30
Mar
2014
Aquinas Shows How God Keeps It Real
Gene Callahan linked to a very interesting post by Ed Feser. It begins in this way, and note that I’m going to abandon my normal formatting style and keep the italics the way Feser wrote it:
[FESER:] For the Thomist, to say that God is the First Cause of things is, first and foremost, to say that He is the cause of their existence at every moment at which they do exist. God creates things out of nothing precisely in the act of conserving them in being, and apart from His continual causal action they would instantly be annihilated. You, the computer you are using right now, the floor under your feet, the coffee cup in your hand – for each and every one of these things, God is, you might say, “keeping it real” at every instant. Nor is this causal activity something anything else could either carry out or even play a role in. Creation – which for Aquinas means creation out of nothing – can be the act of God alone.Where creation is concerned, then, God is “first” cause not in the sense of coming before the second, third, and fourth causes, but rather in the sense of being absolutely fundamental, that apart from which nothing could cause (because nothing could exist) at all. As serious students of the Five Ways know, the sorts of causal series Aquinas traces to God as First Cause are causal series ordered per se, not causal series ordered per accidens. In the former sort of series, every cause other than the first is instrumental, its causal power derived from the first. (See this post for more on the subject.) But where creation is concerned, Aquinas’s talk of intermediate or instrumental causes is only “for the sake of argument”; his point is that even if there were intermediate causes of the being of things, the series would have to terminate in a First Cause. In fact there is and can be only one Creator and He cannot in principle create through intermediaries. (That is not to say that God does not work through intermediaries in other respects. We’re only talking here about His act of causing the sheer existence of a thing or creating it out of nothing.)Why not? Aquinas addresses the question at some length in the Summa Theologiae, the Summa Contra Gentiles, and De Potentia Dei. The arguments are difficult for someone not versed in the metaphysical presuppositions of Aquinas’s philosophical theology – indeed, some of them are difficult even for someone who is versed in the relevant metaphysics.
This is interesting in its own right, but the point I want to make–and one that Gene Callahan has been hammering on, lately–is that there was a philosophical shift such that people nowadays can barely conceive of what somebody like Aquinas is even talking about.
Let’s try an experiment. Suppose I ask you to think about “the real world” and “objective reality.” What did you conjure up? Did you think of the planets revolving around the sun, the hard sidewalk underneath your feet, the hydrogen and oxygen atoms that make up a molecule of water?
I don’t know exactly what you pictured, but I’m guessing it involved material objects, matter. I am pretty sure you didn’t pull to mind the Pythagorean theorem, or the notion that “God exists.” And yet, there is a very defensible sense in which we can know those statements with much more confidence than the ones about matter, which after all are “merely” mental models we construct to make sense of our subjective sensory experiences.
I will surely offend just about every reader with the following statement, but (having been raised Catholic but now calling myself a Protestant) I think the great contribution of Catholic scholars was to show just how much we could deduce about God from the gift of reason He gave us, while the great contribution of Protestant scholars was to remind us of divine revelation.
There is no conflict between science and religion, or logic and faith. Yes, you can in principle reverse engineer your car; the laws of physics “work” even though your car was intelligently designed. But for best results, you should consult the owner’s manual.
(Please do NOT assume I think Thomas Aquinas didn’t read the Bible, or thought revelation wasn’t important. C’mon guys, that’s not what I’m saying. Instead I’m drawing generalizations that help explain the different cultures that have grown up around the two traditions. In America today, I know plenty of Catholics, and they are extremely analytical and “rational.” It’s Protestants who are very suspicious of pointy-head academics etc. I think there are pros and cons in both approaches.)
Someone had to go out on a limb and do something novel in order for there to be a car in the first place. If all people ever did was “consult the owner’s manual” they would guarantee stagnation. This is a problem I see with a lot of the “book oriented” religions, once they have decided that one book is the word of God, there’s no next step… ever.
It is amazing to me just how similar, nay, I would say identical, are Feser’s explanation of God as per Aquinas, and Murphy’s experiment, are to Egoism:
Feser: The “absolutely fundamental” first cause, which is not necessarily temporally prior to the second cause, but rather makes it possible for there to be, that is, known to be, temporal causes per se. That’s Ego.
Murphy: The point that we are certain about mental concepts more so than materialistic ones. That’s exactly the same as Egoism. To posit itself is direct, and thus more fundamental than the indirect positing of the non-Ego that occurs by way of the Ego positing itself.
I could not have said this better: “The gift of Catholics was to show how Reason can deduce God.” It was Ego that created a God to give. God is a man’s gift! The Catholics were the most scrutizing among the Egoist givers of God. They were the best at deluding themselves and others into believing they have shaken off their own Egos. The Ego transcends. It is the creative nothing.
Is God more certain to you than “I am I”? Can you know God without first positing yourself? Think back in your life. Did you posit yourself first, or did you posit God first? Ego precedes, both temporally and logically, God. God is a creative act of pure Ego. The main difference between Egos is whether or not this creative act is made absolute under which the creative Ego then prostrates under to satisfy itself, or whether the absoluteness is transcended and destroyed to satisfy.
I admit to worshiping the God called Humanity. God was secularized into becoming Humanity. All secular ethics are outgrowths of this new religion. This is what almost all atheist Egos worship.
My question is whether society is possible if the God of Humanity is transcended and destroyed. Right now we are letting the atheists of the Humanity religion control us by exploiting our subservient constitution. You know who they are.
Is God more certain to you than “I am I”? Can you know God without first positing yourself? Think back in your life. Did you posit yourself first, or did you posit God first?
Is there any room for synthetic a priori knowledge about God, here?
Yes, you have to posit yourself before you can posit anything else, but the capacity to do so must precede your use of it.
(By the way, I think that the notion that God is creating every moment of our existence has serious problems.)
“Yes, you have to posit yourself before you can posit anything else, but the capacity to do so must precede your use of it.”
Positing that also requires an Ego to posit itself first.
True, but the Ego didn’t create itself.
Ergo, vis a vis, concordantly.
Positing that also requires an Ego to posit itself first.
Notice a pattern?
For every claim of knowledge you make, you have already posited yourself first, including prior causes to your Ego.
The Ego creates itself by positing itself. It is pure activity with no concievable cause. You claim to know of a God that created the universe before you were born? You have already posited yourself first. Then you imagined your self-creation to be in the non-Ego as well, for it is incomprehensible to you to think of anything without an Ego positing itself first. This is the origin of God.
Positing oneself is the “absolute foundation” of all knowledge and all sciences.
Well, to be glib, if we lived in a Euclidean universe then Einstein’s Relativity would not work, and there would be no Lorentz contraction, but observation is not consistent with a Euclidean universe. Therefore I would argue that the Pythagorean theorem is not real, it is a useful idea, and specifies a relationship between variables, but only a rough approximation of reality. I get what you mean though, ideas are “real” in the sense that the idea has a physical interaction with the world around it. That’s kind of meta-knowledge about the propagation of the idea though, not whether this particular theorem can be applied to the physical universe.
Besides that, can God decide to change the Pythagorean theorem? If God decided that maths was going to work differently, then someone could go back to first principles and re-derive the old theorem and get back to where we started from. God would need to actively prevent people from studying the old Pythagorean theorem in order to force them to start using whatever new Pythagorean theorem God decided on. In the world of math, everyone is equally God, and that can be a problem for the real God.
The concept of plane right triangles are not inconsistent with a non-Euclidean universe. Non-Euclidean geometry does not mean plane surfaces are an impossibility. It just means Euclidean geometry is not universal.
After all, successful research in cosmology presupposes Euclidean relations in the equipment used, and in the relations between equipment and researcher.
Sure, the concept of unicorns is not inconsistent with living in a world of horses either. As a concept, unicorns are perfectly well understood, you can paint a picture of one, make a doll, tell a story, it’s a fine concept… but unicorns are not real. Neither is Euclidean geometry. It’s a concept.
For that matter, I put it that supply and demand curves are also concepts but do not really exist. Transactions really exist, supply and demand curves are merely mental framework to assist our understanding of transactions. Useful at times, helpful in communicating ideas, making models, etc.
