The Inconvenience of Truth.

We live in a strange era of fake news and a plurality of truths, where nobody is objectively right or wrong. It is, in fact, hateful to point out someone may be wrong, as though their ideas are identifiable with their person and cannot be corrected, just as much as their height or skin colour. It is, indeed ironic, that so many hold to the view that one may pick their gender, out of an array of 50+/-, I cannot keep track, or that truth is subjective and mind dependant, but that there exists, objectively, fake/real news. Is truth what our peers let us get away with saying? Surely no one doubts the objectivity of a warning label on a bottle of medicine or rat poison or the objectivity of mathematics when designing a bridge, as an engineer. Why, then, are some truths up for grabs by whoever wants reality to conform to their liking and others are accepted as contractually binding as a deal with the devil, so to speak?

Others have grown apathetic towards the truth, like Pilate, who flippantly asked Jesus, “What is truth?” John 18:38. This type of apathy must be eschewed, not to the end of stirring controversy but controversy for the sake of truth is a divine command, as Walter Martin said.

Truth, some people claim to be in it, some claim to have it and others claim to know it, and others claim there is no such thing and that is the truth—and finally, some politicians claim to tell it. How do we describe truth? There are many theories of truth, and this is called “epistemology” which is a theory of knowledge. Is truth knowable, even if it exists? How can it be known in a theory laden universe?

THEORIES OF TRUTH

Pragmatism

What has become increasingly popular, which is what have proffered an idea of truth is what works. Consider a moral action, such as theft, which would be both right and wrong while the act is committed and its value would be determined after the outcome. At best, pragmatism is a negative test for truth. Good intentions, are unfortunately not a criterion for truth.

Coherentism.

Others have argued that truth is what coheres. Under this view, an internally consistent story, with no correspondence to reality, would be true. This view may gain some credibility if the state of affairs were what the story had to cohere with, but an internally consistent idea, alone, does not constitute truth.

Inclusivism/Exclusivism.

Matthew 7:13, Jesus notes that the path to destruction is an easy target to hit, but that the path to life is much more difficult, since there can only be one truth, in this case, as it pertains to the nature of God.

Was Jesus right? Some object to truth being exclusive by saying that some have their truth, while others have theirs. A strong example of the exclusive nature of truth is that “2+2 = 4” to the exclusion of all other answers. Is it arrogant to say those who answer 5 are wrong? Given the infinite amount of possible numbers one may answers with, 6…6.5…7 and so on, it is possible to imagine how the wrong answer has a larger target range than the one correct answer.

What about matters of history? There is little room for debate regarding the truth or falsity of an answer in a mathematics department. All one needs is a chalkboard and some patience.

Matters of history are not known with mathematical certainty. There are those who contend the holocaust never happened, while others, using artifacts of the past and recent eyewitness testimony, argue otherwise. The fact is, there is a truth either way.

A recent, revamped, idea is flat earth theory, that the earth is flat and that we, the public, have been fleeced for years by scientists telling us the earth is really round. Setting aside the discussion on the matter, does the earth become round as people believe it is round? Is its flatness determined by the adherents to the belief it is flat? An examination of the state of affairs will settle the matter abruptly and it will be either/or, not both/and.

Those arguing for the inclusive nature of truth are stuck defending that an idea gains truth value by the noses it can count who hold to it. This would be an awkward thesis to defend, and fortunately I do not have to defend that castle.

TRUTH CANNOT BE KNOWN

Some have thrown up their hands at the knowability of truth and claim it simply cannot be known. However, this is a thesis which cannot satisfy itself, since one is claiming to know enough about truth to assert its unknowability. While truth may be difficult to know, it does exist to be known. Historical truths would be an example of difficult truths to know, but still not impossible, and moral truths are ones which are surprisingly easy to defend. One may claim that moral truth is relative, but as Greg Koukl and Francis Beckwith note, in “Relativism: Feet Firmly Planted in Midair” is that one can pay lip service to moral relativism, but when someone steps on our toes, morally speaking, we want the death penalty and we speak in terms of moral absoluteness.

This view is surprisingly taught from the pulpit, as well, that the effects of sin have estranged us from being able to know anything, but, again, this view cuts its own throat because it claims to know enough about truth that it is unknowable.

THE TRUTH OF THE MATTER

I will argue that truth is a metaphysical notion. (I have written a bit on metaphysics here.)

Truth requires two components, a state of affairs, which is how things are, and a proposition, which is a truth bearer to the state of affairs. More on this later.

