Examples of using Material conditional in English and their translations into Portuguese
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This is called material, conditional life.
However, it is also a counterexample to modus ponens for the material conditional of LP.
But when we are in the material, conditional life, we forget this, hmm?
The material conditional does not always function in accordance with everyday if-then reasoning.
But they do not understand that this material conditional life is always miserable.
Unlike the material conditional, an indicative conditional does not have a stipulated definition.
So association of material attachment means implication in this material conditional life.
The only difference from material conditional is the case when the hypothesis is false but the conclusion is true.
This truth-functional interpretation of implication is called material implication or material conditional.
A further problem is that the material conditional is such that(P AND¬P)→ Q, regardless of what Q is taken to mean.
What is important to the paradox is that the conditional in classical(and intuitionistic)logic is the material conditional.
Neither conjunction, disjunction, nor material conditional has an equivalent form constructed of the other four logical connectives.
Take Kṛṣṇa prasāda and hear some nice philosophy from Bhagavad-gītā, andtry to rectify your material conditional life.
It is logically equivalent to the material conditional of classical logic, combined with the necessity operator from modal logic.
Prabhupāda: Kṛṣṇa consciousness is already there in everyone's core of heart, but due to one's material conditional life, he has forgotten it.
One problem is that the material conditional allows implications to be true even when the antecedent is irrelevant to the consequent.
One approach is to choose a"minimal" set, and define other connectives by some logical form,like in the example with material conditional above.
They are true because a material conditional is defined to be true when the antecedent is false regardless of whether the conclusion is true.
A f B is thebinary relation A requires B, i.e. A materially implies!B. All entailment in the axioms is material conditional.
Another issue is that the material conditional is not designed to deal with counterfactuals and other cases that people often find in if-then reasoning.
Some logicians, such as Paul Grice,have used conversational implicature to argue that, despite apparent difficulties, the material conditional is just fine as a translation for the natural language'if… then….
In most logical systems,negation, material conditional and false are related as:¬p⇔(p→⊥) This is the definition of negation in some systems, such as intuitionistic logic, and can be proven in propositional calculi where negation is a fundamental connective.
Redundancy===Such logical connective as converse implication← is actually the same as material conditional with swapped arguments, so the symbol for converse implication is redundant.
Therefore the whole problem is that we should give up our material conditional life, and in Kṛṣṇa consciousness we should try to elevate ourself to the spiritual platform and thereby be promoted to the kingdom of Godhead, yad gatvā na nivartante tad dhāmaṁ paramaṁ mama(BG 15.6), where going, nobody comes back to this miserable world.
Such a logical connective as converse implication"←" is actually the same as material conditional with swapped arguments; thus, the symbol for converse implication is redundant.
The equivalence thesis states that indicative conditionals and the material conditional have the same truth conditions i.e., they are false when they have a truth antecedent and a false consequent, but true in any other circumstances.
Although the strict conditional is much closer to being able to express natural language conditionals than the material conditional, it has its own problems with consequents that are necessarily true(such as 2+ 2 4) or antecedents that are necessarily false.
Corresponding conditional Counterfactual conditional Indicative conditional Logical consequence Material conditional Graham Priest, An Introduction to Non-Classical Logic: From if to is, 2nd ed, Cambridge University Press, 2008, ISBN 0-521-85433-4, pp. 72.
Feasibility study on exporting construction materials Conditional loan to Saint Vincent and the Grenadines.