Logical Necessity: Part 2

2+2=4

It is imperative to remember that the goal in epistemology is to properly identify objective truth criteria. "Truth criteria" which can only pertain to an individual's subjective experience is of very little value in attempting to know and understand the objective nature of reality. Mistaking one for the other makes a very profound difference -- it is ultimately the difference between objective rationality and functional solipsism.

If certain knowledge is only obtainable through empirical means - i.e. by means of perceptual observation; i.e. by means of personal experience - then "certain knowledge" is reduced to subjective knowledge, and there is no objectivity to speak of. I can not perceive your perception - and neither can you perceive mine. Your "truth" is entirely built upon your own subjective perception - to which I have no access. And vice-versa. Everyone has their own (subjective) truth, but there is no access to truth which transcends personal experience; no access to truth which transcends individual perception; no access to objective truth.

Of course, adherents to this doctrine can (and must) make exceptions in order to play in the world of objectivity -- but they are exceptions; exceptions which necessarily step outside of this doctrine in order to borrow from an other, more rational, more objective epistemological principle: Logical Necessity.

Logical necessity grants to the realm of empirical observation, perception and experience that element which is necessary to break free from the tyranny of the subjective, into the world of objectivity: logic - and with it, objective identity.

Of course, peddlers of various forms of empiricism can also believe in logic and identity - but not consistently. Only as exceptions. They can believe that "A is A" regarding everything which they have perceived, but according to their epistemological principles, there is no way to know that it is true about that which they have not perceived - it can be (and is) assumed - but it certainly cannot be certain. Therefore, to them, the "law" of identity is not so much a law which is and must be true about everything in reality. It's more of a general rule about everything that they have experienced, and it's assumed to be true about everything else.  2+2 equals 4, not because it must, but because we've never experienced an instance of 2+2 equaling anything else -- it could equal 5 somewhere in the universe, or with some object which we have yet to discover. Contradictions don't exist - but not because they can't. Rather, it is because we simply haven't found any. There could be contradictions out there that we simply haven't observed yet. Thus, there are no laws - whether mathematical or logical. Only pragmatic generalizations. Such is the end of that doctrine which attempts to skirt around logical necessity.

The alternative: accepting that there are some things which are simply true whether we have experienced them or not (i.e. accepting objective truth!) "How do we know that such things are true though, if we don't experience them!?". You think. You think about reality, consider alternatives, and realize that sometimes, there is only one option. For instance, you think about the question of contradictions. You consider the alternativses: either contradictions exist or they don't. You realize (hopefully) that the former idea is, itself, contradictory and ultimately destructive to all knowledge, truth, reality and life; that if it is true, then it is false; that it cannot be true. Therefore, the only other alternative - that contradictions do not exist - is necessarily true. It must be.

Notice that I am not claiming that this thought process makes these things true. I am claiming that this thought process is the method (the only method) of discovering these things to be true. The law of identity is universally true about all of reality. It always has been and always will be - and it always would have been even if none of us ever knew about it. My thought process in discovering it no more "makes it true" or "creates it into reality" than the scientist's perception in discovering a new bacteria "makes it true" or "creates the bacteria into reality". This is not "primacy of consciousness" as Objectivists are in the habit of claiming. This is simply another form of discovery - performed by the mind rather than the senses; a form of truth criteria which is analytical rather than empirical.

Apart from this form of truth criteria, the modern empiricist (regardless of the name he wishes to go by) is stuck in his own subjective fairytales. The key - the only key - to accessing the realm of objectivity is to understand that we know some thing to be true simply because of the fact that they must be true - they are logically necessary.

14 thoughts on “Logical Necessity: Part 2

  1. "They can believe that 'A is A' regarding everything which they have perceived, but according to their epistemological principles, there is no way to know that it is true about that which they have not perceived – it can be (and is) assumed – but it certainly cannot be certain."

    Assuming that I perceive your meaning correctly, I must say that this post appears to be well done! I like it, although somewhat cautiously :)

    -Ben

    Reply
  2. James

    "Contradictions don’t exist – but not because they can’t. Rather, it is because we simply haven’t found any. There could be contradictions out there that we simply haven’t observed yet. Thus, there are no laws – whether mathematical or logical. Only pragmatic generalizations. Such is the end of that doctrine which attempts to skirt around logical necessity"

    The only skirting going on is your evasion of a meaning criteria. How do you know what a contradiction is? What does it mean and how do I know?

