• Monist
    41


    Mathematics is one of those things social scientists came up with to keep people from getting bored with life in a modern society. So are science, and other branches of story telling. Things to aim for. Go to school, Get a degree. Get a Job. Don't get bored so soon.Per Chance

    Off-topic
  • Per Chance
    21
    What is the relation between the practicality of Base 10 and the necessity of The Law of Identity?Monist

    You'll have to excuse me. I'm not well versed in Logarithms or the Law of Identity.

    Can you explain why you gave the example of our counting system? I completely miss the point.Monist

    I guess i was just fed up of laymen's evoking of mathematical mysticism in philosophy.

    Instead of 'apple' try 'thing'. Saying "a thing" while pointing at the thing does not explain why the thing identical to the thing. It does not explain the relation between the thing and the thing. x=x does, it simply tells that the thing, is itself. The point is, why?Monist


    Such as the above statement/s for example.
  • litewave
    797
    "an apple is an apple", but why? I do not get why any certain thing called 'x', should be 'x'.Monist

    Well, what would be the alternative? A thing that is not what it is? An apple that is not an apple?
  • Monist
    41
    I appreciate all the answers.

    I accepted the risk of being an idiot when starting the topic, and I see the risk is true, as I see answers underestimating the question. Partly it is my fault. My ability to address the problem may be weak because this is not my native language, I will do my best to re-write my question.

    + To establish any knowledge, I have to believe in it
    + I am not able to believe and/or have no ground to build on with certainty.
    + There is some certainty in the language of math itself and is applicable to the world.
    + The basic idea of math is that any value has an identity(is equal to itself). And here the problem for me starts.
    + When applied to the real world: what is, is(even simpler: `being` or `thing`). It seems to me as a good starting point, because to believe anything, you should believe the thing(being) first.

    But then, how do I believe a thing, is a thing.

    Why x=x ?

    If I can explain the necessity of identity, I can prove a thing can exist.
  • Monist
    41
    Well, what would be the alternative? A thing that is not what it is? An apple that is not an apple?litewave

    Why not?
  • Monist
    41
    Your answers are irrelevant, off-topic and arrogant. The laymens goal is to learn, not to hurt you.
  • litewave
    797
    Why not?Monist

    Because if such an alternative existed, it wouldn't exist.
  • Monist
    41
    Because if such an alternative existed, it wouldn't exist.litewave

    I see a conclusion, but no premises. How and why?
  • SophistiCat
    2.2k
    I think you are not giving due attention to the language angle that was proposed in some of the answers. The very meaning of equality and identity in ordinary language already implies self-identity. To question self-identity is not even a metaphysical move - it is meaningless, like questioning the marital status of bachelors. (In math and logic this has to be set out explicitly though - and indeed it is.)
  • Harry Hindu
    4.9k
    Instead of 'apple' try 'thing'. Saying "a thing" while pointing at the thing does not explain why the thing identical to the thing. It does not explain the relation between the thing and the thing. x=x does, it simply tells that the thing, is itself. The point is, why? :-)Monist
    There is no such thing as a thing that has a relationship with itself. Things establish relationships with different things.

    Again I don't even understand the point of your question. I dont understand the differece between x and x=x. Why not just say x? In saying x, you are saying what it is. x=x is just redundant information and therefore useless.
  • Monist
    41
    There is no such thing as a thing that has a relationship with itself. Things establish relationships with different things.Harry Hindu
    Identity is the relationship one thing bears only to itself.: — The Cambridge Dictionary of Philosophy, 2nd Edition, CUP: 1995

    Again I don't even understand the point of your questionHarry Hindu

    Why is identity necessary?

    I don't understand the difference between x and x=x.Harry Hindu

    Simple, x is an unknown value, x=x is the principle that it is a value.