A property of truth.

Truth can be said to be intentional. One recalling details of an incident and describing it to the court, but lacking some points, cannot be said to be lying. In this sense, truth can be said to be a degreed property of a statement. Some statements are truer than others.

Truth, with a capital “T” is how things actually are, in the mind independent sense while “truth” as we know it is our intellectual, mind dependant, constructs of the state of affairs.

There are theories about Truth and our ideas of it. Some contend that truth is at the center of a web and some ideas are closer or further from the center than others. However, one salient problem with this theory of justification for truth is that it results in an infinite regress of truth as it relates to Truth and there is no way to tell how far or close we are to the center, or the Truth as it really is.

How do we test our current ideas against the Truth, then? Are our models, or conceptual schemes accurate, and how do we tell? I would argue that we can test our ideas against reality by their ability to yield predictive and replicable results. For example, there are those who contend that the evolutionary paradigm contains much truth to it and that one must understand evolution in order to do evolutionary medicine. Now, there are those who rightly argue that evolution is not a complete theory, but it is undeniable that there is enough truth to the theory that we can make predictions based on it. Less controversial, is when one is doing archaeology, and if one has a good understanding of an ancient civilization, that they will be able to make good predictions as where to find ancient artifacts and so forth.

Take a simple statement, “It is raining!” This statement is neither true or false and until examining the state of affairs outside it remains both true and false. In Truth Decay, Douglas Groothuis notes that it is by this that we say “truth is antithetical/exclusionary.” A true statement excludes all other competitive statements. Truth, therefore, can be said to be exclusive, not inclusive. There may be room for diversity in society, but not truth. A popular saying is that the law of non-contradiction isn’t just a good idea, it’s the law. While there are laws that can be broken, like speed limits, there are laws which are inviolable and as soon as we try to violate them they are able to come to their own defence. A denial of normative laws, such as the law of non-contradiction, involves an undeniable use of the law in order to indicate it is said law being denied, not another one.

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The Law of Noncontradiction (LNC) states that “A” cannot be non-A in the same time and place.

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Bertrand Russell, in the Problems of Philosophy says that we should not be amazed that the aforementioned LNC is how we happen to think, but more notably that this is also how the universe behaves. While it seems to be a rule of thought, it also seems to be an absolute law of nature.

It is important to note that there are necessary and contingent truths. An example of a contingent truth would be that Abraham Lincoln was shot on April 14, 1865. It could have been the case he was shot the day before, or the day after, or that he was never shot at all. This is where one gets into modal logic, which surveys the realm of possible worlds. More on this another time, but the important thing to note is that there are contingent statements which are, at first, second or third glances not incoherent or contradictory even if they are not true. An examination of the actual world determines their truth or falsity. This is why it is important to read a newspaper critically, rather than by accepting the source as a sufficient authority on the matter. Even in the case of modal logic, however, the LNC is upheld in all possible world scenarios. It is a ubiquitous feature of all possible worlds we could imagine, including the actual world we live in.

That it is raining outside has no truth value. States of affairs, in themselves, are not declarative like propositions. A state of affairs simply is. States of affairs are what are called “Truth-Makers” in that a proposition exists which affirms or denies a certain state, but the proposition finds a counterpart in reality.

The statement “It is raining in my city” is true if, and only if, the state of affairs exemplifies this in reality.

NOTE: Propositions are not to be conflated with sentences here. Propositions are the meaning of a statement. They pick out, or affirm/deny what a state of affairs obtains. In Philosophical Foundations for a Christian Worldview, the authors note that propositions have neither extension in time and space, nor are they to be confused with the linguistic entities which express them. That they convey meaning is why one may translate from one language to another, or why we have so many Bible translations, different Bible translations attempt to best convey the propositional content of the original meaning in the manuscripts.

THE NATURE OF TRUTH

Back to the simple sentence “It is raining!” This sentence claims to know something about the nature of reality, that it is raining. This sentence is true, if and only if it is raining, or more specifically, that it is raining in a specific location, since it is always raining somewhere in the world. That it is raining in a certain geographical area at a specific time is to the exclusion of its negation, that it is not raining at a certain time and place. As previously mentioned, truth is antithetical and unforgiving. We live in a mind independent reality which shapes our minds, not the reverse. This is why truth is “inconvenient” because it corrects is, we do not correct truth.

