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Archive for the ‘logic’ Category

The virtue and vice of the analytic tradition of philosophy as it has developed (and floundered) in the 20th and now 21st centuries is its focus on dialectic, and this especially over and beyond rhetoric. This may in fact be considered its substantial difference from the continental tradition, for while the continentalists may concern themselves over the dialectic what they are really doing, as I am using the terms in their classical sense (and this will provide an etymology of “the dialectic”), is focusing their efforts on a rhetorical process.

Understood classically, rhetoric is “the art of speaking with persuasion.” It treats of the psychological mode in people as its fundamental category, to see why what is said has such an import on the ultimate ideas which people will implicitly or explicitly act upon. Dialectic, on the other hand, is “the science of treating meanings (ideas) as themselves.” It seeks to “get past” people’s psychological modes, to hash out for-itself that which is meant and what applies to the real.

That I treat one as art and another as science is, I hope, a rhetorical distinction not lightly glanced over, and I should be subject to it even if I were to pretend that I were being plainly and strictly analytic, or participating in mere dialectic. This illuminates the problem of communication, or speaking, in that our rhetoric remains a substantial part of what we say. I believe we can take this to mean that there is really no such thing as dialectic per se, void of rhetoric; likewise, though, there is no rhetoric per se. They are both intrinsic parts of the action we call communicating, the act of “meaning to another, beyond oneself.”

It is relevant to focus and dwell on rhetoric because, no matter the supposed analytic ideal of a “perfectly logical argument,” you cannot crack the egg of understanding in another without prying them open with rhetoric. Even the notion of a merely dialectic discussion is rhetorical. I believe the idea of a “non-rhetorical argument” should be treated as economic models: ultimately oversimplifying and not anything you can find out there in the world. Does this make it beside the point? No. It remains useful, but this to the extent that it does not make of itself the world. This is because the world is filled with people for whom rhetoric is substantial. This is not some cute sociological observation, but rather a description of people as they are. People are rational creatures, but they are also rhetorical creatures. The idea of the purely logical man is not something we can assume of reality. For while logic/dialectic is an essential element to who we humans are, and we would not be human without it, nor should we even attempt to go outside it, rhetoric remains a structure we are placed within and cannot go beyond because it is the very condition of meaning to another at all.

The rhetorical inheres to the dialectical, and the dialectical inheres to the rhetorical.

Logic is just another rhetorical game. It is not a wrong game, but its psychological attributes ought to be appreciated. It is something we undertake and understand from a psychological mode of being human, and were one to remove the psyche, one should also remove the care for logic at all. I am loathe to call it strictly a passion, but logic is a tool we use to fit our purposes. Logic cannot instruct of itself. Its explanation and reason is external.

I do not mean by any of this that dialectic can be done away with, as though we should simply drift off into the dialectic and cease trying to get anywhere. It is only that one cannot truly see the world without knowing something about the glasses they are wearing. But there is nothing to see without the glasses on, without an instrument facilitating the sense. The instrument cannot be left out of the equation! How one sees something is crucial to knowing what one sees.

I will admit that this creates a problem. If rhetoric is substantial and fundamentally colors our view of the world, how can we truly know of the world? For now, my answer is that truly knowing of the world does include rhetoric; one should be not themselves if they try to go without it, since it is an essential element of being oneself as a human. But then how do we get out of the rhetorical circle, with the rhetoric we adopt being arbitrary? After all, if the rhetorical circle cannot be escaped, then you cannot transition yourself to another rhetoric on a reasoned basis. Ah, but that is to miss the point of what I am saying! Rhetoric is substantial, and its substance can be examined for fault. No rhetoric leaves itself without some way of looking at itself, for the glasses analogy aside, rhetoric is truly an apperceptive sense. It perceives itself, such is the matter of the dialectical inhering to the rhetorical!

Therefore, I propose a new project. The study of rhetoric as substantial in facilitating what we are able to understand.

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I am calling the “Counterexample Fallacy” that way of thinking in which, upon being presented a generalizable principle, one thinks they have defeated it by presenting some apparent counterexample. The Fallacy depends upon the assumption that, for a principle, it is meant to apply equally to each specific individual of the kind it is about, rather than it being either a definition of natural possibility or some relation that holds among other. I will give some examples of what I mean to help get the principle across.

