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Sentential Logic (Plz help)

  1. Sep 25, 2004 #1


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    I'm having a tough time determining wether a set of sentences is or is not consistent. I believe the criteria to be that all sentences in the set must be able to assume a True value at the same time. Here are some single sentence sets and my assessment of their consistency. (Mighty thick)....

    Today is Monday. consistent, it could be Monday (its Friday right now)
    That is a Ford. consistent, it could be a Ford (It is really a GM)
    Okay, so far so good.... now, here's where it starts to grab me wrong...
    Plato is dead. Consistent, he could be dead... but that leads to...
    Plato is alive. Consis... wait, Plato IS dead, has been for a while, but,
    consistent? Even if false in the real world?? Could he be alive?
    Help me Obi Kenobi
  2. jcsd
  3. Sep 25, 2004 #2
    Plato lives with Elvis in Carbondale, Ill.

    Sorry, couldn't resist. Wish I could be of more help. :0)
  4. Sep 25, 2004 #3

    Doc Al

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    Sounds good to me. A set of sentences are consistent if it is (logically) possible that they are all true.

    I don't know what it means for a single sentence to be consistent. (Consistent with what? :smile:) Consistency must be applied to two or more sentences taken together.

    Two of your example sentences (Plato is alive. Plato is dead.) are obviously inconsistent, since they both cannot be true.

    And just because sentences are consistent, doesn't mean they are true. "Today is Tuesday" is logically consistent with "Doc Al is a genius", but, sadly, both are false.
  5. Sep 26, 2004 #4


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    Sentential (consistency)

    Tom: Aha! Some meat. If a known and irreversable falsehood is consistent with any other sentence, it must be consistant with itself, leading to the con sistancy of the set of sentences having Plato is alive. as its member.
    I think my only error now may be that I think a set of sentences may contain a single member.
    (I still have trouble accepting the possibility of the consistency of a statement which cannot be true in the real world)
  6. Sep 26, 2004 #5


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    This is not the error, your error is treating consistency of a sentence as something absolute rather than relative. It's kind of like saying a number is bigger, or smaller, or equal to.. And not saying in relation to what.

    Earth is flat. Earth is a sphere.

    This is inconsistent.

    Earth is flat. Earth is big.

    This is ok.

    It doesn't matter if it's true, if this sounds inconsistent to you, it's probably because you're automatically adding in the "earth is not flat" sentence in your mind :wink:
  7. Sep 27, 2004 #6
    Logically consistent statement would not limit the boundary of consistency to a general term.....it must penetrate the atomic depth to uncover it. The Logical structure of this sentence is:


    Therefore, the sentence is already logically conistent. It has no relation to Friday. You are trying to mislead your audience.

    This logical structure of this is:

    That(Car(Ford(Any known Ford's model)))

    Whether GM is one of Ford's model or not, the sentence is already logically consistent, even without a specified Ford's model

    The logic that governs historical reports can only be based on the trust of history and any science used to verify historical accounts. So any statement supported by a combination of these should be equally held to be logically consistent. The statement must take account of and quantify the temporal, spatial, object and subject terms in the same measure as the sentences of the above types with demonstratives. If these terms are general in scope, then their atomic depths must equally be infiltrated as shown above.
    Last edited: Sep 28, 2004
  8. Sep 28, 2004 #7
    If the logic of the two sentences fail on your own part to ply the path of consistency, when brought into a conversation, the built-in devices in the Conversational Theory of Truth would pick any intervening logical inconsistencies up, reverse and divert them to the path of consistency. The Conversational Theory of Truth is a boundary of consistency....and very good at this.
  9. Sep 28, 2004 #8


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    Some of the explanations here appear a bit confusing, but the notion of logical consistency is a pretty simple concept. A given set of propositions is logically consistent if no contradiction arises from assuming that all of them are true. A contradiction is something that assigns conflicting truth values to the same proposition (i.e., saying that A is true and A is false is a contradiction). So if two or more propositions contradict eachother, then they collectively 'disagree' about the truth value of some proposition, and so they are inconsistent about how they 'evaluate' that proposition. Logically consistent propositions do not contradict eachother.