As seen, denials of truth lead to incoherent beliefs and contradictions. There are different theories of truth, all which fail and are unliveable. Truth, then, is what corresponds to reality. If the reality we live in fails to exemplify our ideas, then our ideas simply are not true. There can be degrees of truth, as in the case of history. Some historical or scientific models are partly true, in that they partly describe the objective truth of the matter. This is where one gets into fuzzy logic, where there are degrees of truth, but that there is objective, knowable truth, is undeniable and to say we cannot get to the facts of the matter leaves us without knowing what degree of truth we are even at in our models or constructs of reality.

How this relates to the existence and nature of God: Remember the portion about modal logic and necessary vs contingent truths. Consider how there are ways the world could have gone, such as the assassination of Abraham Lincoln. While some theologians, such as Richard Swinburne disagree, for reasons I cannot fully comprehend, God either exists necessarily or He does not exist necessarily. There is no maybe about this one. Either way, God is a necessary being or He is a necessary non-being. If God does exist, one cannot wish His existence away with fanciful thinking, nor can one wish Him into existence if He does not exist. Therefore, God and His attributes are not subject to modal logic.

Truth is just the way things are and it is our responsibility to proportion our beliefs accordingly. As a philosopher, I am probably more committed to proving truth than I am God. In the order of epistemology I hold God to be a by-product of truth, but my commitment must be to truth, because no matter what that is what I will be left with, even if God does not exist. Truth must be pursued dispassionately and without self interest.

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26 thoughts on “The Inconvenience of Truth.

  1. Colin, reading your article reminds me of Douglas Adams’ philosophers who built a computer to tell them the answer to ‘Life, the Universe and Everything’. The well-known answer is, of course, 42 but the philosophers had to build an even bigger computer to tell them what the question meant before they could understand the answer.

    I think the reason your view expressed here seems confused and even self-contradictory in places is because, as you say in the title, truth is ‘inconvenient.’ The word ‘truth’ is used in very different ways in different contexts (this could in fact be a continuation of the discussion on hermeneutics) so any attempt at a brief, general examination of the subject is inevitably going to suffer from these problems.

    You say that “there can be degrees of truth, as in history…where one gets into fuzzy logic” but you also say that “we live in a mind-independent reality which shapes our minds, not the reverse” and that “truth is just the way things are.”

    I can confidently state that our reality is clearly not independent of our minds – I have a virtually worthless sheet of plastic in my pocket that I can buy £10 worth of goods with in the shops because it has a picture of the Queen on it that means all of the people who share my reality have agreed it has that value. Our reality consists in both the physical world and the mental world, and how they condition each other is almost too complicated to analyse but it does, in fact, change over time which is something your view is unable to account for.

    As an example of this – if you and I were living 500 years ago we would not be able to enjoy the beautiful scenery of our two countries (I live in Scotland). We would be sick with fear and loathing at the sight of wild mountain scenery and ancient forests because nature was the devil’s realm; people built gardens with perfect curves, symmetry and straight lines in order to defeat the horrors of nature. Descartes, the Enlightenment and the Romantic Movement changes all of that so that we now see nature completely differently. It’s very easy to take for granted the way things are as being a universal reality – you take it for granted that there are only two genders, for instance. The great joy of philosophy for me is that it studies the things we take for granted.

    1. Chris,

      There is “Truth” with a capital T, which is the thing itself, then there is truth as we know it. One thing I forgot to include and will add, is that truth is intentional. If a witness tells a court their description of an event but leaves out, unintentionally, some details—by mistake or memory lapse—have they lied.

      You raise a good point, in that there is truth as we know it, our as our ideas approximate it, then there is truth as it really is independent of ours constructs.

    2. In addition to that, truth is inconvenient because it corrects and often rebukes. If we try to act according to our ideas rather than reality itself, it is us who will be set straight and have to proportion our ideas about reality accordingly.

  2. Colin, I sense that you’re misunderstanding my point somewhat in your emphasis on ‘Truth’ with a capital T. I agree that there is a material reality which is unchanging, for example the Earth has always been round rather than flat and I presume that this is what you’re referring to as ‘Truth’. However, it seems clear that our reality containing some knowledge, such as a belief that the Earth is flat, conflicting with the ‘Truth’ is perfectly viable (and, anticipating an objection to this assertion, I would say that it was not the roundness of the Earth that caused the change in this reality but a complicated tangle of ideas in human minds) possibly because whether the Earth is round or flat is marginally less important to us than how we define and understand ourselves as individuals in relation to our social structure.

