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At least two forms of semanticsIn general, semantics (from the Greek semantikos or "significant meaning," derived from sema sign) is the study of meaning, in some sense of that term. Semantics is often opposed to syntax, in which case the former pertains to what something means while t for the slippery-slope formulation exist: the momentum semantics and the induction semantics.
In the momentum interpretation, the occurrence of event A will initiate a process which will lead inevitably to occurrence of event B. The process may involve causal relationships between intermediate events, but in any case the slippery slope schema depends for its soundnessA logical argument is sound if and only if, (1) the argument is valid and (2) all of its premises are true. Suppose we have a sound argument (in this case a syllogism): :All men are mortal. Socrates is a man. Therefore, Socrates is mortal. In this case we on the validity of some analogue for the physical principle of momentumIn physics, momentum is a physical quantity related to the velocity and mass of an object. Momentum is the Noether charge of translational invariance. As such, even fields as well as other things can have momentum, not just particles. However, in curved s. This often takes the form of a domino theoryThe domino theory was a United States political theory advanced by both liberal and conservative Americans during the Cold War, especially regarding Indochina. It asserted that if one country were taken over by Communists, neighboring countries would fall or contagion formulation. The domino theory principle may indeed explain why a chain of dominos collapses, but an independent argument is necessary to explain why a similar principle would hold in other circumstances. To achieve this one might (for example) establish an abstract model for the terms that occur in the argument, in which the momentum principle obtains. This leaves showing the validity of the abstract model as a separate intellectual exercise.
The other interpretation resembles mathematical induction. Consider the context of making evaluative (or accessibility) judgements (good or bad, permit or deny) on each one of a class of events or situations. Assume these events can be arranged in an infinite sequence
such that for each k, event Ak differs from Ak+1 in a uniform way and the difference between events A2 and A1 is small.
Moreover, the following evaluations are given:
By uniformity, it follows that the difference between Ak+1 and Ak for k=1,2,3, ... is small. In particular, Ak+1 should receive the same evaluation as Ak. Therefore by iterating this process we deduce:
For example, the following arguments fit the slippery slope scheme with the inductive interpretation
Appropriately formulating the semantics of the slippery slope scheme can help in evaluating the soundness of the argument. In the naive presentation as an instance of mathematical induction, the argument does clearly have validity. However, in most real-world applications, including the two given above, this naive semantics fails because the inductive scheme fails for imprecisely defined predicates.
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