Discussion of the main problems in the project

Here we discuss the different problems occuring in the progress of development of the pw project. Assuemd is here, that you allready have read the introduction or tested the program. The problems will be presented on an intermediate level (the recent low level description was quite unreadable). But for a detailed level presentation the room here isn't appropriate.
The numbering of topics, subtopics and further detail explenations is thus: 1.), 2.)...1.A), 1.B)...2.A).. and the details in a), b),....


Content:

Introduction and Startup conditions
Logic
Natural language processing


Introduction and Startup conditions

Presumptions at pw start:

For the first computational step in a consitsnevy computation for the, or any choosen and evaluated set of sentences, there must be some requirements specified. Some of them can be set, others not or not exactly. These all are the starting presumptions. Bevor we start with this, we should clarify, which kind of sentences we want to check. As we want to check 'any' kind of sentences, these might be simple assertions, parts of compositions or even whole philosophical books. So we should assume, that they are written in some spoken natural language. We restrict those languages (for now) on these, which can be expresssed written in a sensefull way with the default ASCII character set (i.e., english version without all special signs like german ue, oe,...). Further we assure that the set of sentences is potentially open. That means, anyone can contribute with it's own topics, sentences or versions. That means especially:
I. these sentences aren't restricted beforehand according to any logical or formal schema (except the rules stated in the rules PWR)
II. to be able to analyze such sentences according their consistency, one must/should formalize them in a defined way
III. the/all sentences have to be in some context, as in natural languages most often sentences without a context have no real meaning at all
Example: 'Peter is riding his bike.' You may ask who is that? Why do I tell you this? What do you expect me to do with this information? And so on...If I introduce it with. 'I would like to tell you a funny story about a neighbor I just heared.' zou would be perfectly prepared and awaiting the story...


Which starting assumptions should we chose then? The problem to be discussed now targets the question, which logic should, must or could be choosen from the start? This isn't a problem of the later formalized sentences only, but for the natrual language ones right from the begining.
Example: is the sentence 'Peter is riding his bike, because he is upset.' in a context true, false or perhaps undecidable?. There are some possible variants and extremes to introduce the base logic:
1.) One can allow to chose some (any), but a distinctive logic (like the standard two-valued) and we allow the user, to chose a different logic, or at least some different logic for a subset of choosen sentences
2.) One defines no logic at all (the natural language also has no 'indicator' which (see last example) when a sentence is asserted, i.e. if it is according to classical two valued logic or anything else)
3.) One defines parts of logics beforehand and let others be defined for the consistency checks later


Which problems can be derived from the variants and why we chose variant 3 and which are the consequences ?:
1.A) a choosen logic might have the effect, that other, later choosen logics might not be comaptible with the start logic. If this might be the case, for any choosen logic given berorehand, is a part of pw investigation itself, i.e. just by chossing a specific logic one might narrow the result of the consistency computation in a non-appropriate way, see the discussion in pw S371 (RO for now). As this is an open problem we don't choose the approach of a given logic beforehand for 1BR.
1.B) the natural language has, as told above, no indicator under which logic an assertion is made; thererofore it makes not much sense, from an intuitive approach, to set any arbitrary one
1.C) Topic 1.B) might be a point of discussions (if for example someone is addicted to a special logic), but formaly, according to quite actual investigations, no (formal) logic has a special status, i.e. all are formally equal; see N. Rescher L18 in pw's reference.


2.A) If one doesn't define any logic, one has basically no chance on any other base, except plain intuition, to compute the consistency on a choosen and evaluated set of sentences. Furthermore there is lacking a consistent basis to evaluate the sentences in the same manner (one might perhaps chose for one sentence the value undecidable as a truth value, which might be not really choosable for others without investigation, if this is reasonable, allowed or not).
2.B) especially those sentences, which are choosen to provide a better formal basis for later consistency computation steps (see DPWR), would lack such base logic too. So all possible formal steps later on are also vague.
2.C) with 2.B) we don't say, that we cannot simply handle the rules, which define, how the further computation steps of the sentences should be processed (as part of the sentence set to be evaluated). If this is possible or should be done, is an important part of the pw project to be clarified in (see S371). But when all these rules including their logics would have been defined in front, we would have the same problems like in 1, just one level higher ! For the question, if there exists a predefined metalogic (with which we define all object logics), there holds the same as mentioned above for the object logics. The broader question, what all 'logics' have in common, to be a 'logic', we don't discuss here.