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  3. This seems like a revamp of the false analytic and synthetic dichotomy.

    You are taking for granted how you arrived at the concepts at the base of you're argument -- the premises. For example, 2 + 2 will always equal 4; how do you know it? I.e., how did you form the concept "2"? I've assisted children in grade school who didn't even know (understand) the concept of one-to-one correspondence let alone know what 2 means -- they can't know if 2 + 2 = 4 is true or not.

    According to your theory, how does one learn the meaning of 2? I see a huge blank out in your framework.

    Not one argument, not a single one, can rest its validity ultimately on deductive reasoning. You need a proper method of induction to validate the premises in your deductive argument.

    Reply
    1. It likely seems that way because I reject Peikoff's analysis of the analytic synthetic dichotomy. I believe he misintegrated. I intend to integrate: the analytic synthetic integration.

      No. "How do you know that 2 + 2 always = 4?" is NOT the same question as "How did you form the concept '2'?" This is the problem with Objectivist epistemology (and most other epistemological theories): they don't realize that they are mistaking two separate questions (and therefor two separate issues). They are related issues -- but not the same, and treating them as such creates huge problems. See these posts:

      http://thechristianegoist.wordpress.com/2012/12/15/epistemology-truth-criteria/

      http://thechristianegoist.wordpress.com/2013/01/29/the-anti-truth-laws-objectivist-epistemology/

      I am aware of (and AGREE) with Ayn Rand's theory of Concept Formation. I disagree that concept formation is epistemology. I agree that you form the concept "2" through levels of abstraction based in observation. But the concept "2" and the knowledge that 2 + 2 always = 4 are not the same thing. It can be induced from observation that 2 + 2 has equaled 4 in every instance of my experience -- but it cannot be induced from observation that 2 + 2 will always equal 4.

      But that brings us the the crux of the matter:
      "Not one argument, not a single one, can rest its validity ultimately on deductive reasoning."

      A is A.

      You see, either the axioms are derived from observation (induction) and therefor cannot properly be said to be universally true (and therefor are not really axioms) OR they are not derived from observation and therefor their validity "ultimately rests on deductive reasoning". Although I wouldn't necessarily put it that way. I would say that their validity rests in their axiomatic nature; i.e. in their nature of being logically necessary.

      That is the problem which Objectivist Epistemology has repeatedly failed to solve: If ALL knowledge is derived from sense perception, then how can one know that the axioms are valid concerning that which has not been perceived?

      Reply
      1. I don't think we need to delve into whether or not concepts lie within epistemology or not -- the fact is we agree on the theory of their formation and we can start from there. If you agree that concepts arise from abstractions from observations; and that a concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular measurements omitted; and that for any particular unit that exists the relevant measurements must exist in some quantity, but may exist in any quantity; then why don't you think the concepts of axioms (existence, consciousness, identity) arise from the same process? Concepts are found to be axioms, after all, only after you observe that you must accept them in order to form your argument of disproving them. Where do the axiom concepts come from if not from observation? Revelation?

        In the book "the logical leap: induction in physics", David Harriman does a great job of describing how generalizations are derived from some observations and apply to all; this is induction. He even described how Aristotle used induction to validate his laws of logic (containing one of the axioms), though Aristotle didn't know it was induction at the time. The key lies in the nature of concepts and of their formation.

        "You see, either the axioms are derived from observation (induction) and therefor cannot properly be said to be universally true (and therefor are not really axioms) OR they are not derived from observation and therefor their validity “ultimately rests on deductive reasoning."

        You misunderstand the nature of induction. I urge you to suspend your final verdict on the utility of induction until you look at this new information in the book I suggested. It was a fun read for me and I think you'll like it as well.

        Reply
  4. You seem to be missing the objection I am raising. It is not against concept formation (how concepts are formed). We agree there. Perhaps the following distinction will be helpful:
    There is a difference between the concept "a is a" in my head and the reality to which it corresponds outside of my head. Do you agree with that? The concept in my head was formed through my observation and abstraction, but the reality of identity did not. I discovered identity in many various things, but the identity was there whether I discovered it or not. Right? Isn't that the essence of 'objectivity'? A is A -- whether I get it or not?

