You seem to be using logical terminology in a non-standard way. I’m not sure if this has any bearing on your conclusion (though there does seem to be a risk of confusion with ‘causative’), but I thought you might like to learn the standard terminology; its hard to pick up if you don’t have a philosophy background. If we were intended to make some distinction by your usage, I missed it I’m affraid.
The idea of disjunctive arguments is formalized by what is called a logical disjunction. Consider two declarative sentences, A and B. The truth of the conclusion (or output) that follows from the sentences A and B does depend on the truth of A and B. In the case of a logical disjunction the conclusion of A and B is only false if both A and B are false, otherwise it is true… For example, (A(0)∨B(1))(1), or in other words, if statement A is false and B is true then what follows is still true because statement B is sufficient to preserve the truth of the overall conclusion.
Many conclusions follow from {A,B} whose truth value doesn’t depend on the truth value of B—like A, or (Pv¬P). You probably mean that the conjunction (AnB) and the disjunction (AvB)’s truth values depend on the truth values of A and B; you’re confusing conclusions, which are things arguments have, with disjunction and conjunctions, which have truth values. Conjunctive (disjunctive) arguments is simply an argument with conjunctive (disjunctive) premises.
Generally there is no problem with disjunctive lines of reasoning as long as the conclusion itself is sound and therefore in principle possible, yet in demand of at least one of several causative factors to become actual. I don’t perceive this to be the case for risks from AI. I agree that there are many ways in which artificial general intelligence (AGI) could be dangerous, but only if I accept several presuppositions regarding AGI that I actually dispute.
Soundness is a property of arguments, not conclusions, and possibility is a modal notion that you probably don’t want to bring in. I think you mean;
“Disjunctive arguments are powerful because the probability of the conclusion can be higher than the probability of the disjuncts. However, if each of these disjuncts is in fact a conjunction, then the the disjuncts are a lot less probable than they might appear, which makes the conclusion a lot less probable. You might try transforming the premise into conjunctive normal form to see how conjunctive the argument really is.”
By presuppositions I mean requirements that need to be true simultaneously (in conjunction). A logical conjunction is only true if all of its operands are true. In other words, the a conclusion might require all of the arguments leading up to it to be true, otherwise it is false. A conjunction is denoted by AND or ∧.
Again, you’re confusing arguments and formulas. A conjunction (AnB) is true iff A is true and B is true. The conclusion of a conjunctive argument, (AnB) |- C, is necessarily true if (AnB) is, but might be true even if (AnB) aren’t.
Also, instead of defining ‘presuppositions’, which already has a different role in logic and language (e.g. my saying “The present king of France is bald” might be thought to presuppose that there is a present king of France, if we follow Strawson rather than Russell.), you could simply talk about the logical implications: if A must be true for B to hold, then (A->B) is true.
You seem to be using logical terminology in a non-standard way. I’m not sure if this has any bearing on your conclusion (though there does seem to be a risk of confusion with ‘causative’), but I thought you might like to learn the standard terminology; its hard to pick up if you don’t have a philosophy background. If we were intended to make some distinction by your usage, I missed it I’m affraid.
Many conclusions follow from {A,B} whose truth value doesn’t depend on the truth value of B—like A, or (Pv¬P). You probably mean that the conjunction (AnB) and the disjunction (AvB)’s truth values depend on the truth values of A and B; you’re confusing conclusions, which are things arguments have, with disjunction and conjunctions, which have truth values. Conjunctive (disjunctive) arguments is simply an argument with conjunctive (disjunctive) premises.
Soundness is a property of arguments, not conclusions, and possibility is a modal notion that you probably don’t want to bring in. I think you mean;
“Disjunctive arguments are powerful because the probability of the conclusion can be higher than the probability of the disjuncts. However, if each of these disjuncts is in fact a conjunction, then the the disjuncts are a lot less probable than they might appear, which makes the conclusion a lot less probable. You might try transforming the premise into conjunctive normal form to see how conjunctive the argument really is.”
Again, you’re confusing arguments and formulas. A conjunction (AnB) is true iff A is true and B is true. The conclusion of a conjunctive argument, (AnB) |- C, is necessarily true if (AnB) is, but might be true even if (AnB) aren’t.
Also, instead of defining ‘presuppositions’, which already has a different role in logic and language (e.g. my saying “The present king of France is bald” might be thought to presuppose that there is a present king of France, if we follow Strawson rather than Russell.), you could simply talk about the logical implications: if A must be true for B to hold, then (A->B) is true.