Now it's the question, if we can solve the problems with the variants 1 and 2 ? Here the choosen solution with some remaining questions and problems:
3.A) Basically we chosed a variant which entails all base evaluations which are discussed in philosophical seminars to this topic: true, false, undecidable and not evaluable, but without any further specification/interpretation according their meaning or definition, i.e. all these values base on the short description in PWR and the users intuitive understanding of their meaning and usage. That means that the starting logic values are defined, but not interpreted in detail. This interpretation work has to be done by the user in the following step(s) and all this, without eliminating the possibbilty to compute the first step of consistency check (the 1BR).
3.B) One could have also choosen simple true/false for the starting logic, but I wanted the user to target this issue right from the start. The general further working approach should not be effected by this selection (which according to 2.C is still to be verified, but this would presumably hold for either starting logic choosen!).
3.C) In the history of the development of the pw program, there was a version, where the start logic was an interpreted and defined one. The consequence was, that some sentences couldn't be evaluated and thus got a new exception status (see PWR30 T1-9), because those couldn't be really evaluated according to this default logic. Because of this, the starting logic was revised again in the sense of 3.A, but those exception rules still exist and can be used in case. Any problems due to this, will be handled in later versions and from 2BR step on.
3.D) The problem 2.B) has following direction: According to Tarskis investigation of Truth (in formal languages; L17 in pw's Lit reference), every language which has the possibilty the assert anything concerning it's own language, needs a separate metalanguage (to avoid antinomies). But when our set of rules is a part of the evaluated sentences, this problem might occur. An alternative approach is given by paraconsistent logics (more see below in chapter Metalogics%%L). Which of both variants one choses is of more basic nature then chosing a base object logic and cannot be defined beforehand too, as philosphical discussion on this is work in progress!
3.E) In a detailed view, scientific publications seldom reflect their logical base of argumentation (texts to the logical base of quantum physics are an exception here, but are nevertheless not really successfull in their area). How should texts then be handled according to their base logic (if one want´s to chose another or partial, then the pw base logic)? Which logic should hold? The user has to decide this by himself!
3.F) Another, upper category topic is, which types of sentences we want to distinguish or categorize? In pw we chose WW, EW and DW (see PWR20f.). DW are definitions which are used extensively in sciences, aren't t/f decidable, but affect the evaluation of true/false sentences (the mathematical correct definition of i^2= -1 versus i=sqrt(-1) as an example). But many sentences are, practical philosophy not taken into account here, recommendations on actions, as 'interpret the author xy in such a way, interpret the meaning of the the word xz in such a way that..., becuase its better' ...Both variants aren't t/f decidable and both are different. In pw we regard such sentences as 'should' sentences (EW), they present something that has to be decided according to if something should be (done, taken as, ...) or not. pw uses those three base types (including t/f/...) and allows the addition of others or removing of one of them (except of assertions).
If sentence types EW and DW really need their own logics should be also decided in time of the first computation step! For 1BR this is just assumed without discussion in PWR. 3.G) An important following problem of the approach 3 is, that logical operators without an exact interpretation of their meaning (what does it mean 'undecidable'?), cannot be reagarded as defined. What follows is, that the sentences and relations in pw at 1BR are underdetermined. The evaluations of the relations rely consequently on the users intutitive argumentation when evaluating them ( its own sentences together with all others).
But every user can chose the interpretations of sentences and relations for himself. The consistency in doing so, gets then, at least partly, evaluated further in the next computation step:
The question, if the user does this all consistently in any meaning is postponed to further checks, including backtracing from 2BR back to 1BR users evaluation settings (more see below).
3.H) The above mentioned necessity of a given metalogic (with given uninterpreteted object logics at the beginning) was hopefully resolved quite elegantly for 1BR, see PWR29 !
3.I) On the other hand it showed up, that the, or a setting of a given logic for sentences for 2BR, or the possible setting of the possible XW values for a sentence (LV7 in 1BR still TBD), has its own problems ...This must be investigated case by case first. Often then, even this is not much more clear afterwards and doing this is more a try and error procedure. Why is this such a problem? We'll see by upgrading the 1BR sessions to the next level.

All together, the chosen start restrictions have to avoid some problems without restricting further possibilities. If the chosen ones in pw serve this purpose or other ones would do this or not, is part of the investigation inside the pw project.


Rewriting TS:

In 1BR a/the propositional logic formalization should be already given to support the user when evaluating relations between sentences SE. On the other hand the logics for 2BR will be defined by the user. How can be the TS formulas statically defined when the given logic(s) are not given beforehand? For example the set of available logical opertors may change.
1) We assume only minor changes for the logical formulas given for 1BR allready. An and-operator will be an and-operator in all logics.
2) If, the user has to provide override versions of statical TS versions manually, we let the pw program look always in the 2BR session directory first to get a formula or in case, if there will be possibilities automating this process, we will provide them.
3) Indeed details will occur when getting the project that far (presumably the next pw version!)....


Rewriting TS formulas will also be discussed in the next chapter concerning the exception TS. Both topics belong together.

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