By M.J. Cresswell

In traditional discourse we seem to ta1k approximately many stuff that experience appeared mysterious to philosophers. we are saying that there was a hitch in our preparations or that the answer to the matter required us to envision the entire possible results of our motion. So it's going to look that we converse as though as well as eloeks, mountains, queens and grains of sand there are hitches, preparations, suggestions, probiems, and possible results. it isn't instantly visible after we needs to take such ta1k as fairly assuming that there are such to strengthen exams for issues, and one of many initiatives during this ebook is discerning what has eome to be known as ontological dedication, in naturallanguage. one of the entities that usual language looks to make connection with are these attached with temporal and modal discourse, instances, probabilities, etc. Such entities play a crueial position within the type of semantieal theories that I and others have defended over a long time. those theories are according to the concept a necessary a part of the that means of a sentence is constituted by way of the stipulations lower than whieh that sentenee is correct. to understand what a sentence says is to grasp what the realm must be !ike for that sentence to be true.

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So Re! must be replaeed, in a triple-indexed semanties, by two operators, ReA and Re:A. 'ACfUALLY' 43 We ean now express (20) as (31) Relithe economic climate is favourable ~ Refz D 3x(not(actually(richx» & then(richx) & (poorx») (w"WZ,W3) e V(31) iff where w4 is the nearest world to w, in which the eeonomie climate is favourable, then (32) Refz D 3x(not actually(richx» & then(richx) & (poorx» is true at (w4 ,wz,w,). And this will be so iff in every aeeessible from w4 Ws D- (33) 3x(not actually(richx) & then(richx) & (poorx» is true at (WS'w4 ,w,).

With 'and' for 'or' in (13) you get a sentence equivalent to 'NOW' AND 'THEN' 21 (16) There will be a time at whieh everyone now alive will be happyand there will be a time at whieh everyone now alive will be miserable and (16) is no more eomplex than (10). But (13) requires two variables in addition to to: (17) 3tI3~(fo < t l & fo < ~ &V'x([tolalive x::> ([tllhappy x v [~lmiserable x» Sinee disjunetions ean be extended without limit, this means that we eannot put an upper bound on the number of times that have to be simultaneously considered in the evaluation of straightforward English sentences.

The need to make referenee to k is that eertain values must be 'stored' while the operation is taking place. The defmition is 'NOW' AND 'THEN' 33 I will not go through the proof that (64) in conjunction with (53) and (54) gives (63). It is tedious but straightforward. What you will notice is that p*(k) = peO) and p*(k+ 1) = p(n). Since k is chosen so that only indiees less than k are relevant to whether or not a sequence is in a this does not matter. In Chapter 4 I will shew that the modal analogues of now and then really do amount in power to full quantification over worlds, and the proof there given carries over to now and then themselves, and shews that they amount in power to quantification over times.

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