are symbols of mental experiences, and written words symbolize spoken words. While people do not share the same speech sounds or writings, the mental experiences they symbolize are the same for all. Truth and falsity in speech imply combination and separation. Nouns and verbs alone do not convey truth or falsity without context. For example, 'goat-stag' has meaning but is neither true nor false without further context, such as 'is' or 'is not.'

2 - 2 A noun is a sound significant by convention, not referencing time, and no part of it is significant independently. For example, in 'Fairsteed,' 'steed' alone has no meaning. Simple nouns have no meaningful parts, while composite nouns contribute to the whole meaning. An indefinite noun like 'not-man' does not form a proposition on its own. Cases of a noun like 'of Philo' are not nouns themselves. When coupled with verbs like 'is' or 'was,' they do not form true or false propositions. Thus, 'of Philo is' or 'of Philo is not' are not propositions on their own.

2 - 3 A verb carries the notion of time and signifies something said of something else. For example, 'health' is a noun, but 'is healthy' is a verb indicating present time. Verbs are substantival and significant but do not express judgments on their own. Expressions like 'is not-healthy' are indefinite verbs since they apply equally to existing and non-existing subjects. Tenses of a verb, like 'he was healthy' or 'he will be healthy,' indicate times outside the present but are not verbs themselves. Verbs imply a copulation, needing additional context to form a complete conception.

2 - 4 A sentence is a significant portion of speech, where some parts have an independent meaning as utterances, but not as positive judgments. For instance, 'human' has meaning but does not constitute a proposition. Only when other words are added does it form an affirmation or denial. Composite words have parts contributing to the whole meaning but lack independent meaning. Every sentence has meaning by convention, not as a natural realization of a physical faculty. However, not all sentences are propositions; only those containing truth or falsity are propositions, relevant to our inquiry here.

2 - 5 Simple propositions include simple affirmation and simple denial. Every proposition must contain a verb or verb tense. For example, 'a footed animal with two feet' is not a single proposition without a verb. Single propositions indicate a single fact or a conjunction forming unity. In contrast, separate propositions indicate multiple facts without conjunction. A noun or verb alone is only an expression, not a proposition. Simple propositions assert or deny something in the present, past, or future, divided by time. Composite propositions consist of simple propositions.

2 - 6 An affirmation asserts something positively, while a denial asserts negatively. Affirmations and denials can refer to the presence or absence of something in any tense, allowing for contradiction. Contradictory propositions have the same subject and predicate. For example, 'every man is white' is contradicted by 'not every man is white,' and 'no man is white' is contradicted by 'some men are white.' Contradictions arise when one affirmation and one denial have the same subject and predicate, highlighting their oppositional nature.

2 - 7 Some things are universal, meaning they can be predicated of many subjects, while others are individual and cannot. Propositions can concern either universal or individual subjects. Positive and negative propositions about universals, like 'every man is white' and 'no man is white,' are contraries. Propositions about universals but not universally characterized, like 'man is white' and 'man is not white,' are not contraries. Contradictory propositions oppose each other by affirming or denying the same predicate. For instance, 'Socrates is white' and 'Socrates is not white' are contradictory.

2 - 8 An affirmation or denial is single if it indicates one fact about one subject, regardless of whether the subject is universal or particular. Single propositions include statements like 'every man is white' and 'man is white.' However, if a word has two meanings, the affirmation is not single. For example, if 'garment' means both a horse and a man, 'garment is white' is not a single affirmation but equivalent to 'horse and man are white.' Thus, such propositions may simultaneously be true or false, highlighting their complex nature.

2 - 9 Propositions about the present or past must be true or false. Contradictory propositions about universals or individuals ensure one is true and the other false. However, when predicated about the future, it's different. If affirmations and denials are true or false, then one must correspond to reality. This implies necessity and eliminates chance. Future events must either occur or not, eliminating uncertainty. Deliberation and action suggest potentiality, meaning events may occur differently. Hence, not everything happens necessarily; some events have real alternatives, showing a balance between necessity and possibility.

2 - 10 An affirmation states a fact about a subject, which is a noun or an indefinite noun like 'not-man.' Every affirmation or denial consists of a noun and a verb, either definite or indefinite. The primary affirmation and denial are 'man is' and 'man is not.' Adding 'is' to terms like 'just' or 'not-just' forms four propositions, creating a scheme for these propositions. The universal distribution of subjects shows propositions like 'every man is just' and 'not every man is just.' Subject-predicate inversion, such as 'man is white' and 'white is man,' does not change the proposition's sense.

