Categorical Proposition Calculator

This tool should help deal with most questions asked about a categorical proposition. It will also help in evaluating immediate inferences by various methods.

HINT: You should print this and step through it with the Applet before you.

The applet consists of a large panel with two columns of labels with white text slots on the right. To the right is a tool bar with six buttons. And at the the bottom there is a Venn diagram template with white text slots on either side.

• To enter a proposition:
  • Click on the button, 'Enter', on the toolbar.
  • Click in the text field of the dialog box.
  • Enter the quantifier. It can be:
    All,
    Some,
    No
  • After a space any letter to represent the subject term.
  • After a space enter the copula. It can be:
    are
    are_not
  • after a space enter a letter to represent the predicate term.
• Example:
  • All philosophy professors are academics with doctorates from accredited institutions.
  • This should be entered as:
  • All P are A
  • Where 'P' is a place holder for the subject term:
  • "philosophy professors"
  • And 'A' is a place holder for the predicate term:
  • "academics with degrees from accredited institutions."
• Click the 'Accept' button on the dialog box before the 'Close' button so the parser can check whether the proposition is well formed.
• The proposition will appear in the text slot to the right of the Venn diagram.
• To get answers to questions often asked about categorical propositions, click on the label to the left of the blank, white text slots.
• Buttons on the toolbar:
  • Clicking the 'Venn' button will show the diagram for the proposition.
  • Clicking the 'Qual' button will change the quality of the proposition.
  • Clicking the 'Quan' button will change the quantity of the proposition.
  • If you want to calculate the values of the inferences, from converse to subalternation, assuming what you entered is true---pass the mouse over the 'True' button.
    • If the proposition, All P are A, is true then its:
      • Converse is unknown.
      • Obverse is True.
      • Contraposetive is True.
      • Contradiction is False.
      • Contrary is False.
      • Subcontrary is Unknown.
      • Subalternation True.
  • If what was entered is false, pass the mouse over the 'False' button to get the inferences from converse to subalternation.
• How to enter two propositions: (i. e. the premise and conclusion of an immediate inference.)
• After entering one proposition which appears in the text slot to the right of the Venn diagram, double click the text slot and the dialog box will come back for you to enter another proposition. You will find the premise and conclusion in text slots to either side of the Venn diagram. Single clicking either proposition will make it the active one. A white background indicates the proposition is active and you can get information by clicking the labels to the right of the text boxes. Single clicking any text slot (i.e. converse to subalternation) will send that proposition to the text slot on the left of the Venn diagram.
• HINT: testing immediate inferences:
  • Example:
    • Some scientists are philosophers.
    • --------------------------------------------
    • So some scientists are not non-philosophers.
  • Replacing subject and predicate term with single letters:
    • Some S are P
    • -------------------
    • Some S are not ~P
  • Click the 'Enter' button on the toolbar.
  • Enter the premise in the dialog box. And click the 'Accept' before the 'Close' button.
  • The premise will appear in the text slot to the right of the Venn diagram.
  • Double click the text slot with the premise.
    • The premise will shift to the text slot to the left, and the dialog box will appear.
    • Enter the conclusion and close the box following steps above.
  • Now the premise will be on the left and the conclusion on the right. Click on the premise to activate it.
  • Click on the labels converse through subalternation. Look for the conclusion in the text slots to the right of the labels.
  • NOTE: the conclusion is the obverse of the premise.
  • Place the mouse over the 'True' button on the toolbar. In the text slot to the right of Obverse the conclusion will be replaced by 'true'. This indicates that if the premise is true, the conclusion is necessarily true and the argument is valid.
• DOUBLE CHECK:
  • Click on the premise and then click on the label, 'Boolean Form'. S~P=0 will appear in the text slot.
  • Repeating the above procedure for the conclusion will show that the Boolean forms for the premised and conclusion are identical. Thus if one proposition is true, the other has to be true. Clicking the 'Venn' label for the premise and conclusion, will also show the two propositions to be identical.
  • Another example:
    • All Roman fountains are true works of art.
    • -----------------------------------------------------------------
    • So it is false that no Roman fountains are true works of art.
  • Replacing subject and predicate terms with single letters:
    • All R are T
    • ---------------------
    • (it is false that) No R are T
  • Enter the premise and conclusion following the procedure outlined for the first example.
  • Click on the premise; then click on the labels 'Converse' through 'Subalternation.
  • Look for the conclusion in the text slots to the left. It appears to the right of the 'Contrary' label. No R are T and All R are_not T are, without getting Jesuitical about it, two was of saying the same thing.
  • Now pass the mouse over the 'True' button on the toolbar, and you will see the conclusion replaced by 'false'. The inference is thus valid because it does say that the contrary of the premise is false.