You’re saying unicorns cannot exist anywhere in the entire universe?
Please. Unicorns are most likely real, just not on Earth.
Metaphysics deals with more than just the Earth.
Euclidean geometry is not claimed as being tangible, so I don’t know why you believe that saying it isn’t real, is significant.
Tel wrote:
Well, to be glib, if we lived in a Euclidean universe …
Tel, you are proving my whole point without even realizing it. The Pythagorean theorem is TRUE. That’s why they still teach it. No physicist has shown that the theorem is false.
Now what you mean is, the best model we currently have of this thing called “space-time” that helps us organize our sensory observations blah blah blah.
You are assuming “best description we’ve found yet of the behavior of matter” is the same thing as “reality.”
“That’s why they still teach it. No physicist has shown that the theorem is false.”
Oh, rubbish: asserted as a universal geometrical theory of the geometry of real space-time (that is, as synthetic a posteriori applied geometry), it has been shown to be false a long time ago.
Your problem is you cannot distinguish between pure math/geometry and applied math/geometry.
No one has refuted Euclidean geometry as a pure geometrical theory because it is not empirical, but analytic a priori. Just as no one refutes the statement “all bachelors are unmarried” because it is a mere analytic truth, a definitional tautology, true by definition.
Euclidean geometry has necessary truth only as a property of it being and remaining an analytic a priori system.
In modern philosophy and philosophy of science, it is the view of
Albert Einstein that is accepted, not the absurd bankrupt Kantian epistemology of Mises:
“One reason why mathematics enjoys special esteem … is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts. In spite of this, the investigator in another department of science would not need to envy the mathematician if the laws of mathematics referred to objects of our mere imagination, and not to objects of reality. For it cannot occasion surprise that different persons should arrive at the same logical conclusions when they have already agreed upon the fundamental laws (axioms), as well as the methods by which other laws are to be deduced therefrom. But there is another reason for the high repute of mathematics, in that it is mathematics which affords the exact natural sciences a certain measure of security, to which without mathematics they could not attain. At this point an enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things. In my opinion the answer to this question is, briefly, this:- As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
http://www-history.mcs.st-and.ac.uk/Extras/Einstein_geometry.html
Einstein is right: there are plenty of elegant, rigorous, consistent pure mathematical theories: but many of them have exactly zero relevance to the real world. They describe, model or relate to nothing in the real world.
In so far as a mathematical model is actually asserted as true of reality it becomes contingent and a posteriori.
LK I think addition is commutative. Before deciding if this statement is rubbish, do you have to go try thousands of experiments involving apples?
Nope. LK will say its “epistemic”, which means highly probable in ordinary English.
I’m still waiting for his proof on the law of causality. We may assume all his statements as false until he proves that effects must come from a cause.
Jeez, mathematics when necessarily true is also analytic a priori.
If I have a plate and put one water drop on it, then add another, can you tell me a priori — with necessary and absolute truth — whether there are two water drops or one?
If you understand that thought experiment you will understand why even applied maths — even simple arithmetic — becomes synthetic a posteriori.
How do you know how to even count the water droplets?
If you understand that counting is grounded on action, not observation, then you will understand that mathematics constrained to action is true synthetic a priori.
No, MF, synthetic a priori entails that it gives true necessary knowledge of the real world.
Tel me: If I have a plate and put one water drop on it, then add another, can you tell me a priori — with necessary and absolute truth — whether there are two water drops or one?
Of course, you will run away from this question, because it destroys your position totally..
can you tell me a priori … whether there are two water drops or one?
How much water is in a “water drop”?
Can I tell you, knowing that a water drop is defined as a particular amount of water, how many drops are on the plate? Yes.
Guest, the act of defining a water drop is by necessity also a choice in how to approximate the physical world and describe it. All such approximation already defeats the “proof” of a mathematical theorem, which is exact, not approximate.
You also need a reference, which cannot be a mathematical entity.
LK:
You’re dodging the question.
Again, how do even know how to count the water droplets? You say you drop one, and then another. How so even know how to get from zero, to one, and then to two?
(1) counting is taught. There might also be some genetic basis to human mathematical faculties, but even then this predisposition is caused evolution by natural selection and does not guarantee necessary truth.
(1) yes, you evade the question posed to you, proving my point.
“Einstein is right: there are plenty of elegant, rigorous, consistent pure mathematical theories: but many of them have exactly zero relevance to the real world.”
We can include Keynesianism in that category, minus the elegance, rigorousness, and consistency.
Actually, Kenesianism isn’t even mathematically pure or rigourous according to this guy: http://tugwit.blogspot.com/
And he even points out where Keynes fudged the mathematic order of operations here: https://www.youtube.com/watch?v=WH8Lk1g8am8
Can you imagine if Austrian economics was so easy to disprove as Keynesianism is?
“exactly zero”
Was this measured on your BS ruler? Sorry its not valid until I see the empirical data.
LK:
Why do you a priori assert, implicitly, the law of causality to be constant over time in the very course of a posteriori experimentation?
Clearly, a method that is based on assuming constancies in relations, such as your belief that “Austrian economics is not correct (meaning in the past, present, or future)” cannot be used to prove whether the causal relations are in fact constant over time. The very concept of “falsification” denies the possibility of the laws of causality changing over time. Researchers assert a theory has been “falsified” precisely because they are a priori holding the laws to be constant over time.
Mathematical relationships constrained to action can never be falsified, for they are deduced from action itself, of which falsifying and refuting themselves are. You can’t presuppose action to refute anything that is true by virtue of action.
Causality is not a priori: it is, as Hume argued, a matter of highly confirmed empirical constant conjunction, not de re necessity.
Quite the opposite. As Hume actually noted, causality cannot be observed.
He argued that we cannot rationally defend “uniformitarianism”, or the assumption that constancies in causal relations exist such that induction is reliable. He emphasized the problem of induction.
But this is neither here nor there.
Causality is not grounded on observation. It is grounded a priori. Causality is not merely “highly confirmed.” Causality is derived from an understanding of what it means to act. You understand causal relations because you understand yourself to cause effects by your actions. That is the reason you infer it in the world around you. That is why, as Hume noted, it is not observed. It is understood.
“Causality is not grounded on observation.”
Of course it is: but as the probabilistically true phenomenon we call constant conjunction.
Hume denied that causation is a necessary de re phenomenon.
You are so ignorant you cannot even get Hume’s position right.
LK:
No, causation cannot be observed. You can only observe events occuring one after another. You cannot observe the causal connection.
Causation is understood prior to experiencing events. It is imputed a priori as the description of a relation between observed events.
Hume denied that causation is observable. That is the grounds of his skepticism. It is you who is ignorant of Hume’s philosophy.
Attributing a “probability” to all causal relations, wouldn’t even be on Hume’s radar, or anyone else’s, if he and everyone else did not bring with them an understanding of causality prior to observing subsequent events.
Observing the same event B following A every time, repeatedly, CANNOT by itself convey causality. You are a priori imputing causality as how those events are related. Without that a priori inference, A following B over and over would convey absolutely no causal relation, not even “probabilistically”.
I recommend you reread Hume, or maybe for the first time?
LK:
“asserted as a universal geometrical theory of the geometry of real space-time”
Nope. Not even Kant ventured to claim that extreme of a view.
Hey MF, its called confirmation bias. He has been suffering from this problem for quite some time. He really wants to be on the side of the great Einstein.
LK is making up a theory and refuting it, insinuating that he is refuting every argument grounded a priori.
Hey guys I’ll save you a lot of headache.
He accepts this from Ayer:
“analytic propositions are devoid of factual, content, and consequently that they say nothing”
You see, to LK, there are no mathematical theorems that are “true”.
He fails to understand that by “true”, Bob means in the realm of Euclidean geometry, the Pythagorean theorem is true. However, why not be extremely pedantic? Its so much fun!
Bob means in the realm of Euclidean geometry, the Pythagorean theorem is true.
No, I mean in the realm of logic it is true.
Sorry, I shouldn’t have assumed.
