09.15.05

truth equations, a ’sort-of’ mathematical attempt to quantify truth

Posted in philosophy, life at 7:04 pm by

I suppose I’ve neglected my blog for, oh, say, 48 hours now (which, for me, is some kind of record,) it’s time for an update. I’m afraid that the things on my mind of late haven’t been particularly related to my general content. My thoughts have been more distinctly ‘grad-school-ish’. That is, I’ve been pondering the wonders of Analyses of Variance, Multiple Regressive techniques, and the philosophy of science.

I would, eventually, like to make some sort of response to a comment Kristen from McCarty Musings made about the role of emotion in the discourse process. I’m fascinated by the role of emotion in communication. (And, if you’re interested, you may want to check out some of the work Robin Nabi has done on the subject.) Yet, this is a topic for another day. (Mostly, I just put the idea here because I hope to use this paragraph as a reminder that I want to write a bit about this.)

Today, though, I want to talk (and hear your thoughts on) the concept of the truth equation. Now, you won’t find the term ‘truth equation’ in any philosophy of science textbook (or probably any other textbook for that matter.) I stumbled across one such equation while I was doing a reading for my ‘Contemporary Research on the Family’ class that I’m taking. Essentially, the authors argued that truth could be boiled down to this:

Truth = Fact + Perspective

This, of course, is the most popular definition of a post-modern definition of truth. Truth should only be approached, so the equation goes, as a manifestation of both fact and perspective.

I have some problems with this definition. It might be okay, but I think it depends on the relative weight of fact vs. perspective. For example, let’s apply some values to those variables:

Fact = 42 (the answer to the question of life the universe and everything…of course)
Perspective = 2

Well, then, Truth = 44. Now 42 (the value of fact) and 44 (the value of truth) are relatively similar in comparison to the value of Perspective. Probably, using truth as an approximation for fact is not going to be a big problem. On the other hand, if the value for perspective is much higher, say, 44 itself. I have a problem with calling ‘truth’ true. In fact, truth, in this case, is as much perspective as it is fact.

By utilizing this equation, it’s also possible to see why some post-modern (or non-moderns, but I’ll use the post-modern term as it is more colloquially recognized) folk have such a frustration with modern religious types. You see, in their little equation, they’ve got direct word from on high about fact. That is, the value they are claiming for perspective is zero.

This, of course, pisses people off because if you don’t agree with these modern types–you’re the one whose perspective is getting between fact and truth. Post-moderns find this to be fantastically arrogant.

If it were up to me, I think the equation should go something a bit more like this:

Percieved Truth = Fact + Perspective

There are a few minor caveats/hypotheses to/about this phenomena.

  1. I believe that the set of people whose Perspective = 0 in this equation is null. That is, everyone has a perspective.
  2. Most folks perspective scores are similar. That’s not to say that they’re the same, it’s just that their perspectives are approxomately equally errant from fact–albiet some are errant in entirely opposite directions.
  3. As the number of equal participants in a community increases, the truth equation of the community (that is, the average of all members’ Perceived Truth scores approaches fact).
  4. In communities where there is not equal participation (i.e. the relative weight of individual participant’s truth scores are not equally represented in the cumulative Percieved Truth score of the group) will find that their Percieved Truth scores will, rather than regressing toward the mean, toward actual fact, gravitate toward the more extreme individual’s scores.
  5. This gravitation toward extreme scores happens in part because of the alienation and osteracism of some members (whose perspective the community would’ve otherwise needed in order to approach facts.)

If I’m right about this, it’s the very act of strict adherence to ABSOLUTE truth that may drive communities farther from actual fact.

Of course, little if any of this is empirically verifiable.

So, let’s hear it. What are your truth equations?

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12 Comments

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    kevin said,

    September 15, 2005 at 7:54 pm

    What about the role of community? Beyond perspective, truth involves communal co-creation and production.

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    Mike said,

    September 16, 2005 at 1:02 am

    IMO, the equation should read:

    Truth= Fact +/- Perspective

    There are some perspectives that add the right ingredients to the facts to lead to truth. There are some perspectives that subtract the right ingredients from the facts to lead to Truth.