2 - 11 An affirmation or denial lacks unity if it predicates one thing of many subjects or many things of one subject, unless the multiple subjects form a unity. For example, 'man' may be 'animal,' 'biped,' and 'domesticated,' but they combine into one. In contrast, 'white,' 'man,' and 'walking' do not. Predicates accidental to the same subject do not combine into unity. Terms combining to form a unity are intrinsic, not accidental. Some predicates, though true together, do not combine to form a single proposition, like 'musical' and 'white.' Proper predicates form a unity, while accidental ones do not.

2 - 12 Affirmations and denials expressing possibility, contingency, impossibility, or necessity are interrelated. The contradictory of 'it may be' is 'it cannot be,' not 'it may not be.' The contradictory of 'it cannot not be' is 'it may not be.' These relations apply similarly to necessity and impossibility. For instance, 'it is necessary' is contrary to 'it is not necessary.' Properly arranging propositions like 'it may be' or 'it is not impossible' avoids logical inconsistencies. Necessity and possibility are initial principles, indicating that what is necessary is also possible, showing the complex interplay of logical sequences.

2 - 13 From 'it may be,' it follows that it is contingent, not impossible, and not necessary. From 'it may not be,' it follows that it is not necessary. The proposition 'it cannot be' leads to 'it is necessary that it should not be.' Tables help illustrate logical sequences, showing how contradictories relate. 'It is necessary that it should be' implies 'it may be.' Potentiality has different senses: actualized potentiality and conditional potentiality. Necessity and actuality are primary, indicating that what is of necessity is actual. Thus, universal principles underlie particular instances, forming the basis of existence and non-existence.

2 - 14 An affirmation's contrary is another affirmation, not its denial. For example, 'every man is just' is contrary to 'no man is just,' not 'every man is unjust.' True judgments correspond to reality, while false judgments do not. Contradictory propositions like 'Callias is just' and 'Callias is not just' are clearer contraries than 'Callias is unjust.' True judgments about intrinsic nature are more accurate than those about accidental attributes. Contraries must concern starting points of generation, involving transitions between extremes. Thus, judgments denying the true are more contrary than those asserting the opposite, emphasizing intrinsic nature over accidents.

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3 - 1 Sophistical arguments appear valid but are often deceptive.	3 - 21 "Accent-based arguments solved by altering pronunciation for clarity."
3 - 2 Four argument types: didactic, dialectic, peirastic, and contentious.	3 - 22 Arguments from equivocation resolved by clarifying categorical distinctions properly.
3 - 3 Disputation aims: elenchus, falsehood, paradox, solecism, repeated assertions.	3 - 23 Oppose arguments from diction by reversing composition or division.
3 - 4 Elenchus involves diction and without diction, six forms exist.	3 - 24 Accidental arguments resolved by highlighting non-necessity of asserted attributes.
3 - 5 Seven non-diction paralogisms: accident, simple assertion, ignorance, consequent, begging, non-cause, multiple interrogations.	3 - 25 Resolve arguments by checking for conditional or relational contradictions.
3 - 6 Paralogisms and elenchi stem from misunderstandings and lack definitions.	3 - 26 Address elenchi by ensuring consistent reference to contradictory conclusions.
3 - 7 Equivocation, ambiguity, composition, division, accent, and speech figures deceive.	3 - 27 Identify and reject original question assumptions in manifest arguments.
3 - 8 Sophistical arguments and elenchi use similar deceptive methods.	3 - 28 Disprove arguments by distinguishing true consequences from false ones.
3 - 9 Elenchi require broad scientific knowledge across various disciplines.	3 - 29 Expose invalid arguments by demonstrating impossibility despite assumed premises.
3 - 10 Arguments relate to names and reasoning, involving syllogisms and contradictions.	3 - 30 Avoid false conclusions by addressing multiple interrogations as single.
3 - 11 Peirastic art examines ignorance and pretension through dialectic arguments.	3 - 31 Categories of relatives shouldn't be separated; their meaning changes.
3 - 12 Interrogation techniques reveal false assertions and contrary opinions effectively.	3 - 32 Address solecisms by understanding context and proper grammatical construction.
3 - 13 Trifling arguments create confusion by manipulating definitions and relationships.	3 - 33 Understand argument origins to identify and address logical errors.
3 - 14 Solecisms arise from misinterpretations and gendered language complexities.
3 - 15 Prolixity and rapid questioning obscure truth and create confusion.
3 - 16 Sophistical arguments aid in understanding predication and self-reflection.
3 - 17 Solve contentious arguments by focusing on perceived, not real, contradictions.
3 - 18 Solutions expose false syllogisms through negation or distinction methods.
3 - 19 Equivocation and ambiguity require distinguishing multifarious meanings for resolution.
3 - 20 Distinguish between composite and divided sentences to solve arguments.

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