    For instance, take the following propositions:

    P1: A -> B
    P2: A
    P3: ~B

    These propositions are not logically consistent, because they contradict eachother about the truth value of B. Assuming that A -> B and A are true, B should be true as well. But P3 says that B is false. Thus, we have derived a contradiction; we have shown these propositions to be logically inconsistent.

    It's true that set of sentences can contain only a single member. However, the notion of logical consistency of a set of propositions is meaningless without at least 2 propositions. Loosely speaking, logical consistency vs. inconsistency is all about agreement vs. disagreement among propositions about the truth value of some proposition, and you need at least two propositions to have an agreement or a disagreement.

    Logical consistency doesn't have anything to do with what is true in the real world. It's more like an abstract operation on a set of propositions. If we assume that a set of propositions are true, and assuming that they are true does not lead to any contradictions, then they are logically consistent, regardless of whether or not they are true.

    For instance, let P1 be "the sun is purple" and let P2 be "the moon is green." These are both false in our world, but they do not 'disagree' with eachother about anything, so they are logically consistent (or if you prefer, logically compatible). Now let P3 be "the sun is green." P1 and P3 disagree about the color of the sun; they are incompatible; they are logically inconsistent. It doesn't have anything to do with the actual color of the sun.
    Last edited: Sep 28, 2004
  10. Sep 28, 2004 #9
    The notion of Logical Consistency needs a revision .........infact, it's more than well overdue!
  11. Sep 28, 2004 #10


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    What kind of nonsense statement is that?
  12. Sep 29, 2004 #11
    Perhaps it is.....I am not talking about THAT Logic! Stick to your known procedure. There is nothing wrong with that. I am referring to the one that deals with the real world, not a fantasy world.
  13. Sep 29, 2004 #12


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    There is no 'fantasy world logic' vis a vis 'real world logic.' There is just logic, a family of abstract formal systems which nonetheless can have applications in the real world. When using logic to make inferences about the real world, it is important to check that the inference is sound, i.e. that the axioms are empirically shown to be true. Other important aspects of a logical argument, such as validity and consistency, are no less important than soundness in deducing true propositions about the real world, but they are sufficiently abstract concepts that they do not rely on the actual truth or falsity of the axioms in order to hold. The soundest argument in the world will go astray if it uses invalid reasoning, and likewise we can reason validly even if our argument is unsound.
    Last edited: Sep 29, 2004
  14. Sep 29, 2004 #13
    Then could you be one among many who assume that this remains true even after humanity may have gone?
  15. Sep 29, 2004 #14


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    Philocrat, how does logic not apply to the real world?
  16. Oct 1, 2004 #15


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    I think he's saying, logic does apply to everything but it doesnt have to apply to everything, ie. I'm traveling 10 million times the speed of light right now. And I could be, but like said before if it isnt relitive its not true. but the sentence its self is logical in structure, it can give a window into an idea, but these windows are as vast as they are chaotic, poetry for example. half the time we think we know what a person is saying based on our own experiance but to know what the author really wants to protray cannot be said unless asked.

    what if I said," I'm traveling 10 million time the speed of light by saturn" it could be true but anyone in thier right mind in this day know's I'm not. but what happens if its 10,000 years later and find that souls do exist at 10million c and saturn is thier home (hehe wow). Letters, words, and sentences are vast complex systems 3 dimensions deep to one consept of language.

    1, aoiwejrhlaclj oiaslklehoih
    2, Hi I am sitting down.
    3, I once sneezed and blew myself off the planet and was in orbit for 15 days.
    4, The end.

    4 is funny for some reason its the only sentence that will alow no subject, and we get away with it, because the end is the begining of another story.

    This is a really odd topic, good thou.
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