  3. Sign up at gravatar.com to have your own image

    Leighton said,

    September 16, 2005 at 2:48 am

    With the caveat that I don’t think the following is the best way to approach the topic to nonmathematicians…

    I tend to think (using mathematics as an analogy rather than trying to deploy actual mathematical structures as a way to glean information about truth) that there is no equation for truth; or rather, that we’re forced to get within epsilon of the nonlinear truth by successively larger, longer and more complicated linear approximations of the truth (like a Taylor expansion or something). It’s more of a dynamical system than a fixed equation, and although it (usually) behaves according to very specific guidelines, there are also chaotic elements that make it difficult or impossible to pin down what exactly is going on at all times in all places.

    Here’s where I think this makes for a really good analogy, though: just like in many dynamical systems, we can never be sure we’re exactly right (in fact, we’re almost certain that we’re wrong), we can often place pretty clear boundaries on how wrong we are. (This is all done in a Bayesian fashion, of course, so it’s not as rigorous as modernists would like.)

    Now here’s where I think this makes a bad analogy–there’s usually very little to be gained in the empirical sciences (beyond the personal gain of practicing mental discipline) from throwing out every prior result and reasoning things through from freshly-created first principes, but it can often be extraordinarily helpful in (e.g.) philosophy to look at things from a radically new perspective.

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    Henry said,

    September 16, 2005 at 3:36 am

    Funny thing was as I was reading the top portion, I said to myself “no, it should be Percieved Truth = Fact + Perspective!” and then a paragraph later you said it.

    Mike - I am sure the value of perspective could be by itself +/-, so you can leave the equation simple with

    Percieved Truth = Fact + Perspective

    . But that is a minor caveat.

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    Steve J said,

    September 16, 2005 at 6:56 am

    perceived truth = Fact +/- (perspective - lies)

    I used to find that if someone told me a truth I didn’t agree with I would find a hundred other little truths (also known as lies) to justify my perspective.

    now I just dont care…If I wanted your opinion I would give you it.

    ;-)

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    Brandon said,

    September 16, 2005 at 9:19 am

    Kevin,

    I’m not sure exactly what you mean by the role of community. I did address community in my list of axioms about my truth equation…but I guess I’m not understanding your question. Will you clarify?

    Mike,

    As Henry pointed out, if the value of perspective is negative then there’d be no need for the +/- operator in front of truth. (This, of course, assumes that we’re linearly away from truth…and I’m almost positive that’s not the case. I’d posit that there are at least three dimensions (if not more) of distance from truth. Yet, for the sake of simplicity, I just used a linear model.

    Steve,

    I’m interested in your comment. I think that when one lies (in the sense that you’re using the word) one knows that they’re lying. In that sense, those lies may conceal the real reasons that you hold the perspective that you hold, but they don’t really change your perspective. Maybe I’m missing something. Let me know.

    Leighton,

    Somehow I sensed you’d chime in here and make me look all out-classed. I suppose when mathematicians read your blog, you’ve got to be pretty foolish to go posting equations. Anyway, thanks for your insight…but one question:

    What the fuck is Epsilon?

    ;)

  7. Sign up at gravatar.com to have your own image

    Steve J said,

    September 16, 2005 at 10:33 am

    Brandon,

    to give an example, as a child I knew homosexuality was wrong. I knew that was the case because church people also said it was wrong and if you look for it the bible says it too. As I grew up and learned more facts i.e. many animals in nature are homosexual…it’s widely accepted that you are born with your sexuality rather than just make a choice at a later stage in life..etc I stopped believing that that was the case.

    But as a child or even as a younger adult I had no idea that I was trying to re-enforce an attitude I already had. so I lied to myself without knowing it or more realistically I only remembered things which agreed with my perspective, until I was old enough to think more open mindedly.

    my point is that if we want something to be true we can lie to oursleves to make it so. Not always being aware we are doing it.

    Our perspective is highly coloured by things we want to see rather than things we actually see.

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    bill said,

    September 16, 2005 at 10:41 am

    Firstly, math seems too limited for the subject. In the least, your equation should be multi dimensional. That is, perceived truth approaches fact from multiple dimensions. In the multi dimensional world of perceived truth, an observer of another’s perceived truth looks at that truth along a plane of their own perception. This gives some allowance for the difficulty each of us has determining the accuracy of other’s perception of truth. Convoluted enough? :)

    Secondly, there are very few facts. Most all fact includes some perspective. Especially in the modern world of statistical fact. The main purpose of statistics is to create some amount of objectivity from subjective input. However, the mere existence of perception eliminates objectivity. For example: I hold three apple looking objects in my hand and ask you how many there are. If you intend to make them into a pie (a small one) and one of them isn’t suited for pie, then your answer is: 2 apples. So, now we get:
    perspective + intension + fact = truth.
    But there must be a negative number in that equation to get from 3 to 2.