We probably mean the same thing, but I want to be pedantic because otherwise it plays into LK’s hands. So I am saying that “the Pythagorean theorem” is true so long as we use logic the way it strikes us as self-evidently true.
Now, you’re right, part of what I’m including in “the Pythagorean theorem” are the definitions / axioms of Euclidean geometry.
In the realm of logic? You mean as an analytic a priori system?
It is not necessarily true of the real world?
LK:
Asserting a distinction between analytic and empirical knowledge is a self-refuting exercise.
It is an assertion about the fundamental structure of reality, namely, that there is nothing in reality that can be known one way or the other prior to experience confirming or disconfirming our hypothesis.
If this statement is assumed as true, then it itself must be either analytic or empirical.
If it is analytic, then it self-contradicts, because analytic knowledge is not knowledge of the real world.
If it is empirical, then it is merely a hypothesis that may or may not be true, and you would be obligated to explain on the basis of what criteria one would have to decide whether or not it was.
Yet you have shown yourself to be unwilling to grant any possibility of true synthetic a priori knowledge. You have attempted to avoid contradicting yourself on this score by communicating your absolute rejection in such phrases as “highly improbable”, ” very unlikely”, etc.
The irony is that you believe in many synthetic a priori propositions. For example, you accept that if the world were socialist, there can be no price system for the means of production, before you observe it. You also accept that if the quantity of money doubled next year, then if the demand for money remained unchanged, then the purchasing power of money will fall, before you observe it. You also accept that if the minimum wage was raised to $1 million a minute tomorrow, then assuming no other changes, unemployment will rise, before you observe it.
You also accept the a priori claim that humans need government. You are saying this is true for the future, before you observe it. You also contradict your claim that the past is not a reliable guide to the future for complex systems like whole economies.
“If it is empirical, then it is merely a hypothesis that may or may not be true”
Correct. But nothing else you say follows from this.
lK:
Yes, it does follow. If you didn’t know of any criteria, then you would be making an unconditioned, i.e. an apriori, statement, which contradicts the meaning of an empirical statement.
If you did know of criteria, then you should have understood that action fulfills the criteria of true synthetic a priori knowledge. But you reject that, which means you are unable or unwilling to recognize the very criteria you claim to know about.
No matter what your answer, you will not challenge the very thing you are attacking.
Erk. Maybe I gave Bob too much credit. in my long comment below. ” in the realm of Euclidean geometry, the Pythagorean theorem is true.” is a fair way to put it. Assume EG is true and PT is true. But just assume LOGIC is true you cannot get that PT is true. PT is not provable by logic alone and not true in all possible worlds.
Erk. Maybe I gave Bob too much credit.
Yeah that’s one hypothesis.
All Ayer meant by that statement (“devoid of factual, content, and consequently that they say nothing”) — if you read him properly — is that analytic propositions do not tell us necessary truth of the real world.
He never denied analytic propositions convey real meaning.
For him, as for the logical positivists in general analytic statements:are
(1) not meaningless or nonsense as “metaphysical” propositions were presumed to be;
(2) do have real meaning and sense, and
(3) could and do provide human beings via deduction with analytic a priori “new knowledge,” such as revealing “unsuspected implications in our assertions and beliefs”.
“analytic propositions do not tell us necessary truth of the real world.”
Is that an analytic or empirical statement?
empirical statement
So you empirically observed an analytic proposition?
LK:
If it an empirical statement, then it is at most a hypothesis that may or may not be true.
Why then did you structure that statement with apodictic certainty that denies all future experience as pertinent, i.e. why did you make it a priori?
“not tell us necessary truth of the real world.”
“do have real meaning”
Do you not recognize that these are contradictory statements?
No, there are not. “Unicorns like ice cream” has real meaning, but is not true of the real world, because unicorns do not exist.
That makes sense. If that’s the case, there’s no sense in predicating with “real”. It has meaning, plain and simple.
You see, my problem is that you arbitrarily (seemingly) say the Pythagorean theorem is not true, but you say “pure mathematical statements” are true.
Does truth mean logically consistent or applicable to the outside world to you (or both, or none)?
No, hank, I said Euclidean geometry is not a universally and necessarily true description of the geometry of space-time (that is, when asserted as a synthetic a posteriori theory).
That does not deny that Euclidean geometry is necessarily true ONLY as a analytic a priori system (pure geometry).
I understand what you are saying. However, I really think you are over-reacting. I could be wrong, but I don’t think Bob made that claim.
“universally and necessarily true ”
Honest question: would it be correct to say that these don’t exist in your logical system?
Logical and absolute necessity existed even in logical positivism as a property of analytic a priori statements and analytic a priori deductive systems.
That continues to be the position of moderate empiricism in modern analytic philosophy.
I agree with that.
And I do NOT endorse all tenets of logical positivism at all. My position is in line with modern moderate empiricism, not logical positivism .
So is it correct that, according to you, an impossible or necessary proposition may never be applied to the outside world?
“You see, to LK, there are no mathematical
theorems that are “true”. “
That is BS.
Proper pure mathematical statements (1 + 1 = 2, etc.) are indeed true and necessarily true.
I still find the discussion about the now “obsolete” and “discredited” Euclidian geometry very strange.
To me this sounds as if people would say. “Jeez, all those electro technicians who still teach Vp/Vs = Np/Ns for calculating transformer’s voltage input/output use an “obsolete” and “discredited” method. They are like the people who claim the earth is the center of the universe. The world is of course a non-ideal transformer world but of course a ‘real’ transformer world.”
The assumptions made for calculating ideal transformers (resistance in the winding, magnetic losses, hysteresis and a bunch of other stuff is ignored) are just that; assumption which used correctly help us to approximate and especially understand reality. For many applications this might be enough. Especially for learning what a transformer actually is and how it works. For other applications it would spell trouble to ignore resistance in the winding and magnetic losses because this might cause your transformer to melt and your house to burn down.
However that just means you need to apply the appropriate set of assumptions for the right application. That for Euclid himself it wasn’t clear that there are other factors which might make it impossible to draw a straight line other than the inexactness of a drawing hand and other mechanical limits doesn’t “discredit” his theory, nor does it necessarily renders it useless. Of course it might mean that it is not exact enough for certain applications though, previously thought it was. Maybe relativity has an effect on the transformer as well. However I guess relativity is not considered in ANY formula of calculating a transformer’s input or output voltage…
Therefore it seems to me to be very weird to say the world is non-Euclidian and therefore Euclidian geometry is wrong. Given the factors it considers it is true, just like the formula Vp/Vs = Np/Ns is. Both, by excluding other factors, explain how certain factors are linked with each other. Given that there are other factors involved in the real world, you need to be careful when you want to actually apply it to the real world.
I just see no reason to be smug about a reduced/idealized model, especially since Keynesians are just doing that all the time themselves. They use economic models that IGNORE lots of real world factors all the time…
Maths works by taking certain unproven assumptions and then deriving the logical consequence of where those assumptions (or axioms if you prefer) take us.
The theorems are true to the axioms, that is to say tautological. Pythagoras just says “1 = 1” in a slightly more complicated manner. Because the result of Pythagoras is not obvious, it is useful to learn the technique, and applications of it such as least squares regression being the shortest path in an N-dimensional space… also not obvious. Regardless of whether these things are obvious, elegant, valuable, or whatever… we are still just saying “1= 1” and nothing more than that.
So can God come along, and decide that for today 1 = 2 ?
I argue God is constrained on that one.
The base assumptions of Euclidean geometry don’t match our observation. Whatever God created in the physical world, those axioms are not it. Often they come close, but not close enough to calculate high speeds or large distances, not good enough to calculate the relationship between electric and magnetic fields either.
Why does this stupid iPhone browser keep losing settings? Why has the top banner (where the URL sits) turned inverse video?
I either changed a setting, or I’ve been hit by a virus, or some arbitrary upgrade asserted itself, or it’s just buggy up the whazoo. The best way to describe the iPhone user interface is “arbitrary and surprising”.
Tel wrote:
I get what you mean though, ideas are “real” in the sense that the idea has a physical interaction with the world around it.