    I would disagree with your second response; I think that ‘truth’ is inconvenient because it is a vague, ill-defined concept not because it limits us in some way. There are many examples of our ideas ‘setting reality straight’: religion, for example. Christianity, whether it came from our own minds or was placed there by God, is an idea that has changed our reality many times in the last 2000 years. I’m sure you would agree that both Marxism and Islam are ideas produced entirely by human minds that have changed our reality substantially.

    1. Absolutely, Chris, regarding Marxism and Islam. Humans aside, we live in a very deterministic universe where physical laws would explain events exhaustively. But when we throw in human involvement things are not so deterministic anymore because we have thrown in a rational component. Our ideas certainly do have consequences in reality, but these are social consequences. Do my ideas that “2+2=4” make it so, or that we live in a universe governed by the laws of thermodynamics? What about laws about theft? Do we make it wrong to steal by our laws about stealing? Now, what if one were to construct a political ideology making producers enslaved to those who have less and that we distribute their productions to those who have less. Let’s call it “Marxism”, now does that make it true, morally, that this is an acceptable social paradigm? Will its truth value not be determined by the type of society it produces?

      As for your first paragraph, I am unsure what you are saying. It seems you are saying we are participants in creating our world, such as in a strong anthropic principle or something.

  3. Yes, my first paragraph is probably not as clear as it could be – I was simply pointing out that there is plenty of evidence of societies that can function despite their maintaining ideas that conflict with some area of material reality. I would say that, at most, it’s asserting some sort of weak anthropic principle (although ‘anthropic principle’ can mean all sorts of things these days) which, if you think about the examples I’ve given, is basically just common sense.

    In mentioning Christianity, Islam and Marxism I did not intend to divert the conversation into moral philosophy, I was simply citing them as examples of human ideas that have changed our reality; I think it would be extremely premature to start thinking about whether they constitute good or bad changes at this point.

    Your view seems to be that social and material realities are radically separated. My view is that social and material realities are inseparable, so, yes, we do need to take individual responsibility for the way our world is. Your example of theft is useful in illustrating this – the concept of theft only has meaning for us because the reality we exist in has invented the idea of personal property. For someone living in a reality that does not include the concept of personal property, theft is meaningless.

    1. Chris,

      You make some good points in that we are participants in our world, therefore we do create a reality in a sense, but there are items in reality which are non-negotiable as previously discussed.

      Your quote: “I was simply pointing out that there is plenty of evidence of societies that can function despite their maintaining ideas that conflict with some area of material reality.”

      I agree that this is possible, but who is more likely to have successful behaviour? One who is acting on a true belief, or one who is acting on a false belief? Would not a true belief increase the intentionality of an action and decrease the arbitrariness?

  4. I would say that it’s not just possible but actually the norm and that ‘success’ is, of course, a highly debatable idea. How we measure the success of a culture or society depends on being able to define what they are as well as being able to define what we mean by success. Indigenous tribes in Australia, New Guinea or Brazil could be considered very successful in the way they were integrated in their environment despite having beliefs about the world that we would probably regard as false. However, those beliefs presumably have hampered their ability to adapt to the new situation of being overwhelmed by our modern Western culture; does this mean that we are more successful? If it proved to be true that industrialised societies have begun to alter our climate in a way that makes life much more difficult or even impossible for some of the population I would not see that as success and there are many other indicators that suggest something other than complete success.

    Defining a culture is extremely difficult because we, as individuals, very rarely exactly fit the culture we’re brought up in, especially in modern Western societies that place a premium on individualism. I think this is why nationalism and religion are such strong ideas for us – they ease the difficulty of trying to work out who we are and where we belong. However, in my view that culture is largely responsible for creating us as much as we are responsible for creating it, a view very similar to the idea of reflexivity proposed by George Soros (I’m aware that, for some reason, Soros is something of a hate-figure for the American Right at the moment but I’m not making any political judgment, just that his philosophical view seems very similar to mine) and I would recommend reading his work along with two books by Max Horkheimer, ‘The Dialectic of Enlightenment’ and ‘Eclipse of Reason’, which influenced me considerably when I was at university and explain these ideas a lot better than I can.

    1. You are correct, that while Soros is a bit of a malevolent character he undoubtedly had some brain power and good ideas going for him.