    Personally, I think we need to quit assuming objectivity. To me, that’s one of the hallmarks of postmodernism/anti-modernism: to throw out the notion that any of us can know absolute, objective truth.

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    bill said,

    September 16, 2005 at 10:51 am

    Oh, I forgot to add that, if the apple pie requires more than 2 apples, then the answer is: 0 apples. If we then decide to forgo the pie and just eat them, then there is one each, which is just right.

    So, intention not only changes perception but intention can change as a result of the outcome, creating a new perception and thus a new outcome.

    Relativity includes the time variable, right? So truth changes with respect to time.

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    Mike said,

    September 16, 2005 at 11:01 am

    Henry and Brandon: You are right, of course. My math skills have deteriorated with decrepancy.

    What about this: If we accept God’s perspective as infinite…and add that to the Facts as God sees them…does that mean that God’s Truth is higher than all?

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    Steve C said,

    September 16, 2005 at 11:52 am

    I really should have stayed awake in school more… maybe if I knew “truth” was on the line I would have.

    Damn!

  12. Sign up at gravatar.com to have your own image

    Travis said,

    September 23, 2005 at 5:08 pm

    I feel that the revised equation with of Percieved Truth = Fact + Perspective is much closer to actual reality when regarding truth. However I feel that this equation still begs the question that a complete lack of Perspective OR Fact would still leave one with some amount of Percieved Truth, assuming one of the other amounts is greater than zero. This would be incorrect, for Percieved Truth cannot be unless there is some quantified amount of both Truth AND Perception. A more correct equation would be as follows:

    Percieved Truth=(Fact)(Perception)

    This forbids one to have any amount of Percieved Truth if either Fact or Perception is equal to zero. Alternate eqations help to claify:

    Fact=Percieved Truth/Perception

    Perception=Percieved Truth/Fact

    In either case, it is a mathematical for either Perception or Fact to equal zero. For then we would have a conclusion of {No Solution}.

truth equations, a ’sort-of’ mathematical attempt to quantify truth

Posted in philosophy, life at 7:04 pm by

I suppose I’ve neglected my blog for, oh, say, 48 hours now (which, for me, is some kind of record,) it’s time for an update. I’m afraid that the things on my mind of late haven’t been particularly related to my general content. My thoughts have been more distinctly ‘grad-school-ish’. That is, I’ve been pondering the wonders of Analyses of Variance, Multiple Regressive techniques, and the philosophy of science.

I would, eventually, like to make some sort of response to a comment Kristen from McCarty Musings made about the role of emotion in the discourse process. I’m fascinated by the role of emotion in communication. (And, if you’re interested, you may want to check out some of the work Robin Nabi has done on the subject.) Yet, this is a topic for another day. (Mostly, I just put the idea here because I hope to use this paragraph as a reminder that I want to write a bit about this.)

Today, though, I want to talk (and hear your thoughts on) the concept of the truth equation. Now, you won’t find the term ‘truth equation’ in any philosophy of science textbook (or probably any other textbook for that matter.) I stumbled across one such equation while I was doing a reading for my ‘Contemporary Research on the Family’ class that I’m taking. Essentially, the authors argued that truth could be boiled down to this:

Truth = Fact + Perspective

This, of course, is the most popular definition of a post-modern definition of truth. Truth should only be approached, so the equation goes, as a manifestation of both fact and perspective.

I have some problems with this definition. It might be okay, but I think it depends on the relative weight of fact vs. perspective. For example, let’s apply some values to those variables:

Fact = 42 (the answer to the question of life the universe and everything…of course)
Perspective = 2

Well, then, Truth = 44. Now 42 (the value of fact) and 44 (the value of truth) are relatively similar in comparison to the value of Perspective. Probably, using truth as an approximation for fact is not going to be a big problem. On the other hand, if the value for perspective is much higher, say, 44 itself. I have a problem with calling ‘truth’ true. In fact, truth, in this case, is as much perspective as it is fact.

By utilizing this equation, it’s also possible to see why some post-modern (or non-moderns, but I’ll use the post-modern term as it is more colloquially recognized) folk have such a frustration with modern religious types. You see, in their little equation, they’ve got direct word from on high about fact. That is, the value they are claiming for perspective is zero.

This, of course, pisses people off because if you don’t agree with these modern types–you’re the one whose perspective is getting between fact and truth. Post-moderns find this to be fantastically arrogant.