No Tel, my post is dedicated to blowing up such a position. I am trying to shake you out of that stance, where a bumblebee is “real” but the integers are just vaporous ideas.
Steve Landsburg, is that you?
No, casual empiricism has shown that Steve Landsburg no longer posts on the Internet.
Lord Keynes is right, and Feser, alas, has made a career out of rationalizing the absurd. The way we know 2 + 2 = 4 is not from deductive a priori principles but because every time humans took two and two of thing, they had four of that thing as a consequence.
The contradiction between science and religion is one of evidence, the primacy of observation, the requirement for hypotheses to be falsifiable i.e. to have empirical content or to make predictions.
Saying “God” as an explanation of why the universe works is simply impermissible in a scientific context. This is true for exactly the same reason that you cannot and should not be able to publish a scientific paper “explaining” a depressed economy with the mere phrase “aggregate demand.”
The way we know 2 + 2 = 4 is not from deductive a priori principles but because every time humans took two and two of thing, they had four of that thing as a consequence.
How do you know that the next time you do it, it won’t equal something else?
Science: Philosophy’s Handmaiden
http://www.str.org/articles/science-philosophy-s-handmaiden
What about the statement that math cannot be proven scientifically? He gives an example of how it can be and here is what he writes: “Anybody can do the following scientific experiment. Put two apples in a pile and add two apples to the pile then test the mathematically predicted result of four apples total. Is there a human on this planet that will get a different result? Math is scientifically provable objective truth.”
Now, I agree that math is objective truth. But I don’t think he has given us an illustration of science proving math. He gives a counter example to my statement that math is prior to science. What he does is clusters two apples with two other apples and points to the total as four and thinks he has tested math and proven it true. However, he did not test math. He exemplified math, and there is a big difference. He gave us an example of math at work. Here’s how I know for sure. First, you need no apples or anything physical whatsoever to know that two plus two equals four. You don’t need to do an experiment to know that truth. Not only that, but secondly, the gentleman had math in place before he even started his example. He thinks he proved addition with his example. But he didn’t, because math was necessary for him to do what he did. He says, put two apples in a pile and add two apples to the pile. Now, where did he get the notion of “two”? Where did he get the notion of “add”? Where did he get the notion of “equals”? Do you see that these are mathematical notions which must be in place before you can even do this illustration? They are logically prior to the problem. Again, I agree that math is objective truth, but not because it has been proven by science.
I don’t know with 100% certainty. How do you know with 100% certainty that if you do the logical a priori proof again it will turn out the same way?
Yes, it’s true that theory is necessary to fact as fact is to theory, hence the concept of “two” and “equal.” This is widely known since at least Kuhn. But this doesn’t help the advocates of a priori knowledge either. Where did they get the idea that “two” corresponded in any way to the number of eyeballs a man has?
How do you know with 100% certainty that if you do the logical a priori proof again it will turn out the same way?
With one caveat, you answered your own question, below:
Or do you trust proofs because you learned from experience that if you start from an assertion that corresponds with reality and proceed with valid logical steps (which themselves were distinguished from invalid steps empirically) …
The caveat is this: The proof had to have been true BEFORE you learned, from experience, that certain foundational assertions were true.
I need experience to come to know a priori truths. But I don’t need experience to know that those truths were true BEFORE I experienced them.
Which is why I don’t need to test them in order to know that they’re true.
This is what Rothbard meant when he said:
In Defense of “Extreme Apriorism”
http://mises.org/daily/5195/
Whether we consider the action axiom “a priori” or “empirical” depends on our ultimate philosophical position. Professor Mises, in the neo-Kantian tradition, considers this axiom a law of thought and therefore a categorical truth a priori to all experience. My own epistemological position rests on Aristotle and St. Thomas rather than Kant, and hence I would interpret the proposition differently. I would consider the axiom a law of reality rather than a law of thought, and hence “empirical” rather than “a priori.” But it should be obvious that this type of “empiricism” is so out of step with modern empiricism that I may just as well continue to call it a priori for present purposes.
“I need experience to come to know a priori truths.”
This is what is called a “blatant contradiction,” and when you find yourself professing such nonsense, it’s time to take a good hard look at what’s caused you to come to believe that in the first place.
i.e. I can’t argue against this claim because it’s complete nonsense.
I can’t argue against this claim because it’s complete nonsense.
Did you come to that conclusion because your empirical test, consisting of actually attempting to argue against the claim, lead you to believe it’s complete nonsense?
Or are you relying on a priori truths to make your claim (however false it is)?
The same way I learned 1 and -1 equal 0. Plug it into a calculator and check. Or deduce it a priori if you prefer.
Actually, that would be pretty interesting. Mind demonstrating some a priori knowledge? I’d love to see you start with zero information and proceed to a positive quantity of information without adding information at any point by interacting with the subject.
I’d love to see you start with zero information and proceed to a positive quantity of information without adding information at any point by interacting with the subject.
You’ve completely missed the point.
That one must have information from which to derive logical conclusions HAS ALREADY BEEN CONCEDED.
This is not the issue.
The issue is over the nature of the information, itself – whether or not the veracity of certain axioms depends at all on whether one has discovered them.
Are they true BECAUSE you learned them, or were they true BEFORE you learned them?
That’s the issue.
The Action Axiom of Austrian Economics is synthetic a priori in that sense, as Rothbard argued.
…
I think things because those things are true. Things are not true because I believe them, or else I could make anything true by believing it, and rather than believing I’m arguing on the Internet with people who believe in magic (whoops, “philosophy”), I would believe that I’m the king of the world.
But seriously, information is made of atoms. Look it up. This is standard science over half a century old at the least. I don’t know how much of a quack you are, so maybe that doesn’t mean much to you
Where did they get the idea that “two” corresponded in any way to the number of eyeballs a man has?
Through empirically observing so.
But “two” as a concept is philosophical, not empirical. Which is why you can use the concept to arrive at the correct answer to math problems, even without empirical data with which to associate it.
You can deduce that 2 +2 = 4 without reference to empirical reality *so long as* your conclusion also has no reference to empirical reality. I.e. if the “2” in the equation has no correspondence with the number of nostrils a typical human has and the “4” has no correspondence with the number of limbs a typical human has, then yes, you can deduce 2 + 2 = 4. You can come to this conclusion a priori because you’re not coming to any conclusion at all. You start with no knowledge and you end with no knowledge.
E.g. just as you can prove 2 + 2 = 4 a priori, you can prove 2 + 2 = 5 a priori.
E.g. just as you can prove 2 + 2 = 4 a priori, you can prove 2 + 2 = 5 a priori.
And I’m the “nonsensical” one?
What are you APPLYING to real world calculations, if not philosophy?
You need philosophy before you can do science.
Everyone knows since at least Kuhn of the interplay between science and philosophy, fact and theory, if you will. That’s a completely different question from a priori knowledge.
For you see, it has been demonstrated that fact and theory are one and the same. But I feel like we’re leaving the limits of your knowledge here. You should ask yourself, “Do I think the Second Law of Thermodynamics is false?”
For you see, it has been demonstrated that fact and theory are one and the same.
And I feel as if you’re leaving the limits of science.
You can’t empirically test the future, so for you to make the clame that “it has been demonstrated” requires you to use something OTHER than science.
You are making a philosophic claim, not a scientific one.
Question: Was the demonstrated fact, in your worldview, true BEFORE it was demonstrated, or only afterward?
How could you claim to know, scientifically, since you can’t scientifically test the past (history isn’t science).
…Are you seriously asking me why we think the past and the future probably obey the same laws as the present?
Again, we’ve reached the point where I challenge you to jump off the roof of a tall building, and you keep pretending not to hear me. I’ll let Darwin finish this argument in style if you’re willing to put your money where your mouth is.
Have you ever seen a proof that proofs work? Or do you trust proofs because you learned from experience that if you start from an assertion that corresponds with reality and proceed with valid logical steps (which themselves were distinguished from invalid steps empirically), then you end up with another assertion that also corresponds with reality?
