Even though I am fine with the decision to go with classical logic (which Noah just wants to call consistency and reason since we are not admitting the sunum bonum), I was still thinking a bit about paraconsistency after the meeting on Monday (I bet nobody is to surprised). I mistakenly said that admitting to the probability of the axioms of the world views will suffice in lieu of paraconsistency. The reason that I thought this is that both of these measures weaken the axioms. However, they weaken these axioms in different ways and so paraconsitency is really still needed. Here’s the difference: paraconsitency leaves the axioms themselves 100% certain, it only changes the ramifications when the axioms generate a contradictory statement. By the standard of classical logic any set of axioms that is intended to be more than a trivial tautology is almost certain to fail this test. Then, one or more of the axioms will need to be changed. The other solution, which you have taken, is to define you’re the axioms of your world views so vaguely that no logic can be applied to it. This is fine, since the world views are being evaluated as in a court of law, which is not so rigorous and doesn’t scrap everything over a few contradictions. However, is not the way of classical logic, even minus the sunum bonum.
On Nov 16, 10:36 pm, Isparklaria <[EMAIL PROTECTED]> wrote: > To All, > > as usual I have an objection. Specifically I object to criterion > number three. Compelete consitancy is unrealistic. Paraconsitency is > the way to go, with possible dialethias (true contradictios) These > paragraphs from the article this link goes to explains why. Welcome to > the 21st century. > > http://plato.stanford.edu/entries/logic-paraconsistent/ > > Inconsistent but Non-Trivial Theories > A most telling reason for paraconsistent logic is the fact that there > are theories which are inconsistent but non-trivial. Clearly, once we > admit the existence of such theories, their underlying logics must be > paraconsistent. Examples of inconsistent but non-trivial theories are > easy to produce. An example can be derived from the history of > science. (In fact, many examples can be given from this area.) > Consider Bohr's theory of the atom. According to this, an electron > orbits the nucleus of the atom without radiating energy. However, > according to Maxwell's equations, which formed an integral part of the > theory, an electron which is accelerating in orbit must radiate > energy. Hence Bohr's account of the behaviour of the atom was > inconsistent. Yet, patently, not everything concerning the behavior of > electrons was inferred from it. Hence, whatever inference mechanism it > was that underlay it, this must have been paraconsistent. > > Dialetheias (True Contradictions) > The importance of paraconsistent logic also follows if, more > contentiously, but as some people have argued, there are true > contradictions (dialetheias), i.e., there are sentences, A, such that > both A and ~A are true. If there are dialetheias then some inferences > of the form {A , ~A} B must fail. For only true conclusions follow > validly from the true premises. Hence logic has to be paraconsistent. > A plausible example of dialetheia is the liar paradox. Consider the > sentence: This sentence is not true. There are two options: either the > sentence is true or it is not. Suppose it is true. Then what it says > is the case. Hence the sentence is not true. Suppose, on the other > hand, it is not true. This is what it says. Hence the sentence is > true. In either case it is both true and not true. See the entry on > dialetheism in this encyclopedia for further details. > > Automated Reasoning > Paraconsistent logic is motivated not only by philosophical > considerations, but also by its applications and implications. One of > the applications is automated reasoning (information processing). > Consider a computer which stores a large amount of information. While > the computer stores the information, it is also used to operate on it, > and, crucially, to infer from it. Now it is quite common for the > computer to contain inconsistent information, because of mistakes by > the data entry operators or because of multiple sourcing. This is > certainly a problem for database operations with theorem-provers, and > so has drawn much attention from computer scientists. Techniques for > removing inconsistent information have been investigated. Yet all have > limited applicability, and, in any case, are not guaranteed to produce > consistency. (There is no algorithm for logical falsehood.) Hence, > even if steps are taken to get rid of contradictions when they are > found, an underlying paraconsistent logic is desirable if hidden > contradictions are not to generate spurious answers to queries. > > The Philosophical Significance of Gödel's Theorem > Paraconsistent logic also has important philosophical ramifications. > One example of this concerns Gödel's theorem. One version of Gödel's > first incompleteness theorem states that for any consistent axiomatic > theory of arithmetic, which can be recognised to be sound, there will > be an arithmetic truth - viz., its Gödel sentence - not provable in > it, but which can be established as true by intuitively correct > reasoning. The heart of Gödel's theorem is, in fact, a paradox that > concerns the sentence, G, ‘This sentence is not provable’. If G is > provable, then it is true and so not provable. Thus G is proved. Hence > G is true and so unprovable. If an underlying paraconsistent logic is > used to formalise the arithmetic, and the theory therefore allowed to > be inconsistent, the Gödel sentence may well be provable in the theory > (essentially by the above reasoning). So a paraconsistent approach to > arithmetic overcomes the limitations of arithmetic that