One of the popular counterexamples is to Aristotle’s definition of man as “a rational animal.” That man is an animal is hard to come up with some counter-example, since people are used to thinking of “animal” as just referring to a category (though of course, “animal” does mean “the power to animate”). But when it comes to rationality, people are quick to think up some example of people who either do not exemplify rationality or are not currently acting very “rational.” They mistake “having rationality” for “acting with high levels of intelligence.” As such, they ask how infants can be considered rational, since we don’t think of infants as possessing the potential to exemplify rationality in the way that an adult does. However, this mistakes the definition of man as “rational animal” to mean “Wherever there is a man, that person is presently acting with intelligence.” That’s not what it means at all. Rather, it is about man’s natural power to express such levels of intelligence, to act with self-regard for what he desires. That is what is mean by saying that man is a “rational animal,” and the counterexample people bring up is irrelevant to the principle behind such a definition, namely that it is an expression of that potency which distinguishes man from other animals.

Here is an example of a counterexample which illustrates another element. There is the elementary economic law of demand, which states that “as prices rise, quantity demanded falls.” Many people accept this as intuitively true, but when you try and apply it to some popularly held opinion, e.g. that minimum wage hurts the poor by restricting hiring of low-skilled (and thus most likely poor) individuals, people suddenly act as if there must be exceptions. In order to bear this out, they seek some counterexample in which prices rose and quantity demanded also happened to rise. They insist that this means the principle is either false or at least doesn’t always hold true. What such a counterexample misses is that the principle is applied as a relationship between strictly two variables which also accepts that it isn’t the only variable which matters to forming prices. As such, the counterexample in this case misses the point that it is a description of two variables among others which also matter to forming prices and quantity demanded; from the perspective of the law of demand, one would just say that, were prices lower, quantity demanded would be even higher. It is not a statement that prices and quantity demanded cannot rise at the same time, since there are other factors which inform these things.

A final example which occurs along another line is when someone introduces additional qualifiers to evaluate a principle. I would also call it a “smartass objection,” which is when someone thinks they’re clever for taking a narrow interpretation of a principle, introducing qualifiers it doesn’t (narrowly) take into account, and then pronounce the principle incorrect because they presupposed a narrow interpretation of the principle rather than construing the principle in line with the dimensions they introduced. For instance, when you say that “ought implies can,” someone might say that when you introduce temporal qualifiers, it is no longer true. However, they don’t also construe that principle by the same qualifiers they are introducing, so their analysis is irrelevant. Further, when you do construe the principle by the qualifiers present, such that “ought implies can” construed temporally becomes “ought implies could have, can, or will be able to,” the supposition that because we can introduce instances of ought without a correlating present can becomes trivial and beside the point of the principle.

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I believe that my account of metaphysical and epistemological intuiting as foundations of scientific inquiry also provide an answer to the question of why logic-mathematics* are so successful in not only describing what there is in the world, but also why true propositions can be tautologously manipulated in order to provide more true descriptions of the world. For some given proposition regarding what occurs in the world, say that f = ma, if it were true, then we also know that any manipulation of that proposition which is equivalent to the original f = ma will also be true of the world. So, the first question is why f = ma can work to describe something in the world. The second question is why tautologously equivalent proposition can provide further descriptions of what occurs in the world. Though we might really just rephrase that second question as asking why our propositions can be restated in tautologously equivalent ways in the first place, but I’ll get to that in providing an answer to the second question.

*Logic-mathematics is simply my grouping together of all generalized kinds of propositions with the qualification that they are the description of relations between objects. As such, my title, “The Use of Logic in the Sciences” is the same saying “Using Propositions in the Sciences.” This probably also makes it easy to answer the questions as well.

