Sextus Empiricus claims that arguments are invalid if they are redundant. The example he uses, the premise 'if it is day, it is light' is such a redundancy, though I will overlook my disagreement with even that basic premise. Such a premise, in which the conditions follows directly and obviously from the antecedent, is 'invalid'. This backs Stoic logic into a corner, in my view. Empiricus admits this. If a premise is true, then the conditional can be directly deduced, and so it is invalid. If, on the other hand, the premise is false, than it will certainly be invalid as well. How then, can arguments proceed?
The prevailing attitude of the Stoics towards Sophist arguments was to ignore them. Arguments like the Sorites argument, or Little-by-Little argument. A good example is asking how many grains of corn make a heap of corn. By increasing the number of grains one by one, the addressee must eventually choose a number of grains which makes a heap of grain a heap - however, having picked a number, if that amount of grains is reduced by one then the heap should no longer exist. This is a thought-provoking argument, if rather useless, but the Stoics tend to minimize and ostracize the Sophists. It seems to me such an argument is good food for thought and a good mental exercise, and shouldn't be rejected out of hand.
Diodorus and Chrysippus were also engaged in a long argument, essentially about whether a thing can be possible if it never occurs. I think this is fascinating. If something doesn't occur, was it ever really possible? Likewise, if something occurs, was it not a necessity? For an example, I reach to my own history. Was it ever possible for me to attend Harvard? Conventionally, I would say yes. I have enough raw intelligence that I could have exerted myself sufficiently to be accepted there. In a sense, that future was possible. But in a more literal sense, it was never a possibility. As events in my life have borne out, I was not interested in academics until high school. Even then I came nowhere close to exerting myself. In that sense, then, attending Harvard was never a possibility. Sure, qualifying circumstances would change the truth of that statement - IF my past was different, THEN I could have attended. But that restructures the proposition. As Chrysippus noted, however, this outlook tends to remove moral responsibility from the actor. Let's say I cheated on a test in high school, which I did more than once. Sure, I accept responsibility for that. But on the other hand, the confluence of academic pressure, peer pressure, and the course of events to that point made my actions a necessity. To not cheat was possible, but never a possibility.
Yet, the Stoics anguished over holding on to moral responsibility in the face of this argument. I cannot reject such responsibility, even though I agree with the conflicting theory of relative determinism. Obviously, I don't claim the two are compatible.
Chrysippus' argument: "If there is motion without cause, not every proposition will be either true or false, since anything lacking efficient causes will be neither true nor false. But every proposition is either true or false. Therefore there is no motion without a cause. If this is so, everything that happens happens through antecedent causes - in which case, everything happens through fate. The result is that everything that happens happens through fate."
The prevailing attitude of the Stoics towards Sophist arguments was to ignore them. Arguments like the Sorites argument, or Little-by-Little argument. A good example is asking how many grains of corn make a heap of corn. By increasing the number of grains one by one, the addressee must eventually choose a number of grains which makes a heap of grain a heap - however, having picked a number, if that amount of grains is reduced by one then the heap should no longer exist. This is a thought-provoking argument, if rather useless, but the Stoics tend to minimize and ostracize the Sophists. It seems to me such an argument is good food for thought and a good mental exercise, and shouldn't be rejected out of hand.
Diodorus and Chrysippus were also engaged in a long argument, essentially about whether a thing can be possible if it never occurs. I think this is fascinating. If something doesn't occur, was it ever really possible? Likewise, if something occurs, was it not a necessity? For an example, I reach to my own history. Was it ever possible for me to attend Harvard? Conventionally, I would say yes. I have enough raw intelligence that I could have exerted myself sufficiently to be accepted there. In a sense, that future was possible. But in a more literal sense, it was never a possibility. As events in my life have borne out, I was not interested in academics until high school. Even then I came nowhere close to exerting myself. In that sense, then, attending Harvard was never a possibility. Sure, qualifying circumstances would change the truth of that statement - IF my past was different, THEN I could have attended. But that restructures the proposition. As Chrysippus noted, however, this outlook tends to remove moral responsibility from the actor. Let's say I cheated on a test in high school, which I did more than once. Sure, I accept responsibility for that. But on the other hand, the confluence of academic pressure, peer pressure, and the course of events to that point made my actions a necessity. To not cheat was possible, but never a possibility.
Yet, the Stoics anguished over holding on to moral responsibility in the face of this argument. I cannot reject such responsibility, even though I agree with the conflicting theory of relative determinism. Obviously, I don't claim the two are compatible.
Chrysippus' argument: "If there is motion without cause, not every proposition will be either true or false, since anything lacking efficient causes will be neither true nor false. But every proposition is either true or false. Therefore there is no motion without a cause. If this is so, everything that happens happens through antecedent causes - in which case, everything happens through fate. The result is that everything that happens happens through fate."
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