are supposed > (by many) to follow from Gödel's theorem. > > On Nov 16, 10:32 pm, Isparklaria <[EMAIL PROTECTED]> wrote: > > > > > Steve, > > > Here you go. I see that I had a typo in 3 people’s emails (Steve W., > > Brad and Jason) due to late night (tired) typos in the email > > addresses. Also, in looking at the summary document I noticed that my > > spellchecker had been disabled so there were typos in that document. > > So attached is a spell-checked document that I’m resending to everyone > > on the list. Since I wrote this way past midnight (Wednesday-Thursday) > > it may still have some typos because I haven’t had time to proof it > > carefully, so please overlook any that you see. > > > The document below summarizes our discussion last Monday night and > > some things to be thinking about for our discussion next Monday > > night. > > > Please review this and make sure that you agree that I’ve captured the > > essentials from our discussion accurately and adequately. Our first > > task next week will be to review the attached tentative criteria for > > evaluating the plausibility of a worldview with the goal of finalizing > > our list of criteria. > > > I look forward to seeing you next Monday. > > > Cheers, > > > Steve > > > 1 > > Discussion on the Development of Criteria by which to Evaluate > > the Plausibility Worldviews > > November 10, 2008 > > Introduction > > This document serves as a summary (sort of like minutes to the > > meeting) of the discussion held > > last Monday night. The individuals whose emails are listed below were > > present at the meeting: > > • Jason ‐‐ [EMAIL PROTECTED] > > • Liz (I’m sorry, I don’t know if I’m remembering her name correctly) > > [EMAIL PROTECTED] > > • Michael ‐ [EMAIL PROTECTED] > > • Debbie ‐‐ [EMAIL PROTECTED] > > • Steve W. ‐ [EMAIL PROTECTED] > > • Brad ‐ [EMAIL PROTECTED] > > • Noah ‐ [EMAIL PROTECTED] > > • Trace ‐ [EMAIL PROTECTED] (Trace brought notes from Steve who > > was in England) > > • Steve E. – [EMAIL PROTECTED] > > Steve Ethridge began by: > > 1. Reviewing that, at the previous meeting, Chris had asked him to > > present his idea of > > having the group discuss and try to agree on a set of criteria by > > which the plausibility of > > various worldviews could be evaluated, recognizing that few > > conclusions reach the level > > of 100% certainty or certitude, but that we should be able to evaluate > > them using a > > cumulative case, in the same way that a courtroom makes decisions; > > i.e., “beyond a > > reasonable doubt.” > > 2. Confirming that this was still something that the group wanted to > > do, to which all were > > in agreement. > > Overview of the Process > > Having gained agreement to proceed, Steve then proposed a process for > > the discussion to > > follow, to which the group agreed. This process consisted of the > > following steps: > > 1. Brainstorm criteria. Brainstorming meant to just think about and > > suggest various > > criteria, at first, without (as much as possible) evaluating or > > criticizing the criteria > > themselves; evaluation was to be a later step in the process. It was > > acknowledged that > > during the brainstorming process, it would be necessary to define > > briefly what was > > meant by a criterion, but that the next stage would need to define > > them more clearly. > > 2 > > 2. Define what is meant by each of the criteria in more complete, > > clear terms. This stage > > would involve more critical evaluation of the criteria. > > 3. Critically evaluate the defined criteria to reach consensus on > > which to keep. > > 4. Then, once the group reached a consensus on the criteria and their > > definitions, we > > would pick a worldview and submit it to the criteria, followed by the > > next world view, > > and so on, until all or most of the major ones have been evaluated. > > (Trace wisely > > suggested that we pick a “neutral” one as our first test case, to > > which the group agreed). > > Steve suggested that this process may take several weeks at each of > > these stages and that the > > whole process may take months. Everyone seemed to agree that as long > > as the discussion was > > fruitful we would continue. > > Having gained agreement from the group on this process, Steve then > > presented a few, minimal, > > assumptions that such a discussion implies, to see if the group could > > agree to hold to these > > assumptions. These assumptions were, in no particular order: > > 1. That there is such a thing as truth. The group acknowledged that > > there are various types > > or approaches to truth and agreed not to get bogged down in those > > details at this point, > > but rather to simply agree that, yes, there is “such a thing as > > truth.” > > 2. That we are all honest, ethical, reasonable people and that the > > ethics of belief or > > adherence to a worldview obligate us to search for criteria > > (standards) by which to > > judge worldviews; i.e., standards that can be used to discern the > > truth of a worldview. > > 3. That we should not rule out, a‐priori, the possibility that there > > could be more than one > > valid worldview. Although we may end up concluding that there is only > > one valid > > worldview, our process is to give a “fair hearing” to all of them > > (again, as in a > > courtroom). This requires us to evaluate the belief‐worthiness of the > > various > > worldviews as objectively as possible, meaning that we each have to > > temporarily > > suspend our own presuppositional bias toward our own personally held > > ... > > read more »- Hide quoted text - > > - Show quoted text - --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Memphis Freethought Alliance" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/memphisfreethoughtalliance?hl=en -~----------~----~----~----~------~----~------~--~---