Taking my account of science, then the answer to the first question is that when we metaphysically intuit, we are intuiting propositions. That is, propositions are the content of intuition; it is propositions which we conceive. Thus, when we apply epistemological intuiting, we are making observations regarding the accordance of what’s in the world to our metaphysically intuited propositions. We think in propositions and see by them. Our observations accord to propositions because propositions are fundamentally in order to describe, among other things, observations. The description of relations between objects can include those objects which are out in the world that we know of by our senses.

As such, when we state a proposition like “f = ma,” we are stating some relationship between force, mass, and acceleration, and declaring that they hold together in just such-and-such a way, taking those individual sorts of things as objects in the proposition. This also goes on to explain why science can make use of mathematics, because mathematics deals with a specific kind of propositions, namely those dealing with quantities. However, my account also means that mathematics is not the entirety of science; and this is obvious when explaining what we mean by terms like “force,” “mass,” “motion,” and so on. It isn’t as if you can point to some phenomena in the world, then give an equation, like “5 = 2*2.5” and expect it to be apparent what is meant. Whatever the quantity or degree something is the case, we give a term to that whole continuum of possible degrees, i.e. “force” when we mean anything from zero to infinity.

Now why can we manipulate true propositions of the world and, making sure they remain tautologously equivalent, still be saying true propositions of the world, knowing that they do so without reference to any additional observations or even the re-consideration of those observations which showed the truth of the original proposition? It is easy to see why that is the case when we analyze what we are doing when we propose tautologously equivalent propositions. For f = ma, we also know it would be true that m = f/a. What we are doing is recombining the descriptions of relations in ways that preserve the same essential arrangement of relations. It seems as if, when we introduce a relation like division rather than multiplication, something must be essentially different, but there is nothing essential to the relations themselves in stating what it is that is essentially the case. In other words, we shouldn’t confuse the signs of our propositions with the meaning; while they are instrumental, they are merely instrumental. Using some particular statement of relation is a means to an end, rather than the end. The meaning is not in the proposition expressed, the meaning is in the proposition understood for itself. (Curiously, it just occurred to me that this is another way of showing that logical positivism is incorrect even regarding what propositions are.)

So we see that logic in the sciences makes sense, and also that mathematics is not sufficient for doing science. We must still introduce metaphysically intuited concepts regarding things in the world like space. Perhaps in a future post I will get around to qualifying, on account of these past considerations, the “scientificality” of certain analyses.

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Here’s a riddle.

How many letters are there in the answer to this question?

Here’s some hints. Don’t try counting the numbers of letters in the question, or how many words. The answer isn’t in the question. In fact, the answer is in the answer.

The answer isn’t one. Count the letters; 0-n-e, 1 2 3. That’s not correct. Two? Nope. Three? Nuh-uh.

Four. F-o-u-r, 1 2 3 4. There are four letters in the answer to the question.

Here’s an interesting question in relation to that riddle; what shows that four is the answer? It is the answer which shows that that answer is the right answer. That’s rather curious, since it seems to imply that the answer bootstraps itself into, well, not existence per se, but correctness. The answer makes the answer correct.

There are some related questions, but they have some differences. To wit, I can ask the same question twice, and get a different answer. Have I asked you this question before? No. Have I asked you this question before? Yes. (Some might take this as proof that the same cause can have different effects. Er, no. The principle in this case is much like Heisenberg’s Uncertainty Principle. The means of observation affect the phenomena in question.)

Is there an answer to this question?

But okay, these are logical artifacts. Are there metaphysical examples? That is, are there questions which, in being asked, imply their own answer? I think the answer is certainly yes. The question in mind is “Why is there anything?” In order that the question can be asked, some things must be the case. These things, I hold, imply the existence of God. As such, it follows that the question “Why is there anything?” of its own being implies a particular answer. (Note: This isn’t an argument per se. I have made the arguments elsewhere which supplies those premises which lead to that conclusion, and the question is dependent on these premises in order to be asked.)

 

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Here’s a question I’m sure has been asked.

“Did you take out the garbage and unload the dishwasher?”

If we suppose that our protagonist is only answering with yes or no, then we understand that unless both were accomplished, the answer must be no. The answer will be no whether both are unfinished or only one of the pair is unfinished.

