A sorites is a sequence of enthymemes in which the unstated conclusion of one syllogism is an unstated premise of the next syllogism. For example,
(1). Socrates is a philosopher
(2) All philosophers are human
(3) All humans are mortal
So, (4) Socrates is mortal
(1) and (2) together imply that (5) Socrates is human. Their unstated conclusion (5) becomes a premise with (3). (5) and (3) then together imply (4). However, this analysis did not place the sorites in standard form. Standard form requires that the first premise have the same predicate as the conclusion. In standard form, (3) would be the first premise.
When the exercise screen opens, the top half is in Venn diagram for syllogism layout. But the bottom half shows a grid on which the sequence of sentences is organized. The exercise is done in three steps. Though the Venn circles are shown and can be filled in during steps one and two, the diagram is only evaluated by LogicCoach in step three. In the first two steps, the diagram is available for your convenience. In step three, it is required.
Step One--Pair The Terms
Each term in the sorites has to occur exactly twice. But sometimes, in one sentence a term occurs and in another sentence its complement occurs. So, use conversion, obversion and contraposition to make the expression the same in both occurrences of the term. The grid lists the sentences as stated and then the converse, the obverse, and the contraposition for each, if they are logically equivalent to the original. To replace the original, double click on the replacement. When all terms have been paired, check step one.
Step Two--Put In Standard Form
A sorites is in standard form when all terms have been paired and when the predicate of the conclusion is the predicate of the first premise. In step two, create the missing conclusions and premises. When step two starts, the original conclusion is in the sorites conclusion column of the grid while the other term-paired-sentences are still in the original column. In between these columns are two empty columns labeled premise. The two premises of the syllogisms go in these. To move an original, double click on it. To make the predicate of the conclusion be the predicate of the first premise, first find the premise that contains the predicate and then have it be the first item on which you double click.
Once both premise columns are filled, double click on the blank conclusion column to have LogicCoach create a temporary conclusion. It will do it by finding the two terms in the premises that are not the same (the two that are the same will be interpreted as the middle term), using the one in the right premise column for the major term, for the predicate of the temporary conclusion. The created conclusion will be an A form. To change the form, double click on it. LogicCoach will cycle through AEI and O forms. You can interchange the subject and predicate by converting the conclusion. To do this, right click on the conclusion. A right click will also convert a premise. However, that is the only change permitted to terms of a premise in step two.
The new conclusion will also be listed as the second premise of the next syllogism. Created conclusions may also be changed in step three and lines may also be converted in that step. However, the original conclusion of the sorites cannot be changed in step two. To change it, return to step one. The main feature of the new syllogisms examined in step two is whether the predicate of premise one is the predicate of the conclusion and whether each projected syllogism has exactly three terms. When all syllogisms have been created and have three terms, check step two.
Step Three--Diagram each syllogism and check it for validity
In turn, each syllogism is moved from its row in the grid and the 3 Venn circles are initialized for its diagram. After you diagram the syllogism, check it. When the syllogism in the last row has been correctly diagramed and judged, the exercise is finished.
Hints about the sorites in the text.
A) An existential assumption is not allowed. All syllogisms are either unconditionally valid or invalid.
B) A sorites is valid, if all its syllogisms are valid. A sorites is invalid, if all but the last syllogism is valid; if the last one is invalid. In part I, only the very last syllogism in the sorites may be invalid. All others are to be constructed as valid. In parts II and III, all syllogisms are valid.
C) One way to find the first two premises is to begin with the line that contains the predicate of the original conclusion. Double click this one first so that the predicate of the ultimate conclusion may become the predicate of the first syllogism. Then pair it with the second sorites line that contains the other term, the one in the first line but not in the conclusion. In the example above,
(1). Socrates is a philosopher
(2) All philosophers are human
(3) All humans are mortal
So, (4) Socrates is mortal
the predicate of the ultimate conclusion (4) is 'mortal'. This would mean that you would start with (3) since it also contains 'mortal'. The other term in (3) is 'human' so (3) is paired with (2). Thus the first conclusion would be
(5) All philosophers are mortal
In turn, (5) would form the final syllogism with (1).
D) If you create an invalid syllogism before reaching the ultimate conclusion and no valid syllogism is possible with its premises, then return to step two to reorganize the sequence of syllogisms.