      A culture being difficult to define, but we can safely say it is an emergent property like a flock of birds. It happens when enough people gather together for each other’s benefit, to some extent. The idea of success would be another thing. I suppose it would be measured against their ability to accomplish some end goal which they have in mind. If I have set out to become a bow and arrow hunter and to live off the land, one might say I have failed at that. Fortunately I have not set out to do that. How we test the correspondence of one’s ideas is their ability to produce a desired outcome, but this is a negative test for truth again. One might get the right answer for a math equation but have incorrect premises on the left side of the equation, the antecedent does not substantiate the consequent. This is why in logic and mathematics one must show their work. Consider,

      X = 5, as a postulate.
      2 + n = X
      Now let us have the belief that n = 2 and the sum of 2 and 2 is 5. While it is correct that X is 5, but the belief that 2 and n is equal to X based on these antecedent conditions simply does not follow and even though I produced the correct answer, the antecedent beliefs do not correspond to X. I realize this is a bit convoluted, but I think it illustrates the problem.

      I think Plantinga’s argument against materialism, here, illustrates this much better than I could.

      http://www.christianpsych.org/wp_scp/wp-content/uploads/plantinga-against_materialism.pdf

  5. Colin, I’m intrigued as to why you should describe Soros as ‘malevolent’ when he’s spent most of his adult life working to make Popper’s Open Society a reality; however, that’s probably a conversation for another time!

    I have no problem with your idea of culture being an emergent property like a flock of birds as a starting point but I don’t think cultures or flocks of birds generally set out with a specific end goal other than, as you say, gathering together for mutual benefit with some more or less vague notion of survival (for example, the US Constitution) and the ones that have started with a very specific plan, like the Soviet Union or the Apartheid regime in South Africa, haven’t survived for very long.

    As for Plantinga, I have to say I spent a year of my degree studying logic and I found it an unpleasant, tedious chore so I’m always slightly suspicious of arguments that depend on it to any great extent. Even good logical arguments have had the life taken out of them and, all too often, it’s used to pass off highly dubious statements as true propositions so my usual method of dealing with this is to try and describe the arguments in normal language and see where that takes us.

    Please correct me if I’ve got this wrong but as I understand it you and Plantinga maintain that there is both a material and a non-material reality and that, in some manner, God acts as an underlying mechanism for bringing the two together which seems to be the standard Cartesian Dualism. I have a feeling that Plantinga is arguing this in order to support the belief system that he already holds, his argument being ‘Materialism is logically false, therefore God must be true’, as he doesn’t seem interested in using any empirical evidence to support his view.

    My view is that I’m what you might call a Reluctant Materialist. Materialism doesn’t ‘feel’ right to me and, clearly, I’m aware that we have some sort of mental reality but there is not enough evidence for me to know what it is or how it works so I would have to disagree with Plantinga’s conclusion consigning materialism to the scrapheap of philosophical history – a logical argument, even a good one, is not sufficient by itself to dismiss any disagreement. It needs to be supported by substantial evidence.

    1. Chris,

      I’ll leave the Soroa bit aside for the time being. He is such a controversial character.

      Yes. I would maintain that there are material and immaterial realities. I would even maintain that abstract entities are ultimate realities which are had by particular substances and without abstract entities material substances would be impossible, as they would have no predicates to obtain.

      I an curious why you seem so suspicious of logic, given it is a normative means of thinking and we are all bound by its precepts. When we analyze an argument, logically, we are able to see it for what it is rather than what we think it is, it provides an objective framework for looking at the world.

  6. I should write a book about the problems I have with logic! However, I’ll just mention a few:

    First, is logic actually normative? There are good arguments to suggest that this is not necessarily the case depending on what type of logic we’re looking at and how normative is defined. It is certainly still a hotly contested subject. One possible area of dispute is that logic is a human invention and, more specifically, an invention of a particular ideological view which regards that form of linear thinking as being the proper method for human thought. In which case, describing logic as normative would simply be a tautology in that context.

    Next, is it possible for an argument to be “what it is rather than what we think it is”?
    Remembering your hermeneutics and taking the view from the previous paragraph, it could be that it’s almost impossible for us to think entirely outside of our cultural context (but of course, cultural context can be very restrictive or very open depending on the individual) and translating ideas from one context to another may alter them in unpredictable ways. Now, logic has a peculiar cultural context in that it attempts to remove the context from an argument in order to make it universally applicable but to make sense of the argument we need to return it to a context and this can, in practice, make it very difficult to know if the argument has been affected by the translation.

