Validity of a simple logical argument

Discussion in 'General Philosophy' started by Speakpigeon, Jan 23, 2019.

?

Is the argument valid?

Poll closed Feb 22, 2019.
  1. No

    54.5%
  2. Yes

    45.5%
  3. I don't know

    0 vote(s)
    0.0%
  4. The argument doesn't make sense

    0 vote(s)
    0.0%
  1. Write4U Valued Senior Member

    Messages:
    20,069
    And what if there is a possible situation in which all the premises are true but the conclusion is false.
    Which is what we have here. If the conclusion is that an elephant is logically a giraffe, there is a flaw in the premise, if not in the logic. Based on demonstrable evidence, the argument is invalid, either way.

    Can this be simulated with a mathematical analogy? What happens then?
     
    Last edited: Jan 24, 2019
  2. Google AdSense Guest Advertisement



    to hide all adverts.
  3. Yazata Valued Senior Member

    Messages:
    5,902
    If the premises can all be true and the conclusion can still be false, then it wouldn't be valid.

    For the purposes of discussion, let's accept this definition of validity: 'An argument is valid iff there is no possible situation in which all the premises are true but the conclusion is false'.

    If the premises are mutually self-contradictory, then there's no way that the premises can all be true. Hence this definition of validity is satisfied whenever the premises are contradictory.

    If the premises are mutually contradictory, it doesn't matter whether the conclusion is T or F. It's still going to be a valid inference either way.

    So when we define validity this way, an argument with mutually contradictory premises will always be valid no matter what is derived from it. It doesn't matter the least bit what the conclusion is. It could be anything.

    'P & ~P => Invisible pink unicorns exist' is a valid inference!!

    'P & ~P => Sarkus is the Queen of England'!! (I always suspected it...)

    (Notice that while each of these arguments is made formally valid by the contradiction, for exactly the same reason they can't be sound.)

    Apparently lots of logicians don't like this state of affairs. But it isn't all that simple to get rid of it. Quite a bit of the work of professional logicians in the 20th century has been devoted to these kind of problems. (Above my pay grade.)

    Don't let the names mislead you. In real life, the thing referred to by the word 'elephant' obviously isn't the thing referred to by the word 'giraffe'. That's interpreting the symbolism and it's the province of logical semantics. But we aren't really concerned with what the words mean, we are primarily concerned with the logical form of the arguments in which they are found. Think of them like letters in algebra. An 'elephant' might be an 'a', a 'giraffe' a 'b' or however you want to do it, such that 'a' might be equated with and substituted for 'b' such that 'a = b'.

    That kind of abstraction is what the formal logic is doing. It's already pulling out the logical form and symbolizing it.

    At least that's how it looks to me right now. (An hour ago I was about to go charging off with a very different view.) As usual, my thinking is a work-in-progress. (Hardhats required.)
     
    Last edited: Jan 24, 2019
  4. Google AdSense Guest Advertisement



    to hide all adverts.
  5. arfa brane call me arf Valued Senior Member

    Messages:
    7,832
    There is that self-referential, unavoidable thing about logic.
    Formally, IF an argument is valid THEN its conclusion is true . . .

    Work backwards with implication (or entailment, if you like), and you hit the wall of axiomatic truth.
     
  6. Google AdSense Guest Advertisement



    to hide all adverts.
  7. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

    Messages:
    10,353
    This isn't correct.
    Take the following syllogism: all humans are 3 metres tall, you are a human, therefore you are 3 metres tall. This is valid, but the conclusion is patently false.
     
  8. Write4U Valued Senior Member

    Messages:
    20,069
    Not if it is known that "a" does not equal "b".

    I understand the correct logical form the argument is presented. But it treats "a" and "b" as undefined and that is not true. a and b are known quantities, they are "defined" on their own merit.
    Oh, I have no quarrel with that statement.

    However, I offered a logical non-valid alternative to that statement of validity;
    For puposes of discussion let's accept the definition of non-validity: 'An argument may NOT be valid if there IS a possible situation in which all the premises are true but the resulting conclusion is false'

    Perhaps logically correct processing, but obviously factually incorrect result. Something is wrong. Garbage in (logically)---> garbage out.

    What we have here is a possible situation in which all the premises are true but the conclusion is false.
    Thus the entire exercise proves my argument of "known different qualifiers" in the argument itself.
    Squid and Giraffe are known and defined unequal patterns and values. Thus A and B are defined and not equal. Both are different from the pattern and value of an Elephant.
    Thus A, B, and C can logically never represent the same value, other than as "commonly" defined.

    So, while all the parts of the argument are logically correct, there existed a possible situation where all the premises are true, but the conclusion is false, because there is knowledge aforehand that A and B are not equal, i.e. At this point we are beginning to cheat.

    Therefore, in view of this logical argument, my posit of logical non-validity should hold, unless we accept that logic has nothing to do with results at all. That logic is merely a process.

    The problem is that mathematically there are processing permissions and restrictions on all values.
    It is mathematically impossible for an elephant to be a giraffe. This is a known quantity and quality.
    Mathematically (algebraic) that sounds so wrong to me, regardless what logic is employed.

    Perhaps I give the term Logic more power that it has.
     
    Last edited: Jan 25, 2019
  9. RainbowSingularity Valued Senior Member

    Messages:
    7,447
    indeed
    i believe
    introduced a 'term' as a rule
    is not binary but is asking for a binary result to a natured double possible result

    deductive argument Vs data for a premise for deductive logic to be of reasoned determinant value... ?

    what is the premise ?

