Is everything deducible from a necessary truth itself a necessary truth

Question

I take a necessary truth to be a logical truth : e.g.(1) '[((P v Q) → Q) & P)] → Q'. I'm inclined to say that everything deducible from such a truth is itself a truth but I sense a catch. One possibility that comes to mind is that one might apply 'and' or 'or' introduction to (1) and deduce another proposition, say 'S', which though it necessarily follows from (1) it not itself a necessary truth. 'S' could be a contingent truth or falsehood that necessarily follows but ex hypothesi is not itself necessary, Any ideas welcome. I'm sure this is familiar ground to many of you.

Answer 1

This is too complicated for me to register.

I believe in God

God is truth; logical and necessary.

God is simple.

God is love.

Answer 2

Since you know calculitic logic, you must be familiar with the "analytic-synthetic dichotomy." http://www.thelogician.net/6_reflect/6_B...

"The theory of the analytic-synthetic dichotomy presents men with the following choice: If your statement is proved, it says nothing about that which exists; if it is about existents, it cannot be proved. If it is demonstrated by logical argument, it represents a subjective convention; if it asserts a fact, logic cannot establish it. If you validate it by an appeal to the meanings of your concepts, then it is cut off from reality; if you validate it by an appeal to your percepts, then you cannot be certain of it."

Leonard Peikoff, “The Analytic-Synthetic Dichotomy,” from

Introduction to Objectivist Epistemology; Ayn Rand

"The assault on man’s conceptual faculty has been accelerating since Kant, widening the breach between man’s mind and reality. The cognitive function of concepts was undercut by a series of grotesque devices—such, for instance, as the “analytic-synthetic” dichotomy which, by a route of tortuous circumlocutions and equivocations, leads to the dogma that a “necessarily” true proposition cannot be factual, and a factual proposition cannot be “necessarily” true."

Introduction to Objectivist Epistemology"; Rand

Without resorting to calculus, one of the 15 "valid" deductive syllogisms states (if you use the right mood and figure) that "everything deducible from a necessary truth itself a necessary truth."

Answer 3

Our considered analytical thinking in search of truths falling short of the absolute truth yet to comprehend or attain. The differentiation is gauged by the ability of truth to clarify the complex with ease leaving no room for flexibility or debate.

To draw such conclusive truth rather than deductive random reasoning one must be bold and apply all perspectives, opposing, contrary and intangible. This requires unbiased applied rationale. Constructing truths by the destructuring of possible flawed theories becomes habitual and soon the individual becomes neurologically programmed to think bilaterally.