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| In a message dated 10/8/2002 2:58:22 PM Central Daylight Time, a.rosta@hidden.email writes: << ">And you wouldn't say "very much the case", either? "It's very much the case that people are at their most rebellious when in adolescence" -- that sounds 100% normal to me, but it might be a Briticism. >> Even less than "very true" (I can't think of ever doing so). I do say "pretty (much) true" apparently, but I think that is the high side of "sorta", not the low side of "true" (but am not at all sure in the abstract). Back to the example: Joe, 13x16 room (my living room for example, except for where the door is), truth values (-0+), door in the middle of one 16' wall, doorway four inches deep, no consideraton of angles or ideal spots for the moment, just distnaces from the origin. So, the factor making for truth is here first of all a quantity IN the event (6 on some list or other) I think the ideal spot and items related to it are not so -- or not obviously so to me now. In this case, we can assign truth values directly on measures from our origin (center of inside of sill). Let's be unfuzzy(to, oh, 1/16 inch) and say the value of "Joe is in the room" is 0 when Joe's forewardmost (closest to the wall opposite the door -- indeed closest to the door and the origin) body part is more than -4 inches (has not entered -- however slightly -- the doorway) and any further such measure until this hindermost part is more than 0 inches. From there up to the possible max -- a little over 15' (sqrt 233) -- the value is + (koPRON - I do have to take angles into account to this extent: some distances are within the room at some angles but not at others, so the permission to take a distance as "in the room" extends only to the wall:13' straight ahead, 8' to either side and the rest in some probably formulizable pattern). Any positive distance which does not run into or pass through a wall, for, say the hindmost part (nearest the center of the door) gives the sentence a +. All other values for distances from the origin to any unspecified part of Joe's body gives the sentence -. The -0+ are the truth values (1) and are not in the situation at all, but something we use to talk about the relation between the situation and the sentence. We can take the truth values as generating a partition the relevant points, depending upon what the truth value of "Joe is in the room" is if Joe is standing at that point. We can then define operators (called connectives before) , which give, for example + if standing in the original 0 space. More accurately, it gives + if the truth value of the original was 0, for operators work only on the truth values, not on the realities that underlie them. So they keep the same paritition, merely changing the values assigned for being in that space. These are similar in some respects, but very different conceptually, are modified claims. The go back to underlying reality and change the partition. For example, "Joe is sorta in the room" would likely be true through most of the original 0 section, but might extend a bit further on the plus side (and the -, for that matter) -- or it might cut out some parts. In any case, it would probably creat a new division in both the + and - blocks , the 0 valued spaces on "sorta". And the remainder of + and - space now are -. And this region can be subdivided yet further by further modifications of the sort And describes, each giving a new partition into -, 0, and + spaces. And the other original blocks can be similarly subdivided by modification. But, because this is a tivalent logic, only three blocks can be used directly at a time. However, we could also start out with all the subdivisions in place and create the active divisons in each case by uniting the various small blocks into into the three functioning in a given case. If each subdivision is given a descriptive phrase, we could also speak directly of Joe being in one section rather than another: + if he is in that section, 0 if in one of the adjacent sections up to some agreed distance, else -. The problem here is that these three approaches are likely to sound very much alike, though conceptually very different -- and giving different truth values in many cases. Operators merely change truth values around with in a given partition. Modifiers set up new partitions, more or less systematically related to the original ones. The third pattern is a sort of modification to be sure, but goes back to the underlying reality -- as maximally partitioned -- in a fairly direct way, close to that of actually saying "Joe is 11' north northwest of the origin" (which is another approach to the same reality, but partitions on a very different principle: the rules about how close to an accurate locating counts for how much, and so not a modification of the original "in the room" scale). The same thing seems to happen if the ground for truth is not some physical measure (some quantity in the situation) but, say, a proportion of an idealization. To take somehting like Parkinson's perfect spot in a room (I forget the details but the following pattern is of thr right sort). Although proximity is a factor here, it is not the only one -- even very close places beyond The Spot, receive lower values that some others the same distance away but closer to the door. The Spot is (as I recall -- no that it matters) on an "oval" (a standard race track, really), about the largest that can be incribed in the room without getting "too close" to any wall (a major standing sideways at brace makes a nice measuring rod - the oval just misses him if the other shoulder is touching the wall). It is about 1/8 the track to the left of the door. Standing at The Spot, one is perfectly in the room, moving away from it ones attainment drops rapidly (let's go with percentages, if we need an example. So at the spot is 100%). The drop is more precipitous toward the corners, slightly less toward the center of the room, and markedly less along the track. Indeed, the best way to measure a place is along the track to the nearest point and then to the place in question along a rapidly devaluing line, since points quite far away are markedly more valued than nearer points off the track (certainly those on the far turn from The Spot are much more "in the room" than points in the center). Of course, the value drops once through the door and quickly gets to nearly 0 outside the room -- but not too quickly to give value to late comers, as it were (though not much: the theory of The Spot is that that is where the most important person will be 45 minutes into a party, the other reasonably important people will have arranged themselves in order along the proper way to move at a party, the misfits will have been spun off the track -- either centrifugally to the corners for the socially inept or centripetally for the climbers, while almost anyone who is not here yet is probably too insignificant to count -- and are likely to still be around 90 minutes into the party). The door, where peole can be held up in various irrelevant ways, and the bit of track between it and The Spot, where otherwise proper early arrivals will have gotten to are problem areas and have to be given some sort of neutral value, at least tentatively. Despite all this folderol, when it comes to using this structure to assign truth values, the procedure is the same: some precentages are taken as marking the lines between "in the room" (+) and "sorta in the room" (0) and not in the room (-). Or, as seems more likely here, we may start with a grand partitioning of the percentage scale into discrete chunks "REALLY in the room, " "very in the room, " and so on down to "not noway even possible to think of as in the room." The various truth partitions then are made by combining these smaller segments in appropriate ways. Of course, it is still possible to go behind these partitions and look directly at percentages (the clearest {ni} around in all of this). After all the details, the upshot is that the basic situation, Joe in the room, gives rise to a number of factors that can be used to assign truth values to the claim "Joe is in the room." These factors get partitioned into n groups (for an n-valued logic), one for each values. Operators then create new sentences which get new values on the basis of the sme partition. Modifiers make new sentences which require new partitions that keep some connection with the original ("really in" is going to be a subdivision of plain"in" for the most part, and so on -- but the - partition for "sorta in" is going to contain parts of both the original - and the original +). And it is always possible to go to the underlying data and comment with these directly "Joe is further in the room than Charlie" even though both "Joe is in the room" and "Charlie is in the room" get the same truth value -- and indeed all the modifications that have so far come along give the modified forms the same value. After all, Charlie is 11' 3.5" inches from the door (or 85.35%) and Joe is 11' 3.6" (or 85.37%) Now, what was the question again? Oh yes, what does "more true" mean? There is a modification or a direct report of factors on which it gets a better truth value or more of what makes for truth. |