- Words are symbols of our mental experiences. Words differ between languages, but the mental experiences are the same. For example the English word ‘house’ differs from the Spanish word ‘la casa’ but the mental experience of both symbols is the same.Nouns and verbs have no truth or falsity.
- A noun indicates a conventional subject, without reference to time. For example, Alexander the Great indicates the same subject now as it did when he was alive more than 2,000 years ago.
- A notion of time is inherent in verbs. An untensed verb indicates the present, while tensed verbs indicate time outside the present. For example, He is healthy; He was healthy; He will be healthy.
- Only when words are combined do we have truth and falsity, affirmation and negation. A sentence is an expression whose parts have meaning. The noun of a sentence indicates the subject, but does not have meaning by itself.
- A simple proposition is the expression of one fact. A complex proposition is several propositions compounded together. A proposition must have a verb.
- “An affirmation is an assertion of something of something, a denial an assertion denying something of something. (For example, ‘a man is an animal’ asserts ‘animal’ of ‘man’. ‘A stone is not an animal’ denies ‘animal’ of stone’).”
- Terms are either universal or individual. A universal affirmative proposition – Every man is white – and a universal negative proposition – No man is white – are contraries. A universal affirmative proposition – Every man is white – and the non-universal denial of that proposition – Some man is not white – are contradictories. Of contradictories, one must be true and the other must be false. Of contraries, both cannot be true, but both can be false. If both contraries are false, then both of their contradictories are true. For example, ‘Every man is honest’ and ‘No man is honest’ are both false; and therefore their contradictories are both true – i.e. ‘Some man is not honest’ and ‘Some man is honest.’
- A single affirmation expresses a single fact. ‘Every man is white’ is a single affirmation. However, if we used a noun that indicates more than one subject, then the proposition would not be a single affirmation. For example, if the symbol ‘garment’ meant both a man and a horse, then the proposition ‘Every garment is white’ is not a single affirmation. The proposition can be separated into two simple propositions – i.e. ‘Every man is white’ and ‘Every horse is white.’
- “Of contradictory propositions about the past and present, one must be true, the other false. But when the subject is individual, and the proposition is future, this is not the case. For if so, nothing takes place by chance. For either the future proposition such as, ‘A sea battle will take place,’ corresponds with future reality, or its negation does, in which case the sea battle will take place with necessity, or not take place with necessity. But in reality, such an event might just as easily not happen as happen; the meaning of the word ‘by chance’ with regard to future events is that reality is so constituted that it may issue in either of two opposite possibilities. This is known as the problem of future contingents.” Aristotle solves this problem by explaining that a sea fight must either take place tomorrow or not take place tomorrow, but it is not necessary that the sea fight take place tomorrow and not necessary that it does not take place tomorrow. “What is necessary is not that there will or that there won’t be a battle tomorrow, but the dichotomy itself is necessary.”
- Aristotle makes a distinction between the use of ‘is’ as a mere copula and as a term indicating existence. For example, ‘A man is white’ and ‘A man is.’
In this short text, Aristotle discusses the basics of logic. He provides definitions of terms and propositions, and also addresses the now famous future sea-battle dilemma. The dilemma considers the necessity of future events, and has major implications to the free will debate. The dilemma is as follows: There are two propositions that can be made with respect to a future event. For example, ‘There will be a sea fight tomorrow’ and ‘There will not be a sea fight tomorrow.’ One of these propositions is true, the other false. Because one of these propositions is true, can we conclude that whatever does happen must happen of necessity? Aristotle says no. He argues that the dichotomy itself is necessary, but not the future event. In other words, it is necessary, at the present time, that there will either be a sea fight tomorrow or there will not be a sea fight tomorrow, but the future reality is not necessary. This is because the validity of the proposition cannot be established until the events it considers are in the past or present.