A proof has to be logical, but it doesn’t have to correspond to reality.
Certain conclusions can logically follow from a flawed premise. This doesn’t make the proof invalid.
You can also start from a valid premise and reach an invalid conclusion.
Which means that proofs are philosophical, not empirical.
I say all this to introduce the idea that the Scientific Method, itself, is philosophical in nature, not empirical.
You can’t prove that the Scientific Method is valid by using the Scientific Method – that’s circular reasoning.
“Which means that proofs are philosophical, not empirical.”
I’m talking about the *reason* people think proofs are useful. Why, when someone proves something, does anyone care? Because it’s a fun philosophical game? Or because people have learned that if a proof follows certain valid steps following an assertion that is known to correspond to reality to some degree, then the conclusion will also correspond to reality?
“You can’t prove that the Scientific Method is valid by using the Scientific Method – that’s circular reasoning.”
The scientific method asserts the primacy of observation, and all its rules (such as “no saying the word ‘God’ and thinking you’ve explained something) are based on the experience of applying and misapplying that deceptively simple premise.
As for what is the basis of asserting the primacy of observation…why, it’s observation, of course. We’ve observed that the scientific outperforms the, what to call it, Aristotelian Method of Making Things Up.
In fact, using their powers of observation, scientists came up with this thing called The Second Law of Thermodynamics, which says you can’t output more information than you input. So if you start with zero information, you end with zero information. Yes, the laws of physics say that a priori knowledge isn’t real, but I guess Austrians wouldn’t care, since they already know a priori that a prior knowledge can be created.
But obviously if you wish to deny that observation (really, “interaction” in general) is the one way to gain information about a subject, no one can persuade you. After all, any proof I have to offer is based on, well, observation. So go jump off the roof of a tall building. It’s only observation that says you’ll die a horrible painful death. But a priori, who knows? Maybe you’ll deduce something different.
So when the religious and various other proponents of shucksterism like the a priori wing of the Austrian school say “You can’t prove the scientific method with the scientific method that’s circular reasoning,” they’re not being clever, they’re being idiots. But perhaps this problem will solve itself in a Darwinian fashion as believers in a priori knowledge put their money where their mouths are and take a leap of faith.
But obviously if you wish to deny that observation (really, “interaction” in general) is the one way to gain information about a subject, no one can persuade you.
Why is that obvious, in your world view? Did you test that?
And saying that you tested it before doesn’t help you, it helps the Austrians. Because the only way you can presume to believe that the conclusion you reached will always hold true, is to assume that it was true BEFORE you tested it, thereby revealing the unnecessity of testing it.
Yes, the laws of physics say that a priori knowledge isn’t real …
Physics has nothing to say about knowledge – knowledge is philosophical in nature, while physics is empirical.
(Really, it’s philosophy APPLIED TO empirical things, rather than to philosophical concepts.)
“Physics has nothing to say about knowledge – knowledge is philosophical in nature, while physics is empirical.”
Here you reveal your total ignorance. Knowledge is physical in nature. It’s called information theory. Knowledge is measured in bits. Look it up. You’re ignorant of the relevant science, like a creationist asking where the fossils are.
But really, we’re at the point in the conversation where I challenge you to jump off the roof, and you stick your fingers in your ear and hum loudly.
Here you reveal your total ignorance. Knowledge is physical in nature. It’s called information theory. Knowledge is measured in bits.
Knowledge doesn’t take up space in your head, dude; It isn’t physical in nature.
Think about what you’re saying, for a moment:
You’re reaching the logical conclusion of your belief that there is only matter, energy, and causal relations.
From this follows that your thoughts must be of a physical nature.
But for you to believe this, you also have to believe that everything you have ever thought about was the result of causal relations, and there is no way that you could have ever NOT have thought those things.
Which means that your ideas are not the result of careful consideration; You would have thought those same things whether or not they were true.
And you have never really chosen anything, either.
You can go this route, and since each person’s ideas are only observable to himself, I won’t be able to prove to you otherwise.
But going this route means you have to give up all pretention of knowledge and intelligence.
The flip side of that is that in order to claim intelligence, you must concede that your free will comes from your ability to be a first cause in your own actions – that your thoughts and actions can not be explained by mere causal relations.
And, therefore, that science can not explain everything we observe.
Bothered:
The idea that knowledge is physical in nature does not imply that our minds are causally determined.
“Which means that your ideas are not the result of careful consideration; You would have thought those same things whether or not they were true.” Why does your thoughts being causally determined imply that they’re not the result of careful consideration? And why does it imply that your thoughts are uncorrelated with the truth?
Guest,
Free will is not magic. Choice is a real physical process that happens in your brain, which is a real physical organ made of squishy matter that obeys real physical laws. Choice is perfectly compatible with a view of universal determinism because what *determines* the actions you take is the physical process of choice that happens in your brain.
But please, tell me what knowledge is, if it isn’t atoms. It’s “philosophical.” What does that mean? How is it different from saying that knowledge is “magical” or “divine?” What can you predict with this claim that knowledge is not physical in nature? Inquiring minds would like to know.
“Lord Keynes is right, and Feser, alas, has made a career out of rationalizing the absurd. The way we know 2 + 2 = 4 is not from deductive a priori “
On the contrary, I did say that pure mathematics is analytic a priori.
Mathematics constrained to action is synthetic a priori.
What does mathematics constrained to action mean?
Easiest and shortest way is to give an example.
Non-discrete mathematics is mathematics not constrained to action, because action is structured discretely.
Gibberish.
Cool story.
Next time LK decides on the marginal utility of a car based on whether there have been one or two atoms scrapped off the wheels, he’ll have totally demolished my claim that action is structured discretely.
So do you mean the part of mathematics implicit in the reasoning that people employ in their decision-making process?
Oh, well, that’s wrong then.
Bothered:
“The way we know 2 + 2 = 4 is not from deductive a priori principles but because every time humans took two and two of thing, they had four of that thing as a consequence.”
That is wrong. You are presupposing counting. How do you know how to count? Why aren’t you thinking 1,2, 36, 0.004? Counting isn’t “in” the things you see.
“1” is just a symbol and doesn’t inherently relate to the number of noses the typical human has. The reason I specifically count 1,2,3,4 is because that’s how people do it in my society and why would I bother doing otherwise?
As for how I know how to count in the first place, it’s an interesting question with a long history. Quite a lot has been written about the history of counting. You should look it up
Not good enough.
“Because everyone believes it”
And
“Read more”
Nope.
The Montessori system teaches the concept “1” through a single bead, 10 through a string containing exactly 10 beads, 100 through a plate containing exactly 10 strings of 10 beads each and 1000 through a block containing 10 plates of 10 strings of 10 beads each.
You should specifically look into how the concept of zero is taught. It is very educative.
The D’ni use an interesting system …
When I think of “the real world” and “objective reality”, I visualize a annual rate of inflation of 1.1% in Feb 2014 while since 2008, Austrian economists have predicted an imminent dollar collapse and hyperinflation.
Is that an annual rate of price inflation as expressed in the CPI?
Because the CPI is rigged:
[Time stamped]
Peter Schiff – The Fed Unspun: The Other Side of the Story
http://www.youtube.com/watch?v=zdB9I79BQRI#t=1h20m12s
Inflation Propaganda Exposed
http://www.youtube.com/watch?v=pwI3Nya5L9g
Also, since the banks aren’t lending, a lot of the new money isn’t circulating in the economy. When that finally happens, price inflation will be even more recognizable than it is, now.
[Time stamped]
So Where’s the Inflation? Tom Woods Talks to Mark Thornton
http://www.youtube.com/watch?v=n0RusrwYsRE#t=5m16s
Hyperinflation is the logical progression of policies which refuse to allow the reallocation of malinvested resources. So when we say that there will necessarily be hyperinflation, we’re assuming that the Keynesian policies will be maintained.
We’re also assuming that the purpose of Keynesian policies is to “not default” (even though by printing money that IS a partial default; as Ron Paul says, we’re defaulting all the time). So, if the United States outright defaults – as it has always done – then that’s a lot of people you don’t have to print money for, and the prospect of hyperinflation magically disappears.