    Now, I formed the concept of identity in my head via abstraction from observation, and to the extent that I was referring to that being observed, I was perfectly justified in ascribing identity to it. My observation of a computer screen in front of me is justification for the idea in my head that I am looking at a computer screen. The observation that it is not a computer screen and an elephant at the same time and same respect is justification for me to ascribe identity (a is a) to it while I am observing it. However, where is the justification once the observation stops? Or apart from observation of other things? I've formed the concept 'cat' through abstraction and observation, but that in no way justifies me in ascribing it to every entity in existence. What justification is there for ascribing identity to every entity in existence, based on observation alone? Do you see what I am after? Not formation, but justification. Not the subject's journey, but the the nature of the objective reality. How can I, the subject, know that 'a is a' regarding everything in reality which I have not perceived? I do agree that "for any particular unit that exists the relevant measurements must exist in some quantity, but may exist in any quantity", but I can't observe that in perception -- and neither can you. What is it that justifies your belief that 'a is a' refers to all of reality (particularly that which has not been perceived)?

    Reply
    1. I apologize for missing your objection. I took the following to mean that we don't derive our knowledge (i.e., concepts) from observation: "...either the axioms are derived from observation (induction) and therefor cannot properly be said to be universally true (and therefor are not really axioms) OR they are not derived from observation and therefor their validity “ultimately rests on deductive reasoning”." Now it seems to me that you meant the nature of reality derives not from observation (most of it certainly does not).

      A clear distinction needs to be made between reality and knowledge of reality. Our knowledge of reality -- all of it --derives from observation of reality -- this is objectivity. Objectivity is a metaphysical and an epistemological concept (http://aynrandlexicon.com/lexicon/objectivity.html).

      "I do agree that “for any particular unit that exists the relevant measurements must exist in some quantity, but may exist in any quantity”, but I can’t observe that in perception..."

      Do you mean to say that you are not aware of the abstraction that occurs in your mind when you omit the measurement(s) of a particular existents and replace those measurement(s) with a variable(s) while forming a concept of the existents? Or do you mean that you can't observe the variable(s) of a concept being filled in by every and all possible existents possessing particular measurement(s)? The later is certainly true. Are you saying that this somehow make the variable aspect of a concept invalid?

      If variable aspect of concepts are valid, then I know the law of identity applies to every physical existent due to the system of concepts, and therefore, the system of variables involved. A thing is itself -- identity -- is a concept that must be accepted as true in any attempt to disprove it. Inescapable acceptance makes identity (or any concept) an axiom; it meals that it is assumed and implied for every other concept. E.g., a thing is not itself -- I've assumed that the words I used (including "thing") have identity and meaning, and therefore, grant the truth of identity; or my words have no identity and meaning, and therefore, disprove nothing. Thus, inescapable acceptance serves as irrefutable proof that a thing is itself.

      Applying the concept of identity to all: the concept "thing", being the most general concept of any particular existent with all measurements omitted and every variable taking its place, is justification to apply knowledge gained about the concept (and therefore the variables) to every instance of a particular filling in the variable. In other words, the concept "thing" means that any truth discovered about it is true about everything.

      The book on induction does a better job than I at explaining the process of acquiring knowledge of some and applying it to all, but the key is the variable aspect of concepts.

      Reply
      1. "Or do you mean that you can’t observe the variable(s) of a concept being filled in by every and all possible existents possessing particular measurement(s)?"

        Bingo

        "The later is certainly true. Are you saying that this somehow make the variable aspect of a concept invalid?"

        No -- at least not according to my epistemological system. However, according to the Objectivist system, where all knowledge must be derived from perceptual observation, the assumption of the validity of the variable aspect seems like a very unwarranted one.

        "A thing is itself — identity — is a concept that must be accepted as true in any attempt to disprove it. Inescapable acceptance makes identity (or any concept) an axiom; it meals that it is assumed and implied for every other concept ...Thus, inescapable acceptance serves as irrefutable proof that a thing is itself."

        Yes. And this is my argument for the validity of the the law of identity (and the other axioms), but it is only valid if one accepts that an argument from logical necessity is a valid one. (By 'logical necessity', I simply mean that the concept being argued for -- identity, in this case -- cannot be denied with contradicting itself or reality).