    It’s that translation process that makes human thinking so creative and probably the reason no one has managed to make a General Artificial Intelligence that works yet. For those reasons (and several others) I prefer to make arguments in ordinary language if possible as it makes it much easier to see how they work in real life. As an example, I would say I’m not sure what you mean by “…abstract entities are ultimate realities which are had by particular substances…” and it would be easy for you to give some examples that would clarify the point.

    1. Logic as being normative:

      I defend this thesis and do more extensively in another post, titled “Faith Hope and Logic”, on the grounds that this very conversation presupposes the validity of logic and the law of contradiction. Such doctrines are normative in that they are undeniable and any attempt to refute them presupposes their validity.

      Could logic be a culturally sensitive subject, where we have western and eastern logics? Maybe, but they all seem to presuppose the laws of logic, which seem inescapable as far as I can tell; so, thus far logic seems to be intersubjectively true and it does not matter which culture you are born into, the validity of these laws seems very unforgiving.

      By abstract entities being what ultimate reality is made up of is a view which hold substances or events to be particulars, while their properties are universals and are held by multiple instances of different substances. One might say that substances can have no extension in space without there being physical properties, such as shape or size.

  7. Your answer to my question is actually even better than I had hoped for as it gives me a clear indication of the context that your view is coming from, that is the nominalism of Medieval Christian philosophy, which brings what you’ve written, particularly about logic, into a much sharper focus.

    The history of Logic is long and complicated and I can guarantee that no one with a philosophy degree regards logic as easy. Aristotle invented the idea, as a matter of personal preference rather than as a result a logical proof, possibly in the hope bringing some order to the politics of a society that was starting to disintegrate (it was made up of hundreds of separate states, some democratic, some oligarchies and some tyrannies) but he saw no reason to doubt that his senses gave him an accurate view of world so his basic syllogistic logic, although it went virtually unchallenged for more than a thousand years, was unable to adapt to the more complex mercantile society that began to develop as part of the change from the medieval to the modern world. The epistemological problems created by the scientific revolution eventually led to a complete re-thinking of logic and we now have (and I don’t think this is an exhaustive list):

    Deductive logic
    Inductive logic
    Modal logic – Alethic
    – Temporal
    – Deontic
    – Epistemic
    Propositional logic
    Predicate logic – First-order
    – Second-order
    Meinongian logic
    Para-consistent logic

    One of the results of that revolution that started in the mid-19th century and led to Russell and Whitehead’s Principia Mathematica was Russell’s discovery of the paradox that bears his name. In working on set theory, which is necessary for defining numbers, Russell realised that there are two types of sets – ‘normal’ sets that are not members of themselves (the set of all squares is a set, not a square) and ‘abnormal’ sets that are members of themselves (the set of all non-squares, for example). If P is the set of all normal sets is it a normal set? If it is then it is a member of P since P contains all normal sets but if that is the case then P contains itself therefore it is abnormal and so on in endless circles.

    Both Russell and Zermelo. who independently recognised the paradox, tried to solve the problem by introducing external qualifiers (Zermelo’s axiomatic method and Russell’s theory of types) but because these don’t arise necessarily from the system, they are not generally considered legitimate solutions. This led to Kurt Goedel’s famous Incompleteness Theorems which seem to prove that this is a real paradox and had a considerable effect on the way logic has developed.

    I’m interested to see that you quote Jacquette in your logic article; I would imagine that, as a nominalist, you find his Meinongian logic very difficult to accept. One of the things that concerned him was the question of how far the maths of modal theory should take precedence over empirically discernible facts because of the way formalism always distorts the properties they represent to some degree, which is what I referred to as the translation problem in my last post. Goedel recognised something similar as early as 1929 as apparently he said this to Carnap: “We admit as legitimate mathematics certain reflections on the grammar of a language that concerns the empirical. If one seeks to formalize such a mathematics, then with each formalization there are problems, which one can understand and express in ordinary language, but cannot express in the given formalized. It follows from Brouwer that mathematics is inexhaustible – one must always again draw afresh from the ‘fountain of intuition.’ There is, therefore, no characteristic universalis for the whole mathematics and no decision procedure for the whole mathematics.”

    This posts a bit long and I’m only half way through what I was going to say so I’ll post this now and add the rest later when I have a bit more time.

    1. Chris,

      I think the big point you made was regarding Aristotle’s logic, that it was somehow invented as a convention. I do not see logic as something that is invented anymore than I do math. Sure, I see there being conventionalism’s within both disciplines, such as the symbols and terms used. However, saying logic was invented is like saying gravity was invented. Aristotle, rather, made us aware of how we think and codified it into succinct terms. If logic is to be taken as a human invention, and not how we ought to think in every circumstance, then it becomes a branch of psychology, and psychology is inept at telling us how we ought to think, except in terms if statistical averages.