    In saying x, you are saying what it is. x=x is just redendant information and therefore useless.Harry Hindu

    If x=x is useless because it is redundant information, is first-order logic useless as well? Because, it literally depends on this axiom. For every x | x=x
  • Harry Hindu
    4.9k
    Why is identity necessaryMonist
    Does identity exhaust what it is for the thing to be itself? Isn't an identity a label? A label is not the thing. Words are not the thing itself. Are you talking about the thing, or what we call it? Both are different things that have a relationship with each other.

    Simple, x is an unknown value, x=x is the principle that it is a value.Monist
    If the value is unknown, how can you say they are equal? It seems that you need to know what x entails for the = to be useful. x does not equal x because both x's are on opposite sides (they occupy different space and are typed at different times on the screen (one is after the other) of the =, so I don't know what you mean for two different x's to be equal.
  • Monist
    41
    Does identity exhaust what it is for the thing to be itself? Isn't an identity a label? A label is not the thing. Words are not the thing itself. Are you talking about the thing, or what we call it? Both are different things that have a relationship with each other.Harry Hindu

    Any word can be counted as a label then, that perspective does not help much.

    And again, we are not talking about the x`s on your screen, which have different locations :-)

    We are talking about a thing, being itself.

    I should have used the word variable instead of unknown, in my language, we call that variable idea unknown. Semantic problems...
  • Enrique
    842
    Maybe the concept of mathematically or algebraically exact equality is produced by a synthesis of the counting and spatial structure modules of cognition, whatever these are. We assign a set of structures such as objects a quantitative label, and then we assign a relatively similar enough set of structures the same quantitative label. The structures are never absolutely the same, but with the reference point of a particular quantitative label, they can be regarded as such, which turns out to be a very practical perspective, though philosophically befuddling.
  • Artemis
    1.9k


    Well, first things first: X is just a stand-in symbol for any object or number you wish it to be. But I think you got that far yourself already.

    To a more specific example with your apples. Everything is what it is and not some other thing. If you have an apple--like a real world apple, it can't be anything else at the exact time you are holding it. It has to be itself. What else could it be? If your apple were to be a not-apple, say a banana, then it wouldn't be apple=banana. It would be banana=banana.

    You can even expand the equation: apple=apple=not-banana. Or x=x=~y. Or apple=apple=nothing that is not apple. Or x=x=~(~x).

    Five minutes from now it can be mush in your stomach, and five hours from now it can be released as energy and water and air, etc. Five months ago it was in the clouds and the earth and the tree. But right here, now, it is just itself.
  • Monist
    41


    Let's try it this way:
    Apple=Banana is true, if the properties of apple and banana are completely identical. Certainly, they are not. So Apple≠Banana. It would explain why an apple couldn't be not an apple. But this logic is only true, if the properties of apple are identical to themselves.

    If I start counting the properties of Apple now.......yes, they do meet the properties of Apple. As far I could observe the properties of x, they are identical to the properties of x, therefore x=x is true. This is inductive reasoning which does not guarantee anything.
  • litewave
    797
    Because if such an alternative existed, it wouldn't exist. — litewave

    I see a conclusion, but no premises. How and why?
    Monist

    It follows from the contradiction "X is not X", because from a contradiction, anything follows:

    https://en.wikipedia.org/wiki/Principle_of_explosion

    But even without explosion, the original assumption that an object is not what it is, is absurd enough.
  • Monist
    41

    Thank you so much!

    For now, I am satisfied with the answers. But not with the constitution of beliefs on these given Axiomatic Laws and Logical Principles. So I will continue my journey with questioning them.

    And absurd is okay.
  • jgill
    3.5k
    https://en.wikipedia.org/wiki/Equivalence_class

    If you are using mathematical symbols, then the above should suffice. If you are arguing why a thing is the same as itself, then jump into the deep end of the metaphysical pool and splash about.

    :yawn:
  • christian2017
    1.4k


    Actually the definition of 2 in the dictionary is 1+1. the definition of 10 is 9 + 1

    You can actually get good at math just by memorizing definitions.