I bring this up because it suddenly occurs to me that answering a question requires some self-reference. We must take the question and posit it in a statement form, i.e. our question above becomes “The garbage was taken out and the dishwasher was unloaded” before then testing against the collected facts. Suppose a question in logical form is in bold. A negation of something indicates it hasn’t been done, by the symbol “¬”. Thus, our logical work goes like this;

1. G • D
2. ¬G
3. D
4. no

What does a yes or no indicate in response to the question, in terms of logical form? Considering the selected facts, it means something like “The facts are not currently in such a relationship.” That is, it is not true that both G and D are the case.

In everyday life when we’re speaking about house maintenance, such is trivial and we perform these sorts of logical operations without even thinking about them. However, in the midst of debate picking out the logical form is very useful and can be understood in terms of asking questions. How a person answers the question determines what position they take. For instance, this is an atheist;

1. God
2. ¬God
3. no

Theist;

1. God
2. God
3. yes

Agnostic;

1. God
2. …

That is, the response of “I don’t know” depends on someone not filling in for the state of affairs which follows the question. (On the other hand “No one can know” is something else we’re not talking about right now.) However, usually what are analyzed is not just one’s happenstance conclusion but the argument one uses to get there. Consider an argument over omnipotence.

I say that “God can do everything; God cannot do the logically contradictory, because they are not anything that can be done.”

The obstinate dullard responds in turn “So you’re saying that God can do everything but this one thing.”

This is where the logical form is good to pick out. First, let’s describe omnipotence;

Omnipotence = x(Dx -> Dgx)

This states “For all x, if x is something to be done, then God can do x.” I think this is an apt logical description of omnipotence.

Now consider the claim about what God can’t do. I am saying something like this;

¬Dx • ¬Dgx

“x is not a thing to be done and God can’t do x.”

See how this does not produce any contradictions when joined with omnipotence. Omnipotence states that, if something can be done, then God can do it; if the thing in question is not something to be done, then it doesn’t matter for omnipotence. Why do we care about God doing things which can’t be done? (Of course, when you extrapolate to semantics and go beyond mere logic formalism, i.e. “filling out the x,” then its easy to see. If the x were ‘grabe the groob’ then we’d understand that it refers to nothing; it is nothing to be done in the first place. Hence such a thing would be described as ¬Dx. Likewise with equally meaningless linguistic contrivances like ‘square circle’ which use words we are familiar with in a grammatically correct form, but still fail to refer to anything and are just as meaningless.)

So, our discussion of omnipotence might go like this;

1. x(Dx -> Dgx)
2. x(Dx -> Dgx)
3. ¬Dx • ¬Dgx
4. yes

3 is added in this case because it appears, for the hypothetical debate, a point of contention. That is, it seems contradictory to the claim of omnipotence as logically defined. However, upon a complete analysis no such contradiction results. Therefore, 3 can be stated and still leave us with a ‘yes’ for omnipotence.

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If you have spent time on the internet, then undoubtedly you will have heard this chestnut in one form or another.

If God is omnipotent, then can He create a rock so large He cannot lift it?

Two ways of looking at this. The first is to point out that this is asking whether or not God can revoke His own omnipotence, at which it becomes a question of whether God must or must not possess omnipotence. This resolves into the second way of looking at this, and it is the way that is profitable for examining what we mean by omnipotence.

Omnipotence quite simply means “the power to do all things.” This does not include the power to instantiate logical contradictions (i.e. a ‘square circle’) because such things are not any thing to be done in the first place. In order for something to be instantiated, the term by which we refer it must possess denotation; ‘circle’ denotes something and ‘square’ denotes something, but ‘square circle’ does not. Alas, ‘square circle’ just means nothing. If you take the negative expression of omnipotence, that omnipotence “implies nothing cannot be done,” you see that this expressly excludes logical contradictions. Logical contradictions are nothing; nothing cannot be done. And this is to say that everything can be done.

That is quite sufficient to point out that the atheist’s demand that omnipotence include the ability to perform logical contradictions is silly and beside the point. When omnipotence is attributed to God, “the power to do all things,” the all never included nothing, i.e. logical contradictions.