      Where Aristotle’s logic proves itself as an axiom for normative human reasoning is the terms, as I have mentioned elsewhere, defend themselves and their denial results in a contradiction or absurdity.

      I take the foundationalist view that there is a first principle from which all other principles are derived. Rather than espousing de constructivism, which leads to an infinite regress of justification, and where there is no way to tell where one is in relation to the core idea, this seems proper and less counter intuitive.

      I do agree with much of Jacquette and found his book on symbolic logic to be invaluable, but part ways with him in reducing logic to a branch of psychology. I, rather, would seek out more normative means of human reasoning to buttress a given psychology.

      You rightly noted several different types of logic earlier in your post and these are all very valid forms of logic, which utilize first principles.

      Deductive logics are ones which reason from a particular to a general and are a priori.

      Inductive logics, or forensic logic, reasons from a general to a particular and is more experiential.

      Propositional logic deals with well formed formulas and their atomic constituents, while predicate logic deals with the atomic statements and attempts to split said atom and deals with existential and universal quantification.

      But all of these rest on first principles which seem normative and none have managed to impeach any of them yet.

  8. OK, the second half of the post was going to be about how logic has developed in light of the paradoxes, especially in the area of artificial intelligence, and how that has affected philosophy but as you’re having difficulty accepting things that really are standard academic ideas I’ll try a different approach. Before I do, however, I will offer a couple of bits from much longer quotations I was intending to use:

    Ben Goertzel – “Aristotle’s syllogisms made good psychological sense, although we now know that much useful human reasoning relies on inferences which Aristotle deemed incorrect.”
    Alan Bundy – “Logic is not enough to understand reasoning. It provides only a low-level, step-by-step understanding, whereas a high-level, strategic understanding is also required.”

    Looking back through the conversation, I can see that these relatively short posts (short relative to the difficulty of the subject) may give a slightly false impression that I’m speaking from some dogmatic, systematically complete position. This is, of course, not the case and I’ve spent today thinking how I might correct it. I think part of the difficulty is that the disembodied words on a computer screen may make the sort of views that I’m expressing look more odd or unreal than they actually are so I’m going to try and ‘re-embody’ them, which would seem to be an appropriate strategy for the idea that thought can’t be detached from the whole human experience.

    I was brought up in a family where religion was almost entirely absent; in typically English fashion, religion (including atheism) and politics were not suitable subjects for polite conversation but after my dad died I found a diary he’d kept when he was in Egypt and Palestine during WW2 in which he wrote very movingly about visiting the holy places in Jerusalem and Bethlehem. I also found out that he voted Labour in the 1945 Election, as many servicemen did having served together during the War, for which crime his family shunned him for some time but, of course, he never spoke about any of this.
    In the summer of 1967 (still regularly referred to here as ‘The Summer of Love’) I was 15 and, perhaps influenced by the opposition between the intense optimism of social science that was going to right all of the wrongs that had created totalitarianism and war in that century and the pessimistic spiritualism of hippies who thought only about themselves and how they were going to reach Nirvana, beginning to become aware that there was perhaps more to reality than met the eye. I didn’t like the idea that I was simply an object of scientific study but nor did I think that drifting off into a spiritual nothingness was a good idea.

    However, I had no context, either religious or political, which would provide a ready-made starting point for considering this problem so I found myself doing what I now recognise as philosophy but in a very random fashion. Over the next 20 years philosophy remained a hobby while I emigrated to Australia, worked in many factories, offices, army facilities, warehouses, and spent time as an athlete in East Germany and Czechoslovakia in the late 70s and early 80s. By this time I had come to think of reality as, largely, a social construct but had not found any evidence of anything other than material substance so, although I believed that I had free will, I had no idea how that worked.

    It was at this point that I went to university and spent five very happy years (apart from those logic classes!) studying philosophy full-time up to PhD level although I didn’t start my doctorate because by then I was married and we were about to have a baby. What amazed me was just how much I had underestimated what a monumental subject it is and that the ultimate truth of philosophy is that no one has an answer – it’s all about engaging with the problems. I also found myself having more respect for intuition as my final dissertation was written under intense pressure in about two weeks using a very intuitive approach and I actually spent the next 20 years working my way through it in detail before I could fully understand what I had written. This strongly suggests to me that the human mind works by being embodied in a world and can make random connections in a very creative way but, after 50 years of philosophy, I don’t think I’m any closer to an answer.