    10 ofcourse to some extent requires knowing the defintion of 1 through 9.

    The reason 2 was ever defined is because humans are much deeper thinkers than all known animals.

    I'm sure some animals understand what 2 is to some degree.
  • jorndoe
    3.2k
    The Law of Identity states that a certain thing is identical to itself, and I ask why.Monist

    (I suppose your inquiry itself is meaningless, if identity was abandoned; not just your inquiry, every inquiry.)

    There cannot be anything in particular prior identity.

    Why is identity necessary?Monist

    It's not. (Necessity presupposes identity, if we're talking modal logic at least.)
  • Artemis
    1.9k
    If I start counting the properties of Apple now.......yes, they do meet the properties of Apple. As far I could observe the properties of x, they are identical to the properties of x, therefore x=x is true. This is inductive reasoning which does not guarantee anything.Monist

    Ah, I think I see a problem here. You're introducing an observer into the mix. Our observations of the world are always (to some extent) inductive. (And, as an aside, people often demand too much of inductive reasoning. You can be justifiable and reasonably sure of something without having to be 100%, infallibly sure of it, but that's a subject for a later day.)

    The point that the law of identity simply makes is that any object, like (let's call it, for sake of specificity, and to make clear we're not taking about general apples, but of one specific apple in the time-space continuum) Apple#1 is the same as Apple#1 because Apple#1 DOES have the exact same identical properties, including their location in the space-time continuum as Apple#1. Whether or not you the observer can verify that the apple you're holding is actually the apple you're holding is not as certain, because there is always the off-chance that you're insane/a brain in a vat/under some magicians illusion.
  • SophistiCat
    2.2k
    Apple=Banana is true, if the properties of apple and banana are completely identical. Certainly, they are not. So Apple≠Banana. It would explain why an apple couldn't be not an apple. But this logic is only true, if the properties of apple are identical to themselves.Monist

    You just pushed this back from X to properties of X, but that doesn't really change anything. Just do a variable substitution: let Y designate what used to be called X, and let X now be a property of Y. Everything that was said of X would still apply, since it does not actually depend on the meaning of X - it's a purely syntactical exercise. Metaphysics doesn't come into this.
  • TheMadFool
    13.8k
    "an apple is an apple", but why? I do not get why any certain thing called 'x', should be 'x'.



    I know that, proving 1+1=2 is hard, whilst it is so simple(logically and practically), but I do not see anyone trying to prove x=x, because it may seem so simple and obvious, as it may look pure stupidity to question it, but that is absolutely my point. The simpler it gets, the complexer explaining it.

    Can someone help me out please?
    Monist

    My two cents...

    Imagine x = God
    Then, by definition, x is all good, all powerful and all knowing

    If x is NOT = x then x is NOT God and so x is not all good, not all powerful and not all knowing

    So we get the following contradictions:

    x is all good AND x is not all good
    x is all powerful AND x is not all powerful
    x is all knowing AND x is not all knowing

    These contradictions arise because we assumed x is not = x

    Therefore, x = x

    In more general terms every x has a set of properties and let's call it P so Px (x has properties P) is true

    If x is not x then x will not have properties P i.e. ~Px

    Px & ~Px is a contradiction

    Therefore x is not = x is false i.e. x = x

    In argument form:

    1. If x = x is false then x has property P AND x doesn't have property P
    2. It is false that x has property P AND x doesn't have property P (contradiction)
    Ergo
    3. x = x is true (modus tollens)
  • TheMadFoolAccepted Answer
    13.8k
    "an apple is an apple", but why? I do not get why any certain thing called 'x', should be 'x'.



    I know that, proving 1+1=2 is hard, whilst it is so simple(logically and practically), but I do not see anyone trying to prove x=x, because it may seem so simple and obvious, as it may look pure stupidity to question it, but that is absolutely my point. The simpler it gets, the complexer explaining it.