        This is the justification I am after: the justification for believing that the law of identity (and therefore its corollaries) is universally valid. The universal validity of the axioms (and therefore of the entire structure of your 'concept formation', since every concept assumes the validity of the axioms) cannot be justified from observational perception. It certainly requires the use of perception in the formation of it in your mind, but it cannot be justified via perception. Its only justification is its axiomatic nature; the fact that it cannot be escaped; that it must be the case; that it is logically necessary.

        Reply
    2. "However, according to the Objectivist system, where all knowledge must be derived from perceptual observation, the assumption of the validity of the variable aspect seems like a very unwarranted one."

      The variable aspect is derived from observation, though. It answers the question, what measurement is not essential to a particular observed existent when considering other observed existents that's similar to it but of different size? It's the result of abstraction.

      "The universal validity of the axioms (and therefore of the entire structure of your ‘concept formation’, since every concept assumes the validity of the axioms) cannot be justified from observational perception."

      I just proved the axiom through observation. You observed that the concept "thing" has to be itself because it is either itself, or my argument has no meaning. And since "thing" is a concept abstracted from observation, using the concept "thing" in this proof is using information derived from observation. I'm not sure why you don't think this formulation is sufficient: all knowledge of concepts come from abstracting observations; all knowledge is of direct perception, or are concepts derived from perception; therefore, all knowledge comes from observation. Where else would knowledge come from, if not from observations (or your awareness) of reality?

      "It certainly requires the use of perception in the formation of it in your mind, but it cannot be justified via perception. Its only justification is its axiomatic nature; the fact that it cannot be escaped; that it must be the case; that it is logically necessary."

      Why is it not justified via perception or from concepts derived from perception? How do you know, how are you even aware of the axiomatic nature of identity without observing it? You say it cannot be escaped. Aren't you observing this? Perhaps you're not considering introspection (your thoughts and use of concepts in your mind) as a form of observation?

      Reply
      1. I'll skip right to where the crux of the matter is:

        "Why is it not justified via perception..[?]"

        Because we are talking about claims pertaining to that which has not been perceived.

        ... or from concepts derived from perception?"

        This is a separate question. If by "concepts derived from perception", you mean: "the analysis of concepts which we happen to have derived from perception", then I would absolutely say that the axioms are justified in that way -- however I would emphasize that it is the analysis which discovers the justification, not the concepts, in and of themselves.

        "You say it cannot be escaped. Aren’t you observing this? Perhaps you’re not considering introspection (your thoughts and use of concepts in your mind) as a form of observation?"

        Woah. There seems to be some equivocation going on here. Yes, that is a type of observation, but it is not a type of sense perception -- and it is sense perception which I am claiming cannot justify the universal validity of the axioms.

        The Objectivist position is (correct me if I'm wrong) that the validity of the axioms is justified via sense perception (i.e. "I perceive the table being a table and not a dog"). Do you reject that position and agree with me that the validity of the axioms is justified via another sort of observation (which is not sense perception)? What would you call the observation that "the concept 'thing' has to be itself because it is either itself, or my argument has no meaning."? Or the observation that A cannot be non-A?

        1) Do you agree that those observations are not sense perceptions?
        and
        2) What problem is there in referring to such observations as "logical necessity"? Is it not logically necessary that A is A? And are you not 'observing' a logically necessary fact when you consider in your mind that this idea is inescapable?

        Reply
        1. I think a person who claims that conceptual knowledge (such as knowledge of axioms) is gained from strictly sense perception isn't rational and cannot justly claim to be an Objectivist. That certainly is not what Rand seems to have advocated. What may be correctly advocated, however, is that axioms are like any concept and ultimately are derived from perception, but not directly obtained via perception. No Objectivist should advocate that abstract ideas are acquired via direct perception and can be perceived directly -- this is not what is meant by "based on perception."

          E.g., a child can stare at a blueberry all day and not gather the idea that it's a fruit. Nor can a child stare at a blueberry all day, knowing that it is a fruit, and see the fruitness of it. This is the platonic idea of forms, as you might be familiar, and it's silly. What a child can do is consider what he knows about fruit and what he observes about strawberries and come to the conclusion that a strawberry is a kind of fruit. The same process applies to axioms, e.g., one considers what they know about identity and axioms and integrates the two. In both cases the data originates from sense perception.