    1. Outstanding academic background, however, I am not, as you say, having difficulty accepting standard academic ideas. I merely disagree with them, as do many other scholars in the field of philosophy. I believe it was Edmund Hussrl who advocated that psychologism was the death kneel to logic. I would agree, it most certainly is philosophical suicide, and I will say why:

      As I have said before, counting noses does not determine truth. If logic is a form of reasoning which happens to be utilized by particular entities, we cannot say it is a universal. The thesis of psychologism cannot even satisfy itself. It claims to be descriptive of human reasoning, not prescriptive, yet it makes this as an objective claim. Logic, then, would be a useful fiction and it would be a happy coincidence that we have all adopted this form of reasoning.

      I would be curious as to why your cited scholars reject logic as a normative tool of thinking. How can one say I was illogical in rejecting their proffered notion of logic if it is not a necessary and universal truth?

  9. Colin, as I said in the previous post, I don’t have the answer and philosophy properly doesn’t provide any final answers but what it can do (and what I’ve tried to do in my posts) is to shine a light on the problems that it engages with so that they become a bit clearer. Disagreeing with widely-accepted ideas is, unequivocally, a good thing to do in philosophy but it’s well to remember that the views we disagree with are part of a long process of intense debate and deep thinking so shouldn’t be lightly dismissed (which is what I meant by having difficulty accepting standard academic ideas).

    Things are almost always more complicated than we think they are; for instance, Husserl’s emphasis on opposing psychologism became apparent after 1894 when Frege criticised his Philosophy of Arithmetic for its psychologism but I think that Husserl was always more interested in promoting ‘pure logic’ to support his central idea of Phenomenology as a proper science than seriously dismissing psychologism as something that would weaken his claim to be scientific. In dealing with the ‘Paradox of Subjectivity’ (how can the consciousness that constitutes the world also be part of that world) as a way of overcoming Cartesian Dualism (as one text book puts it) “after demonstrating that kinaesthetic capability is an essential structural moment of transcendental subjectivity itself, he asks how kinaesthetic consciousness as an ongoing flow of purely experiential potentialities (the possibilities of primal motility per se), and of ever-changing actualizations of these possibilities, can come to count as a mundane entity apprehended as one thing among others in the world.” I have only the vaguest notion of what this may mean, possibly something about how the way we continually physically interact with the world can allow us to know ourselves as individuals, although he seems to have been sufficiently influenced by Descartes’ agenda to see it in epistemological terms – how the dynamic process of embodying affects our knowledge of the world and, like any text, it is open to several interpretations.

    My current view is that logic is a very useful invention, that there seems to be no evidence that it is in any way universal and that any description of human thinking is subjective. I think that, since Descartes, we can aspire to objective thinking about ourselves but that aspiration is probably unachievable ultimately. My evidence for this would be historical; if Aristotle had discovered a true, eternal, universal, normative logic either we would still be living in ancient Athenian society or, if we had somehow developed our present technology despite Aristotle’s idea of science, we would all be slaves in a totalitarian society run by machines because, if logic was as Aristotle thought, a general artificial intelligence would have been very easy to produce and our idea of the human individual would not have been sophisticated enough to withstand tyranny. As it is, a general artificial intelligence has so far proved too difficult despite the development of logics that work without the law of non-contradiction. The fact is that human societies have changed and those changes have tended to correspond with changes in how people understand logic and define themselves as individuals. As I pointed out in my first post, it’s very difficult to see how a logic independent of human mind can account for the sort of social change that we have experienced over the last 2500 years. Of course, as a relativist I can’t be sure that we will never discover an independent logic or an absolute reality behind the one we see in our everyday lives but I don’t think we have that at the moment.

    1. Chris,

      “Of course, as a relativist I can’t be sure that we will never discover an independent logic or an absolute reality behind the one we see in our everyday lives but I don’t think we have that at the moment.”

      How would you know, under relativism? Do you have a criteria for recognizing absolute reality if it even slapped you in the face, so to speak!?

  10. That’s a very good question. I really can’t imagine what it would be or how I would recognise it. I presume it would be somehow non-material as the material world is subject to change – our planet has only about another 5billion years left before it gets vaporised by the dying sun – but the only non-material thing I’m aware of is our social reality and that is, presumably, something that only exists through human agency.

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