    Can someone help me out please?
    Monist

    Whatever an x is, x has a set of finite properties, say Ax, Bx and Cx.

    If x is not x then one of the following will be true: ~Ax or ~Bx or ~Cx or all.

    We then have a contradiction: Ax & ~Ax or Bx & ~Bx or Cx & ~Cx.

    So, it's false that x is not x or it's true that x = x

    An argument:

    Px = x has all properties that x has
    Ox = x doesn't have at least one of the properties x has
    x = x the law of identity
    ~(x = x) the law of identity is false

    1. Px
    2. ~(x = x) > Ox
    3. Ox > ~Px
    4. ~(x = x).....assume for reductio ad absurdum
    5. Ox.....2, 4 MP
    6. ~Px.....3, 5 MP
    7. Px & ~Px....1, 6 conj (contradiction)
    8. x = x 4 to 7 reductio ad absurdum
  • Monist
    41
    An argument:

    Px = x has all properties that x has
    Ox = x doesn't have at least one of the properties x has
    x = x the law of identity
    ~(x = x) the law of identity is false

    1. Px
    2. ~(x = x) > Ox
    3. Ox > ~Px
    4. ~(x = x).....assume for reductio ad absurdum
    5. Ox.....2, 4 MP
    6. ~Px.....3, 5 MP
    7. Px & ~Px....1, 6 conj (contradiction)
    8. x = x 4 to 7 reductio ad absurdum
    TheMadFool

    Awesome, but excuse me please, can you explain why Ox > ~Px ?
  • TheMadFool
    13.8k
    Awesome, but excuse me please, can you explain why Ox > ~Px ?Monist

    Well, if x lacks one property from a set of properties P that defines x then it follows that it's false that x has all the properties P. Right?
  • Harry Hindu
    4.9k
    Any word can be counted as a label then, that perspective does not help much.Monist
    Why? Words are things. If x is a variable, then x can be anything, including a word.

    And again, we are not talking about the x`s on your screen, which have different locations :-)

    We are talking about a thing, being itself.

    I should have used the word variable instead of unknown, in my language, we call that variable idea unknown. Semantic problems...
    Monist
    I doesn't make a difference. If you don't know what x is, then how can you say it is equal?

    Why talk about a thing being itself? What problems do you hope to solve, or answers you expect to get?

    Why not just talk about the thing, as opposed to the thing being itself? How is that any different than talking about the thing being itself?

    And absurd is okayMonist

    No it's not. Philosophy is rife of absurd questions. Some questions just aren't worth asking.
  • Monist
    41
    Any word can be counted as a label then, that perspective does not help much.
    — Monist
    Why? Words are things. If x is a variable, then x can be anything, including a word.
    Harry Hindu
    x=x being true, can be put in words as 'the necessity of identity.'
    If that is understood, now;

    A. I did not understand the underlying reason of your statement:''words are not the thing itself'', how did you come to the conclusion that I am talking about the words. And how did you relate that conclusion with the word 'identity', without considering the concept of identity.
    B. Words are things. Agreed. x can be anything, including a word. Agreed. What has this to do with the context here?
    C. Where did you see that I am defending that x=x is true, I do not know. I ask why it is necessary to be so, since axioms are based on this very idea.
    D. It is important to talk about a thing being itself, to understand what constitutes the being of a thing. For example; if identity is false for things, nothing may even exist. I try to catch what is going on, and why I do that is explained in my other reply.
    E. You can talk about many things about the thing, one of them is their identity.
    F. The absurdity of rational thought constituted on axioms is okay, but me questioning it is not... I prefer being free.
    Some questions just aren't worth asking.Harry Hindu
    G. It reminds me of a Greek tossing Socrates on the street :-) I wish I could have that certain statements, without knowing the answers :-)

    Thank you,
  • Mac
    59
    Congrats! You just discovered the property of identity.
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal
youtube
tweet
Add a Comment

Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.