Venn's equations corresponding with the fourpropositional forms of common Logic.
For the text is rather a vague symbolical expression of a propositional function which is asserted to be true at all instants.
Until this theory was brought forward, there were occasionally discussions as to whether an object which did not belong to the range of a certain propositional function possessed the corresponding property or not.
Now consider a propositional function F[chi] in which the variable argument [chi] is itself a propositional function.
Call it a propositional function; and, if [phi]x be a propositional function, the undetermined variable x is the argument.
A similar theory holds for relations which arise from the consideration of propositional functions with two or more variable arguments.
There is no reason why the propositional form should not be called the Converse by Contraposition, or the Contrapositive Converse, in accordance with traditional usage.
Footnote 5: The mediaeval word for the opposite of a term, the word Contradictory being confined to the propositional form.
This may be more simply expressed by saying that the propositional function "x wrote Waverley and Marmion, and no one else did" is capable of truth, i.
What is meant seems to be this: "A proposition is necessary when it is a value of a propositionalfunction which is true under all circumstances, i.
The first point to notice is that, if any meaning is to be given to the phrase "would be true under all circumstances," the subject of it must be a propositional function, not a proposition.
Thus when it is worth saying that something "would be true under all circumstances," the something in question must be a propositional function, i.
But if we adopt this definition, the same proposition will be necessary or contingent according as we choose one or other of its terms as the argument to our propositional function.
A propositional function is necessary when all its values are true.
Such judgments, therefore, can only be analysed by breaking up the descriptive phrases, introducing a variable, and making propositional functions the ultimate subjects.
Thus the true subject of our judgment is a propositional function, i.
Only propositions can be "true," and onlypropositional functions can be "true under all circumstances.
According to the zigzag theory "definitions (propositional functions) determine a class when they are very simple and cease to do so only when they are complicated and obscure.
A propositional function (that is to say a definition) does not always determine a class.
The different cases of Equipollency, or “Equivalent Propositional Forms,” are set forth with some fullness in Professor Bain’s Logic.
The case is one under the head ‘Greater and Less Connotation’ in Equivalent Propositional Forms, or Immediate Inference.
The sign that results from correlating the mark 'I' with truth-possibilities is a propositional sign.
And it is easy to see that the propositional sign in 4.
I call the sign with which we express a thought a propositional sign.
In a proposition a thought can be expressed in such a way that elements of the propositional sign correspond to the objects of the thought.
So the expression for a formal concept is a propositional variable in which this distinctive feature alone is constant.
For in a printed proposition, for example, no essential difference is apparent between a propositional sign and a word.
Although a propositional sign is a fact, this is obscured by the usual form of expression in writing or print.
The general propositional form is the essence of a proposition.
The propositional variable signifies the formal concept, and its values signify the objects that fall under the concept.
A propositional sign, applied and thought out, is a thought.
The description of the most general propositionalform is the description of the one and only general primitive sign in logic.
The essence of a propositional sign is very clearly seen if we imagine one composed of spatial objects (such as tables, chairs, and books) instead of written signs.
When a propositional element signifies a complex, this can be seen from an indeterminateness in the propositions in which it occurs.
N(E) is the negation of all the values of the propositional variable E.
And a proposition is a propositional sign in its projective relation to the world.
In propositional form it may be stated that catastrophe is attended by phenomena of social psychology, which may either retard or promote social organization.
Put in propositional form it would be that catastrophe is attended by phenomena of social psychology which may either retard or promote social reorganization.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "propositional" in a variety of sentences. We hope that you will now be able to make sentences using this word.