If it were up to me, I think the equation should go something a bit more like this:

Percieved Truth = Fact + Perspective

There are a few minor caveats/hypotheses to/about this phenomena.

  1. I believe that the set of people whose Perspective = 0 in this equation is null. That is, everyone has a perspective.
  2. Most folks perspective scores are similar. That’s not to say that they’re the same, it’s just that their perspectives are approxomately equally errant from fact–albiet some are errant in entirely opposite directions.
  3. As the number of equal participants in a community increases, the truth equation of the community (that is, the average of all members’ Perceived Truth scores approaches fact).
  4. In communities where there is not equal participation (i.e. the relative weight of individual participant’s truth scores are not equally represented in the cumulative Percieved Truth score of the group) will find that their Percieved Truth scores will, rather than regressing toward the mean, toward actual fact, gravitate toward the more extreme individual’s scores.
  5. This gravitation toward extreme scores happens in part because of the alienation and osteracism of some members (whose perspective the community would’ve otherwise needed in order to approach facts.)

If I’m right about this, it’s the very act of strict adherence to ABSOLUTE truth that may drive communities farther from actual fact.

Of course, little if any of this is empirically verifiable.

So, let’s hear it. What are your truth equations?

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12 Comments

  1. Sign up at gravatar.com to have your own image

    kevin said,

    September 15, 2005 at 7:54 pm

    What about the role of community? Beyond perspective, truth involves communal co-creation and production.

  2. Sign up at gravatar.com to have your own image

    Mike said,

    September 16, 2005 at 1:02 am

    IMO, the equation should read:

    Truth= Fact +/- Perspective

    There are some perspectives that add the right ingredients to the facts to lead to truth. There are some perspectives that subtract the right ingredients from the facts to lead to Truth.

  3. Sign up at gravatar.com to have your own image

    Leighton said,

    September 16, 2005 at 2:48 am

    With the caveat that I don’t think the following is the best way to approach the topic to nonmathematicians…

    I tend to think (using mathematics as an analogy rather than trying to deploy actual mathematical structures as a way to glean information about truth) that there is no equation for truth; or rather, that we’re forced to get within epsilon of the nonlinear truth by successively larger, longer and more complicated linear approximations of the truth (like a Taylor expansion or something). It’s more of a dynamical system than a fixed equation, and although it (usually) behaves according to very specific guidelines, there are also chaotic elements that make it difficult or impossible to pin down what exactly is going on at all times in all places.

    Here’s where I think this makes for a really good analogy, though: just like in many dynamical systems, we can never be sure we’re exactly right (in fact, we’re almost certain that we’re wrong), we can often place pretty clear boundaries on how wrong we are. (This is all done in a Bayesian fashion, of course, so it’s not as rigorous as modernists would like.)

    Now here’s where I think this makes a bad analogy–there’s usually very little to be gained in the empirical sciences (beyond the personal gain of practicing mental discipline) from throwing out every prior result and reasoning things through from freshly-created first principes, but it can often be extraordinarily helpful in (e.g.) philosophy to look at things from a radically new perspective.

  4. Sign up at gravatar.com to have your own image

    Henry said,

    September 16, 2005 at 3:36 am

    Funny thing was as I was reading the top portion, I said to myself “no, it should be Percieved Truth = Fact + Perspective!” and then a paragraph later you said it.

    Mike - I am sure the value of perspective could be by itself +/-, so you can leave the equation simple with

    Percieved Truth = Fact + Perspective

    . But that is a minor caveat.

  5. Sign up at gravatar.com to have your own image

    Steve J said,

    September 16, 2005 at 6:56 am

    perceived truth = Fact +/- (perspective - lies)

    I used to find that if someone told me a truth I didn’t agree with I would find a hundred other little truths (also known as lies) to justify my perspective.

    now I just dont care…If I wanted your opinion I would give you it.

    ;-)

  6. Sign up at gravatar.com to have your own image

    Brandon said,

    September 16, 2005 at 9:19 am

    Kevin,

    I’m not sure exactly what you mean by the role of community. I did address community in my list of axioms about my truth equation…but I guess I’m not understanding your question. Will you clarify?

    Mike,

    As Henry pointed out, if the value of perspective is negative then there’d be no need for the +/- operator in front of truth. (This, of course, assumes that we’re linearly away from truth…and I’m almost positive that’s not the case. I’d posit that there are at least three dimensions (if not more) of distance from truth. Yet, for the sake of simplicity, I just used a linear model.

