When one talks writes or thinks about concepts one forms assertions (also known as propositions, statements or claims). Assertions are judgements of truth (as opposed to judgements of goodness or beauty etc.). When one asserts, one indicates or judges "this is true". These judgements are usually about relationships between concepts or between concepts and reality. Assertions are always either true or false. Oddly, assertions do not have to be asserted; they may also be merely expressed or considered. In believing something one asserts an assertion at least to oneself. The positions we hold on various topics are assertions. If we are to think critically about our beliefs and the positions of those around us on any topic, then, we must pay careful attention to what is really being asserted. Unless one understands what is being asserted how can one know whether one agrees or disagrees?

We use declarative sentences to communicate or stand for assertions. Other kinds of sentences (for example: questions, commands or exclamations) do not have to be either true or false. Different sentences (for example sentences of different languages) can convey the same assertion. The actual physical marks or sounds used to represent sentences may be called sentence tokens. If a more general concept is substituted for a narrower one or vice versa, the two sentences do not stand for the same assertion.

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To determine whether two sentences convey the same proposition:

An assertion can assert or express more than one assertion. Conjunctions (here meaning any logical connective) are terms used to join assertions into more complex ones. When 'and' is used both the joined assertions are themselves being asserted. When 'or' is used, neither of the joined assertions is itself asserted, although a relation between these propositions is asserted. Similarly when 'if . . . then . . . ' is used, the component assertions are merely expressed, but a relation between them is asserted.

The use of commas can make all the difference between what is being asserted. If I say that my students who study hard will get A's, I am only asserting that the subgroup of my students who study hard will get A's. On the other hand, if I say that my students, who study hard, will get A's, I am asserting both that my students (all of them) study hard and that my students (all of them) will get A's.

Terms indicating mere expression of an assertion (or denial)
Terms indicating assertion of an assertion (or denial)
is convinced
is aware