The objection is much like refusing to accept that someone can read all the pages in one book because they haven’t read a page in another book. A category error. Of course, here we go much wider, i.e. everything, but then when we ask what everything includes, the logically contradictory is not included.

Here’s another way of stating it. What God can do and what is possible are the same. If God can do it, it’s possible. We can say logical contradictions are such because they are impossible. If it were possible for God to do them, they wouldn’t be impossible, because clearly they are possible.

So the whole objection to omnipotence in this vein (“God isn’t omnipotent until He can instantiate the impossible!”) is a plain confusion of language. It seems to take it that whatever can be written as a grammatically correct proposition also denotes something possible that might be done. Any atheist who holds to this line of reasoning will naturally not believe in God, because they’ve just defined Him as impossible. Any theist will not believe in this God, since a theist will believe that the logically contradictory cannot be done, which clearly contradicts this “God” who can “do” the logically contradictory (whatever that is).

Why do atheists concern themselves with attacking these fantasies? Why do they attack a God no one (except perhaps themselves) believes in, and believe they have shown the belief of the theist mistaken? I can see that it is a mistake of language; but those atheists who persist when this has been adequately explained, there is something else wrong that won’t let them grasp this simple point.

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L-Machines, aka Laplacean machines, were first discussed here. A problem with the way they’re meant to be set up has come to my attention. It’s especially relevant, since now I’m thinking these L-machines can be used to definitively link logic and metaphysics.

The problem is this; in what respect can we consider them to be “trying to predict their own future?” It’s an ontological question, and comes in virtue of the consideration of intentionality. To propose that something is trying to make a prediction about some phenomena, i.e. to gather together a unified account of some set, that thing must have understanding or else by a machine operated by a being with understanding. Understanding being “someone who recognizes what is being calculated.”

An L-machine is much like a computer, though in a more logically bare way; more like a Turing machine. Though it is a Turing machine with a specific purpose and the parts are atomic. This means there will be a 1:1 correspondence between parts predicated in the logical schema and things named by the logical schema, i.e. A corresponds to part A which is composed only of part A and nothing else that would have to be individually named in order to have a complete description. Each part must then be given to calculating some kind of logical distinction, however many logical axioms we want to set up, rules of inference, a mode of representation, and assuming that whatever is set up is sufficient to calculate about itself, whatever axioms those would be. We aren’t worried about specifying those axioms per se (though it would be a fun exercise, perhaps later).

So I think there are three possible conclusions, each being useful for their own metaphysical implications.

1. Intrinsic intentionality – The L-Machine is, in fact, a mind, though a mind set up only to try and calculate its own future.

I wonder if this makes sense at all. Are minds mechanical logic machines? A lot seems to indicate that this isn’t the case; for instance, where Gödel’s incompleteness theorems indicates that no interesting formal logic system can be both complete and consistent. But what’s to stop a mind from knowing everything? That, and minds might be essentially willing beings, which a deterministic machine (as the L-machine is supposed to be) couldn’t be. So perhaps intrinsic intentionality is out.

2. Extrinsic intentionality – The L-machine is essentially a computer, and possesses derived intentionality from some mind who stands apart from it.

This mind can’t be a part of the world, which means the mind must be some extra-world being like an angel or God. This seems to make metaphysical sense, and actually seems appropriate to our own way of thinking about it. But can we stand apart from another world and understand a thing within it to have a meaning it does not possess intrinsically? That is a metaphysically sticky topic, and is really the root of the problem which brings about these considerations.

3. Non-intentionality – The L-machine is properly considered to be a machine which has all appearances of predicting its own future to us, but it isn’t actually doing any such thing.

This is really the most interesting fork. This seems to be the kind of conclusion our intuitions might lead us to accept (though there’s no reason to accept that only this fork is acceptable, it still seems to me work is possible for the others, each kind of L-machine representing a different kind of being though alike in trying to predict its own future). But if the L-machine we are considering here is a kind of fiction, just what is it actually doing? In fact, how is this kind of L-machine distinct from any other world which endures change? Is an L-machine of this type just a world?

The more I consider these Laplacean machines, the more work there seems to be to make them consistent and meaningful.

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