    Steve,

    I’m interested in your comment. I think that when one lies (in the sense that you’re using the word) one knows that they’re lying. In that sense, those lies may conceal the real reasons that you hold the perspective that you hold, but they don’t really change your perspective. Maybe I’m missing something. Let me know.

    Leighton,

    Somehow I sensed you’d chime in here and make me look all out-classed. I suppose when mathematicians read your blog, you’ve got to be pretty foolish to go posting equations. Anyway, thanks for your insight…but one question:

    What the fuck is Epsilon?

    ;)

  7. Sign up at gravatar.com to have your own image

    Steve J said,

    September 16, 2005 at 10:33 am

    Brandon,

    to give an example, as a child I knew homosexuality was wrong. I knew that was the case because church people also said it was wrong and if you look for it the bible says it too. As I grew up and learned more facts i.e. many animals in nature are homosexual…it’s widely accepted that you are born with your sexuality rather than just make a choice at a later stage in life..etc I stopped believing that that was the case.

    But as a child or even as a younger adult I had no idea that I was trying to re-enforce an attitude I already had. so I lied to myself without knowing it or more realistically I only remembered things which agreed with my perspective, until I was old enough to think more open mindedly.

    my point is that if we want something to be true we can lie to oursleves to make it so. Not always being aware we are doing it.

    Our perspective is highly coloured by things we want to see rather than things we actually see.

  8. Sign up at gravatar.com to have your own image

    bill said,

    September 16, 2005 at 10:41 am

    Firstly, math seems too limited for the subject. In the least, your equation should be multi dimensional. That is, perceived truth approaches fact from multiple dimensions. In the multi dimensional world of perceived truth, an observer of another’s perceived truth looks at that truth along a plane of their own perception. This gives some allowance for the difficulty each of us has determining the accuracy of other’s perception of truth. Convoluted enough? :)

    Secondly, there are very few facts. Most all fact includes some perspective. Especially in the modern world of statistical fact. The main purpose of statistics is to create some amount of objectivity from subjective input. However, the mere existence of perception eliminates objectivity. For example: I hold three apple looking objects in my hand and ask you how many there are. If you intend to make them into a pie (a small one) and one of them isn’t suited for pie, then your answer is: 2 apples. So, now we get:
    perspective + intension + fact = truth.
    But there must be a negative number in that equation to get from 3 to 2.

    Personally, I think we need to quit assuming objectivity. To me, that’s one of the hallmarks of postmodernism/anti-modernism: to throw out the notion that any of us can know absolute, objective truth.

  9. Sign up at gravatar.com to have your own image

    bill said,

    September 16, 2005 at 10:51 am

    Oh, I forgot to add that, if the apple pie requires more than 2 apples, then the answer is: 0 apples. If we then decide to forgo the pie and just eat them, then there is one each, which is just right.

    So, intention not only changes perception but intention can change as a result of the outcome, creating a new perception and thus a new outcome.

    Relativity includes the time variable, right? So truth changes with respect to time.

  10. Sign up at gravatar.com to have your own image

    Mike said,

    September 16, 2005 at 11:01 am

    Henry and Brandon: You are right, of course. My math skills have deteriorated with decrepancy.

    What about this: If we accept God’s perspective as infinite…and add that to the Facts as God sees them…does that mean that God’s Truth is higher than all?

  11. Sign up at gravatar.com to have your own image

    Steve C said,

    September 16, 2005 at 11:52 am

    I really should have stayed awake in school more… maybe if I knew “truth” was on the line I would have.

    Damn!

  12. Sign up at gravatar.com to have your own image

    Travis said,

    September 23, 2005 at 5:08 pm

    I feel that the revised equation with of Percieved Truth = Fact + Perspective is much closer to actual reality when regarding truth. However I feel that this equation still begs the question that a complete lack of Perspective OR Fact would still leave one with some amount of Percieved Truth, assuming one of the other amounts is greater than zero. This would be incorrect, for Percieved Truth cannot be unless there is some quantified amount of both Truth AND Perception. A more correct equation would be as follows:

    Percieved Truth=(Fact)(Perception)

    This forbids one to have any amount of Percieved Truth if either Fact or Perception is equal to zero. Alternate eqations help to claify:

    Fact=Percieved Truth/Perception

    Perception=Percieved Truth/Fact

    In either case, it is a mathematical for either Perception or Fact to equal zero. For then we would have a conclusion of {No Solution}.