Wilberforce1860 wrote:You are taking "fabricate assertions" a little too seriously.
Wrong. It seems you need me to teach you more elementary concepts.
Wilberforce1860 wrote:By "fabricate assertions" I simply meant how do we "come up with ideas". Whether we believe they are true, or think they might be, or know they are not.
Oh wait, what was it I said in
this post about the proper rules of discourse? Here it is again:
[1] Assertions, when first presented, posssess the status "truth value
unknown".
[2] The purpose of proper discourse is to
remedy that deficit, and assign a truth value to assertions presented.
[3] This is achieved by
testing assertions, to see if they are in accord with extant knowledge. Assertions that cannot be thus tested are useless, as they tell us nothing.
[4] Assertions that
are testable only tell us something
when they are tested.
[5] If the test tells us the assertions are
false, then those assertions are discarded.
Apply those five steps, and the rest follows.
Now, after revisiting those proper rules of discourse, here's another of those elementary concepts you apparently need.
Our ideas generally fall into two categories:
questions, whose initial status is "unanswered", and
assertions. An assertion is
any statement purporting to present substantive knowledge about a given system of interest. The rules [1] to [5] above then apply thereto. Assertions are our first attempts to answer questions, but they only provide
genuine answers thereto, if rules [2] through [4] are applied in a diligent manner. Without said diligent application of those rules to an assertion, that assertion remains indistinguishable from fantasy. This is why, when contemplating the business of ideas in a
rigorous manner, those of us who understand the issues speak of assertions, and the fabrication thereof., because
this is how all our attempts to answer questions begin. But without methods for
testing those assertions, the process goes no further, and those assertions remain forever in the limbo of "truth value unknown".
At the moment, we have two tests that have been demonstrated repeatedly to be reliable. One, demonstrating that the assertion is in accord with observational data. Two, demonstrating that the assertion, where this is possible, is the conclusion of an error-free formal deductive proof. However, in the latter case, epsecial care needs to be taken, to demonstrate that the assertion can indeed bemade the subject of a formal deductive proof in the first place, by careful reference to the axioms and extant theorems of the formal system in question. Not least, because it is easily demonstrated, for example, that logically true statements of the propositional calculus, can have substituted into their variables, a veritable infinity of nonsense statements, without affecting the truth-value of the symbolic expression representing the requisite instances. For example, the statement:
"If the moon is made of mouldy Emmental, than I am a purple banana"
has the form of a material conditional
sensu Quine, and that material conditional has the following truth table:
- Code: Select all
P Q P ⊃ Q
F F T
F T T
T F F
T T T
The expression "P ⊃ Q" is usually read "If P then Q", and Quine, in his text
Methods of Logic, is careful to stress that this does
not equal implication. Implication, rather, consists of a situation where a particular material conditional
is true for all possible input values of the contributing variables, this logical condition being described in his work as
validity. From that text, on page 28, we have (my explanatory notes in blue):
Willard Van Ormand Quine wrote:A truth-functional schema
[namely, an expression involving variables combined by logical operators] is called
consistent if it comes out true under some interpretation of its letters;
[substituting the constants 'true' or 'false' into those variables, to determine the resulting truth-value of the expression, is in this work the initial meaning of 'interpretation'] otherwise
inconsistent.
[in short, a propositional expression is inconsistent, if all possible substitutions of the logical constants into the variables, result in the entire expression being false - to be consistent, only one combination of those constants needs to yield the value 'true' for the whole expression]. A truth-functional schema is called
valid if it comes out true under every interpretation of its letters.
Examples are illustrative here. The expression "P ⊃ Q" is consistent: substituting "false" for P and "true" for Q, results in the entire expression being true, courtesy of the above truth table. The expression"P ⊃ P" is valid: no matter what value we substitute for P, the resulting expression is always true. The expression "P ∧ ~P", where ∧ is the logical AND operator, and ~ is the logical negation operator, is inconsistent: no value of P will make this expression true.
The value of the propositional calculus, of course, is that we can substitute into those variables,
statements possessing a known truth-value, and derive substantive arguments therefrom. Or, in reverse, we can convert statements into symbolic form, substitute the relevant logical constants, apply the method of truth tables (or quicker derivatives thereof such as appear in Quine's textbook), and arrive at a truth-value for the entire statement.
The above example I have provided, however, informs us that being merely
logically true, is no guarantor of
material fact. No sane person would consider my nonsense statement above as being remotely applicable to the real world, yet, despite being utter nonsense, it takes the form of a logically true statement. Which is one reason why particular care is required, before attempting to apply the propositional calculus to any argument couched in natural language, because natural language is replete with ambiguities, that require careful detection and removal before proceeding.
Having indulged this particular tangential diversion, not least because of my fondness for Quine's rigour on the matter, I now return to the matter at hand. Namely, the application of those rules of discourse above, and the nature of assertions. Quite simply, I concentrate upon the detection of
assertions, precisely because of the provisions of [1] in the above list of rules of discourse: mere assertions
do not have a known truth value, regardless of whatever wishful thinking to the contrary the presenter thereof may indulge in. The purpose of rules [2] to[4] is to generate a known truth value, and only once this process is properly completed, does the assertion
cease being a mere assertion, and become a truth or falsehood. This is the process applied here, hence the terms used.
Wilberforce1860 wrote:I was using assertions because that was the wording Calilasseia used. From his context, I thought he meant something more general. My apologies to him if he did not.
See above.