          Knowledge ultimately being derived from sense data, is the application of the primacy of existence to epistemology, and it means that knowledge cannot be acquired nor validated without data of the external world -- sense data is the beginning of any path to knowledges. E.g., how do you arrive at the idea of fruit without seeing or sensing any? Likewise, how do you even postulate an hypothesis of the idea of identity without referencing multiple entities and abstracting from that data the idea of identity? How do you test either idea without sense data?

          There are two inseparable parts to discovering conceptual knowledge, the sense data (or concepts abstracted from sense data), and the abstraction and integration of that into a new connection. Without either, conceptual knowledge isn't gained. The primary source of any knowledge, however, is sense data, since you can't perform a process of abstraction without that data and get anywhere meaningful that references reality. We may be saying the same thing here but slightly different, if your idea of logical necessity is the logical integration of two different concepts into a new concept -- and that knowledge too must be based on sense data.

          If, however, we're not talking about the same thing and you don't think the starting point of all knowledge -- including axioms -- is sense data, then hence doth that knowledge came? Can you please derive that knowledge without using any concepts that are ultimately derived from sense data?

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  5. Again, we agree on how we, as humans, form concepts via abstraction from sense perception, but there is another separate issue that I am after, and that is: how certain ideas (no matter how they got into our heads -- we agree there) can be justified as truth -- particularly the axioms and their corollaries.

    We agree that we form ideas in our heads via abstraction from sense perception, but the only justification sense perception can give us is in regard to that which is directly perceived. Sense perception does not give me any justification to assume that "a is a" regarding that which has not been perceived. Of course, I can assume it because I must in order to make sense out of the world, but that is sort of a pragmatic assumption. I am looking for epistemological certainty; epistemological justification. I am looking for a criteria by which to judge the truthfulness of ideas. The only criteria the Objectivist sets forth is: sense perception, but that criteria alone cannot justify the universal truthfulness of the axioms. There must be some additional criteria which justifies the axioms -- and thereby justifies every application of the axioms to sense perception. Apart from justifying the axioms, there is no justification for using the axioms in concept formation; which means there is no justification for assuming identity in concept formation; which means there is no justification in abstracting particular attributes (since abstraction implicitly uses identification -- as admitted by Rand in the opening of ITOE).

    So, what is your justification for the universal validity of the axioms, if not logical necessity?

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    1. "The only criteria the Objectivist sets forth is: sense perception..."

      I don't agree that Objectivists set forth sense perception as the only criteria. It is necessary, as they have advocated; however, there is a difference between necessary, and necessary plus sufficient. I don't think they ever said it was sufficient.

      I totally agree that sense perception data alone is not sufficient to derive concepts or prove them. But you also can't derive or prove concepts without sense perception. It seems like your agreeing with the first statement but disagreeing with the second; maybe I'm misunderstanding you.

      If data collected from sense perception is necessarily true information about reality, then a valid method of concept formation makes the concepts (including not directly perceived concepts) true information about reality too. If concepts are true, then integrating wider and wider concepts into new ones makes them true as well.

      I would say the validity of concepts is the validity of axioms since axioms are concepts, but it doesn't seem like you agree with that argument. So am I correct in assuming that your request for the justification of the truthfulness of axioms apart from their conceptual formation means that you are challenging or do not recognize the validity of the method for forming concepts as a means of arriving at truth? Or is it something else?

      If you are challenging the method, then what exactly do you think is wrong with it? If it is an invalid method, then you are in the strange predicament of needing to use invalid concepts, derived from the invalid method, in order to explain the (invalid?) concept of logical necessity. How do you even begin to arrive at the certainty of logical necessity as being true apart from valid method of concept formation? You say it's the nature of the axiom that gives us the truth, but the nature of things alone do not automatically translate into knowledge for us. We must acquire knowledge through some valid method, and that method is Rand's theory of concept formation. If not, what method, or is no method needed?

      I am not denying that the nature of axioms makes it possible for us to discover their nature -- the nature of anything is a necessary (but not sufficient) part that makes it possible for us to discover their nature -- but are you really suggesting we have no means of discovering them; or are you suggesting there is a means apart from concept formation; or is no method necessary?

      Reply

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