     
  10. Quantum Quack Life's a tease... Valued Senior Member

    Messages:
    23,328
    "This sentence is false" ...a logically valid paradox?
     
    Last edited: Jan 25, 2019
  11. Write4U Valued Senior Member

    Messages:
    20,069
    OTOH, the argument may be considered invalid when valuation (definition) of its terms make all of its premises true, but its conclusion false.

    IMO, "valuation" here means "defined".
    I agree.

    But that would make the OP argument invalid, no? All of its premises are logically true, yet the conclusion is clearly false. This due to the fact that all values are known beforehand and true or false is already known before the argument is codified.

    1. A squid is not a giraffe -------------------- "A is not B"
    2. A giraffe is not an elephant--------------- "B is not C"
    3. An elephant is not a squid --------------- "C is not A"
    4. Joe is either a squid or a giraffe --------- "D is either A or B"
    5. Joe is an elephant -------------------------- "D = C"
    Therefore, Joe is a squid --------------------- "D = A" = False

    { "D = C" in (5)}.... and.... {"C is not A" is already given in (3)}

    error,..........error...........

    Please Register or Log in to view the hidden image!

     
    Last edited: Jan 25, 2019
  12. Speakpigeon Valued Senior Member

    Messages:
    1,123
    Then the argument is not valid.
    According to the definition of validity assumed by Yazata, the only way to prove an argument not valid is to exhibit a counter-example, i.e. a case in which the premises are true and the conclusion is false.
    No.
    There is no case in which the premises are true, therefore there is no case in which the premises are true and the conclusion is false.
    Where is the evidence? Please exhibit a case in which the premises are true and the conclusion is false. There is no such a case.
    You're the specialist of mathematical perfection, you tell us.
    EB
     
  13. arfa brane call me arf Valued Senior Member

    Messages:
    7,832
    Yes, I see that, I think I meant to say "the conclusion is valid".

    IF A THEN B, is a formal representation (hence valid) of two things that can be true or false.
    Although we can apply the formality to real-world examples, in fact the logic says nothing except things can be true or false.
     
  14. Speakpigeon Valued Senior Member

    Messages:
    1,123
    No.
    Definition of validity: If an argument is valid, then if its premises are true, then its conclusion is true.
    Not quite.
    That people accept as being true.
    You're people, right?
    So, please assume your own beliefs.
    Example of an axiom: A and B implies A.
    Instanciation of this axiom: It rains and I am hungry, therefore it rains.
    Now, you're people, so it's up to you to decide if you believe that this sentence is necessarily true or that it is not. But if you do, please assume your beliefs and don't complain.
    An axiom is not a wall. You're the wall.
    EB
     
  15. arfa brane call me arf Valued Senior Member

    Messages:
    7,832
    Not quite.
    I'm just another brick in the wall. You're the plonker who's trying to tell us a brick can think.
     
  16. Speakpigeon Valued Senior Member

    Messages:
    1,123
    And that's just as incorrect. Conclusions are true or false, not valid or invalid.
    Only arguments (or implication, inferences, etc.) are valid or not valid.
    "IF A THEN B", as written, is not valid.
    Logic says that if there is a valid implication in the real world, then if the premises are true in the real world, then the conclusion is true in the real world.
    That has to be very good. The whole of science is based in that.
    EB
     
  17. arfa brane call me arf Valued Senior Member

    Messages:
    7,832
    It so totally is valid. It says nothing at all about some "real world". So there, cabron.

    Yippee!
    It so totally isn't.

    AB
     
  18. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

    Messages:
    10,353
    It's a sentence, not an argument. So logical validity doesn't apply, only the assigning of true/false.
     
  19. Quantum Quack Life's a tease... Valued Senior Member

    Messages:
    23,328
    I quoted the paradox in reference to preceding posts about logicality. The point being that even something seemingly illogical can be proven logical especially when dealing with a paradox.
    For example : Humor is often based on paradox ( contradiction ) and is quite logical. IMO
     
  20. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

    Messages:
    10,353
    What you're missing is that the premises can not all be true at the same time. E.g. If premise 4 is true then premise 5 can not be, and vice versa. As such, it is impossible for the premises to (all) be true and for the conclusion to nonetheless be false. Thus it is a valid argument.
    Or, as you are alluding to but not quite expressing adequately, it is, as it stands, a worthless valid argument due to contradictory premises. The person who put the argument together would need to resolve the contradictions before the conclusion can be considered of use/value.
    It's logical validity in this case is a quirk of the definition, and nothing to do with the relationship between premises and conclusion.
     
    Write4U likes this.
  21. RainbowSingularity Valued Senior Member

    Messages:
    7,447
    im no philosophy student... but yes
    i agree
    it renders the content to be data instead of premise because no premise has been defined.
    (though i freely accept i could be quite wrong, that is just my opinion)

    which IS in the question and the title
    so it remains to be questioned if it is logic or philosophy
     
  22. Quantum Quack Life's a tease... Valued Senior Member

    Messages:
    23,328
    What makes an argument an argument?
     
  23. Sarkus Hippomonstrosesquippedalo phobe Valued Senior Member

    Messages:
    10,353
    Simply put, an argument is a set of premises and conclusion, with the intention being for the premises to justify the conclusion.
    If you just state a premise or the conclusion in isolation, they are just statements.

    Or, being somewhat more facetious... angry disagreement!

    Please Register or Log in to view the hidden image!

     
    Quantum Quack likes this.

Share This Page