If you don’t have to print the money to pay people, then hyperinflation won’t happen. Of course, the effects of what would have been hyperinflation still occur through a concentrated default (rather than the dispersed default which happens whenever money is printed in excess of specie).
“Austrian economists have predicted an imminent dollar collapse and hyperinflation.”
[Citation please]
Citation = “Jerry Wolfgang’s” assertion that it is true.
Feser’s argument that God is an existence-explainer is *exactly* the logic that used phlogiston to “explain” fire and used elan vital to “explain” biological activity. Which is to say, he takes a question he does not know the answer to and rather than saying, “I don’t know,” he says, “God” and thinks he has thereby learned something.
It’s a darned shame that a professional scientist like Bob can’t cut through these basic fallacies outside the specific domain of his specialty, rather like a mathematician who knows probability theory backwards and forwards but still buys lottery tickets every week.
I don’t think Aquinas’ argument here is a “God of the gaps” argument. Aquinas isn’t just saying “It’s not known what causes existence, therefore the explanation must be God.” He’s using his principle of proportionate cause to conclude that the only thing which can bring something into existence which did not exist before is existence itself. Now you may disagree with the principle of proportionate cause. I’m not really familiar with Aquinas’ work, so I’m not sure what the principle precisely says, what its justication is, or whether it’s being applied correctly in this case.
To me, the bigger problem that Aquinas’ argument seems to have is that he’s apparently defining God as existence. Well, under that definition atheists might all believe in God as well, but is it really a useful definition? I’m not sure how Aquinas would be able to connect that to the properties that God is believed to have in Christianity. How can existence know something, for instance?
It’s not a “God of the gaps” argument. It’s an “explaining a mysterious phenomenon by reference to a vacuous label” argument. “God” in Aquinas/Feser’s argument *is not an explanation.* It’s the *absence* of an explanation gussied up to appear otherwise.
As in “what explains esistence is the essence of existence”. What explains life is the essence of life — the elan vital.
It’s just a relabelling “essence of existence” as “first cause” or “god” , which partly disguises the emptiness of the argument.
Yup. Dormitive properties.
In what sense can we describe god as being less of a mere mental model than physical reality? And in what sense is this assertion defensible?
RPLong that was the whole point of Feser’s post about Aquinas.
I thought Feser’s point was that god is logically prior to the existence of all things. My point is that this assertion seemingly affirms the consequent.. I could replace the word “god” with “magic rubber ducky” or “The Eternal Karl Marx” or “quantum physical mechanism that is presently not fully understood” and arrive at exactly the same conclusion.
Reducing all the terms in the “equation” seems to give me: “Existence presupposes existence.”
But maybe I just don’t get Feser’s point.
Yep, vacuous labels devised to mask ignorance are totally interchangeable with other vacuous labels devised to mask ignorance. But not all vacuous labels are equally as convincing.
Presuppositional apologetics, the Kalam Cosmological Argument, and “the infinite regress to god” are so much nonsense. Aquinas appears no different. Just watch any Sye Ten Bruggencate video on YouTube and you will be balder than Gene Callahan in about two mintues – so frustratingly stupid and filled with appeals to ignorance.
RPLong I am not going to go to the barricades on this particular point, because I actually said previously that I think the type of God you can logically prove is not what people in the monotheistic traditions mean by “God.”
But, I do think people like Aquinas showed a lot that we can say through introspection.
Agreed with you there.
And I really like this:
In what sense can we describe god as being less of a mere mental model than physical reality? And in what sense is this assertion defensible?
This will help:
How to Know Immaterial Things Exist
http://www.str.org/articles/how-to-know-immaterial-things-exist
“When you gaze, as it were, on the content of your mind so that you know what it is you are thinking, is the thing that you’re aware of neurons, brain tissue, and electrical impulses? No. The things you’re aware of are your own thoughts.
…
You can just tell by reflecting, if you will, upon your thoughts themselves that you are not gazing upon something that has chemical properties. Thoughts have propositional qualities. They are not governed by the laws of physics, yet your brain chemistry is. They must be something different.”
…
The way we know the contents of our own thoughts is not by somebody else telling us, by some scientist taking a measurement, by using any of our five senses to apprehend it; rather, we have direct, unimpeded access to our own thoughts. We are directly aware. We simply introspect, and we know.
…
There are lots of things in our minds that we don’t know about. Still, at the same time, when we are beholding a particular thing in our mind we know it directly, and we know it incorrigibly. That means we know it without the possibility of being mistaken.
…
Could they be mistaken, though, about the pen on the table, which was the earlier discussion? … There’s no good reason to be skeptical, but it is possible that they’re mistaken about that. However, it is not possible–and this seems obvious just on reflection–for us to be mistaken about the content of our own minds.
Here is the way this cashes out. I have really asked questions about two categories of things – material and immaterial things. We concluded that we knew things about both areas: the physical that we knew based on our senses (and this would be the way science tells us things) and immaterial things that we knew based on reflection.
We also realize that it’s possible to be mistaken about one, but it’s not possible to be mistaken about the other. Clearly we could be mistaken about virtually anything that we discover with our senses, even though we may not have good reason to believe so. So I’m not a skeptic in that regard. But it is not possible to be mistaken about the contents of our own mind and other kinds of immaterial, abstract objects that we’re aware of, like the laws of logic and reasoning and math, and a host of other things.
See the discussion below re: Euclid’s 5th Postulate.
I read all of these comments. This came to mind.
1 Corinthians
8 Now about food sacrificed to idols: We know that “We all possess knowledge.” But knowledge puffs up while love builds up. 2 Those who think they know something do not yet know as they ought to know. 3 But whoever loves God is known by God.
My two cents. Our brain is not capable of understanding infinity. We cannot think of an infinite amount of space. So we also cannot think of infinite time (which is nothing more than change). But if space was limited, then there has to be some kind of wall, and what is behind it? If time (change) started at some point then obviously something was before it started.
I don’t know. Infinity in terms of space and time seems to be less unbelievable to me than some starting point without a before, or a wall without a behind..
“But if space was limited, then there has to be some kind of wall, and what is behind it?” Not necessarily. Space can be finite and yet have no boundary. Picture ants walking on the two-dimensional surface of a balloon. They can walk in a straight line without ever hitting a wall, yet the space they’re in is finite. Similarly we could be living in the three-dimensional hypersurface of a four-dimensional hypersphere.
The ant not being able to get at some point, doesn’t mean that this other point doesn’t exist. I mean read what you said. It is a 2 dimensional surface of a “BALLOON”. How can it be a ballon if there is nothing? Obviously a ballon cannot exist in a 2 dimensional space.
What is done here is using our 3 dimensional understanding of space and position less dimensional “space” in it, and somehow pretend we didn’t use a 3 dimensional superstructure on top of it. That especially shows that it is not possible to not think 3 dimensional.
2x *balloon*..
I was just using an analogy to help you visualize things, but you don’t need a higher-dimensional space to embed things in. You can simply have a three-dimensional non-Euclidean geometry that’s not part of a higher-dimensional space. There’s a subject called differential geometry that’s devoted, in part, to describing curved spaces without positing a higher-dimensional flat space.
I was just using an analogy to help you visualize things, but you don’t actually need a higher-dimensional space to embed things in. You can simply have a three-dimesnional non-Euclidean geometry without positing a higher dimensional space. There’s a subject called differential geometry that is devoted, in part, to describing curved spaces without reference to higher-dimensional flat spaces.
I am not sure you know what I mean. If you call it curved space. Then this begs the question of curved in reference to what?
You can talk about something being intrinsically curved without reference to some higher-dimensional space. To take a simple example, you can define curvature as the extent to which the angles of a triangle add up to something other than 180 degrees.
Look at this at Wiki:
“Gauss’s Theorema Egregium (Latin: “Remarkable Theorem”) is a foundational result in differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces. The theorem says that the Gaussian curvature of a surface can be determined entirely by measuring angles, distances and their rates on the surface itself, without further reference to the particular way in which the surface is embedded in the ambient 3-dimensional Euclidean space. Thus the Gaussian curvature is an intrinsic invariant of a surface.”
All that “intrinsically” means in this context is that it is possible only by making measurements on that surface, without reference to another dimension, to determine the shape of the curve, which is the 3 dimensional shape of the surface.
However that a surface is “curved” only makes sense in context of an additional dimension to the surface. Just look at all those pictures of those curved surfaces. Without the third dimension you cannot make a picture of a curved surface.
No skylien. A space can be curved just by itself. Curvature is a relationship between measurements you take. Curvature 0 means that when you add up the angles of a triangle you get 180. Curvature 2 means you get something else ( the answer depends on the area of the triangle). You can do measurements like that without any extra dimensions. You can derive theorems from axioms just like you did in EG, but you get different theorems. Those theorems may fit your actual physical measurements better.
No need for extra dimensions.
You *can* “visualize” embedding a space in a higher dimensional EG space, but you need a lot of extra dimensions. And there isn’t just one way to do it either. If you can visualize 9 dimensions …
Ken B,
Nothing that follows “No skylien” contradicts what I am saying.. I agree with all of it.
“However that a surface is “curved” only makes sense in context of an additional dimension to the surface.” No, we can talk about something being curved even if we’re not talking about an additional dimension. Look up manifold.
“Then this begs the question of curved in reference to what?”
Replace the word curved with the word gaussed. The extent to which a space is gaussed determines how many degrees there are in a triangle. You can measure the gaussing of a space with accurate instruments.You and I can discuss and compare aour gaussometers.
You feel a burning need for higher dimensional worlds to understand gaussing? “Curved” is an analogy, useful for some purposes harmful for others, but not needed for the idea.
Wow. This is one of the most confused discussions in blog history.
The PT is entailed by the axioms of EG. That does NOT make it true. It is perfectly possible to have other geometries with other axioms where the PT fails. You can have, under different axioms, an equilateral right triangle. That is completely inconsistent with the PT.
The most interesting way to create new geometries is to replace Euclid’s 5th axiom, about which he himself with astonishing insight, had doubts. When you do that you get different theorems and you do not get the PT.
There are more general ways to define geometries.
Is the PT true of the real world? No. And phycists have indeed shown the answer is no.
Yes, they have shown it to be inaccurate as applied to reality.
No, they have not disproved it within the realm of the Euclidean framework.
This is where I think the major confusion is.
KenB
You’re confused as usual. If the truth of non-Euclidean geometry is based on experiment, and experiment is based on Euclidean geometry, then if the experiments are claimed as the basis for the truth of reality, then Euclidean geometry MUST be true of reality as well.
Like the confused and befuddled who don’t recognize that quantum experiment and general relativity experiment are for studying separate phenomena, so too are you confused and befuddled in not recognizing that Euclidean geometry and non-Euclidean geometry are for understanding separate phenomena.
Your implicit premise, which you have not once addressed in detail nor subjected to critical analysis, is that the universe is supposedly monistic. In other words, that any true theory must describe everything about and in the universe. You are taking it for granted without even realizing it. Befuddled, befuddled, befuddled.
Major_Freedom, what do you mean “experiment is based on Euclidean geometry”? Do you mean our rulers and measuring equipment are based on Euclidean geometry? Isn’t that just a contingent fact of the world, because things are approximately Euclidean on the length scales that humans typically interact in? If the curvature of space were much greater, wouldn’t our experiments be based on non-Euclidean measurement equipment?
Ken B. wrote:
The PT is entailed by the axioms of EG. That does NOT make it true. It is perfectly possible to have other geometries with other axioms where the PT fails.
Ken, you and I both agree on “the facts,” and we are disagreeing on the interpretation. But that interpretation is the very thing in dispute in my original post.
If the PT weren’t true, then we should stop calling it a “theorem,” shouldn’t we? We should call it “the Pythagorean conjecture” or better yet “the Pythagorean falsehood” since you guys keep claiming it isn’t true.
Suppose I say:
“Premise: Aristotle is a man.
Premise: All men are mortal.
Conclusion: Aristotle is mortal.
I, Bob Murphy, claim that this syllogism is true.”
Are you, LK, Bothered, et al. going to come back and say, “No way Murphy! I can use a different set of axioms which include the premise that men could be immortal. (After all, biology has shown that not 100% of men who have been born, have died.) So your syllogism isn’t true in the real world.”
I can’t believe we are stuck in this rut. You guys keep taking “the real world” to be THE SAME THING as “the laws governing the material universe as currently understood by physicists,” and then you conclude that “the laws governing the material universe are the real world,” and think you’ve discovered something interesting. No, you are assuming your conclusion at the outset, which is ironic, because that’s what you are angrily thinking I’m doing.
Sigh. I was kinda hoping to stay out of this.
“If the PT weren’t true, then we should stop calling it a “theorem,” shouldn’t we? ”
No, this is a fundamental confusion. A theorem is a statement that is proven within a mathematical theory. We should properly say “PT is a theorem of EG.” A theroem is always a theorem of a theory. Just calling it “a theorem” is imprecise. We do it all the time, because the theory of interest is usually clear from context. But sometimes this imprecision bits, and this is one of those times.
For our purposes it suffices to identify a mathematical theory with a set of axioms and formal rules for making deductions from those axioms. A valid decution is a theorem of the theory. The theorem may not be true, it is only provable (from the axioms.). Provable and true are not the same thing.
The statement “The PT is provable from the the axioms of EG” is true. The statement “The PT is true because it describes reality accurately” is false.
I think the natural reading of Bob’s claim is the second, false, one.But from his other comments it may just be a failure to articulate the point carefully — not surprising since there are difficulties formulating this exactly.
On Ken B’s point, I can recommend Howard DeLong’s A Profile Of Mathematical Logic, especially re: discussions of Euclid’s 5th Axiom. One of my favorite books, and I try to plug it every chance I get. 🙂
The statement “The PT is true because it describes reality accurately” is false.
In this sentence, your use of the word ‘reality’ is evidence that you do not comprehend Bob’s argument.
When you figure out why replacing the word ‘reality’ with the phrase ‘the physical world’ makes this statement more accurate, then you will begin to understand what Bob is talking about.
Replace it with whatever you want. The statement is still false.
This is one of the joys of explaining formal logic on this blog: the wilfully ignorant.
Who is explaining the formal logic? It’s certainly not you.
Speaking of crap logic,
Ken B isn’t even aware that “replacing it with whatever you want” makes it possible for that statement to be true.
Replace “reality” with “the only absolitely true theory”, or, “the only theory that is absolutely true.”
Every statement that accurately describes the only absolutely true theory, is itself absolutely true.
No wonder Ken B is spending his time on a blog full of losers and logic simpletons. Birds of a feather…lol!
Ryan, you see what I mean about the willfully ignorant.
Look in the mirror
What Ken B is trying to say, guys, is that PT follows logically from EG, granted; But he’s also saying that EG is false.
He’s saying your logic is sound, but your premise is not.
“Premise: Aristotle is a man.
Premise: All men are mortal.
Conclusion: Aristotle is mortal.”
That syllogism can be necessarily true, but only by remaining an analytic a priori system.
Both (1) “All men are mortal” and (2) “Aristotle was a man” (if you are talking about the historical Aristotle) when asserted as synthetic a posterori statements cannot be known with apodictic and necessary truth. Of course, the truth of (1) is extremely probable and (2) extremely probable (but perhaps to a lesser degree given we are dealing with a person who died long ago). But extremely probably truth is different from apodictic truth.
Since there is always some slight or tiny doubt about the truth of synthetic a posterori statements (for the only possible exceptions see below), no deductive argument like yours that is really asserted of the real world can be regarded as absolutely sound. Therefore its necessary truth does not hold when asserted of the real world.
The only way it really does have absolute necessary truth is by regarding all premises as analytic a priori and the conclusion .analytic a priori too.
Just reading your comment it sounds like you’re incredibly ignorant of 250 years of Western philosophy.
Haven’t you ever heard of Hume’s problem of induction? If you have, can’t you see how it arguably destroys the necessary truth of all things known a posteriori? We cannot even know with absolute certainty that other minds exist or that the past was real: these things are inductive inferences known a posteriori.
Haven’t you ever of the highly influential view that all necessary truth is merely de dicto truth?
Haven’t you ever of Quine’s radical empiricalism and web of belief epistemology? His take on epistemology makes the logical positivist one look tame, and gives no comfort to Kantian synthetic a priorists like you.
And even if we take the more moderate empiricism in modern analytic philosophy (following Kripke) which admits the existence of some limited necessary a posteriori truths, that does not help you either, because Kantian synthetic a priorism is still rejected in this epistemology.
Lord Keynes, when Bob says the syllogism is true, he means that it is valid, i.e. that the premises imply the conclusion, not that the conclusion is necessarily true.
Keshav wrote:
Lord Keynes, when Bob says the syllogism is true, he means that it is valid, i.e. that the premises imply the conclusion, not that the conclusion is necessarily true.
Thanks Keshav, I probably should’ve brought up that distinction earlier, but I didn’t think it was necessary in light of the giants chiming in here.
It is ironic that LK lectures me on Hume’s problem of induction, in a post where I explain that we have more certainty of the PT than of the “fact” that planets revolve around the sun.
Sarcasm is unbecoming when you’ve made a series of rather sloppy statements that worsen the confusion.
Why are insisting on giving credence to non-praxeological logic systems? You might as well be including biblical scripture.
True and valid are two different things. Bob may have meant valid, but he said true, and that was an error. It’s a forgivable one, but once we start using the language of formal logic, these things become important. All kinds of things can be valid but false. I assume what we are interested in is truth.
Put another way, a valid but false religion does not keep anyone warm at night.
RPLong wrote:
Bob may have meant valid, but he said true, and that was an error.
Hold on a second. Consider the following proposition:
[(p–>q) AND p] –> q
Are you telling me Ryan that we can definitely say that this proposition is “valid,” but before we call it “true” I need to tell you what “q” is?
Hmm. Maybe, yes. I’d say you’d have to know what p and q both are before you can say the statement is true, even if we can prove that it is valid. But I’m getting shaky here, since I am only a formal logic hobbyist.
Restricting myself to Keshav’s clarification and your endorsement of it, I think we can say this much: Validity and truth are two different things. True logic is necessarily valid, but valid logic is not necessarily true.
The three competing versions of Euclid’s 5th Postulate really are the perfect example here.
RPLong I don’t think I’m out of line (though Ken B. will surely correct me) for saying that a tautology is true (not “valid but possibly false”). Not that Wikipedia has all the answers, but here ya go. In fact that’s often a definition of a tautology, that it’s true no matter what.
Try it this way RPLong: The statement “P OR Not-P” is true, regardless of P? Do you see how that statement is different from the statement “P”?
OK. Details.
You have swapped a proposition for a syllogism,
and replaced a quantified premise with a simple one.
Remember I mentioned rules of inference? Those are ways of getting new propositions from other ones.
say you have these propositions as true
p
[(p–>q) AND p] –> q
You get q from a rule of inference applied to them.
But this is not even quite what you had.
What you had was
something with quantifiers which is more complex
(x){man(x) ->mortal(x)}
man(socrates)
from which you infer
mortal(socrates)
Notice this is NOT in the format you gave with p and q. There is a quantifier involved, and there is a bare statement q involved.
The jargon is that this is a VALID inference not a true one. Propostitions are true, inferences are the application of inference rules.
Did you make an error calling it a true syllogism? A small technical one that should have confused no-one. LK is off the mark here as Keshav notes. But it really is better to avoid this crap by talking about valid inferences or syllogisms and true propositions.
As I said this is mostly a matter of slightly sloppy usage, not a crime against logic.
Ken B. wrote:
Did you make an error calling it a true syllogism? A small technical one that should have confused no-one.
OK Ken B. so you’re saying that what I said in the original post was perfectly correct, except for a small technical confusion on the word choice? This is why I find your discussions so frustrating. You surely knew from Step 1 what I was saying, and that LK was going off on a wild tangent. And yet the innocent reader would probably have thought you were agreeing with LK that my whole position was “rubbish.”
Bob, suppose “P” is “offsides” and the scenario is “baseball.” In that case, “P or !P” is valid but not true. There is no offsides in baseball, much as there is no Euclidean space in physical reality.
No Bob. no. What you said these many moons ago *in the original post* is wrong. I explained why.
What you said about a ‘true syllogism’ was basically right, just *as I commented* sloppy wording. I did not call it wrong.
Look, in the original you said the PT was TRUE that’s why we call it a theorem. That really is an error. The PT is a theorem of EG, it is not true.
After that you made several rather confused and confusing comments, one of which was you meant to include the axioms of EG in what you meant by the PT.
If you are amending/clarifying to something like “if you assume EG then PT, being a theorem, is true” than that would be correct. But that ain’t what you said.
(Much less what some of the other confused posters here said.)
LK:
“Haven’t you ever of the highly influential view that all necessary truth is merely de dicto truth?”
Is that statement merely de dicto truth then? If so, that it isn’t saying what you are suggesting it is saying.
“Haven’t you ever of Quine’s radical empiricalism and web of belief epistemology?”
Haven’t you read critiques of radical empiricism?
LK:
Have you heard of the “highly influential” bible?
It’s highly influential. We must therefore give it the same seriousness as we do empirical experiments.
Both (1) “All men are mortal” and (2) “Aristotle was a man” (if you are talking about the historical Aristotle) when asserted as synthetic a posterori statements cannot be known with apodictic and necessary truth.
…
We cannot even know with absolute certainty that other minds exist or that the past was real: these things are inductive inferences known a posteriori.
Ok, I see now why you believe that there is no such thing as synthetic a priori knowledge.
You’re technically right, but you will agree with me that scientists and historians don’t typically use this level of precision.
It’s not like the Theory of Evolution could survive this level of precision, for example.
But, as Rothbard noted, this precision is irrelevant to determining whether or not the Action Axiom is true:
In Defense of “Extreme Apriorism”
http://mises.org/daily/5195/
Now the crucial question arises: How have we obtained the truth of this axiom? Is our knowledge a priori or empirical, “synthetic” or “analytic”? In a sense, such questions are a waste of time, because the all-important fact is that the axiom is self-evidently true, self-evident to a far greater and broader extent than the other postulates. For this axiom is true for all human beings, everywhere, at any time, and could not even conceivably be violated. In short, we may conceive of a world where resources are not varied, but not of one where human beings exist but do not act.
…
Whether we consider the action axiom “a priori” or “empirical” depends on our ultimate philosophical position. Professor Mises, in the neo-Kantian tradition, considers this axiom a law of thought and therefore a categorical truth a priori to all experience. My own epistemological position rests on Aristotle and St. Thomas rather than Kant, and hence I would interpret the proposition differently. I would consider the axiom a law of reality rather than a law of thought, and hence “empirical” rather than “a priori.” But it should be obvious that this type of “empiricism” is so out of step with modern empiricism that I may just as well continue to call it a priori for present purposes.
So, LK, when you ask us a question, and we respond “you didn’t test that; rather you’re presuming a law, here”, it’s because you’re doing the same kind of thing we are with the Action Axiom, but you don’t find fault with it like you do when we do it.
This is from where our frustration comes.
No matter what you call it (synthetic or analytic), you sometimes are presuming a law is in effect that you didn’t empirically test every single time. Even if you tested it before, this is not enough – the most you could ever say with your approach is that it was true in the past, when you tested it then.
As a (lapsed) Catholic, I’m kind of insulted by the insinuation that being rational doesn’t allow one to be suspicious of pointy headed academics.
A true follower of reason is suspicious of the academic no less than anyone else.
Actually, the larger problem is the adherence to the Kantian system. All this talk of “a priori” vs “a posteriori” or “analytic” vs “synthetic” is bullshit anyway. Once you dispose of that warped epistemology, things will actually be clearer.
What is wrong with those Kantian distinctions? What epistemological distinctions would you replace them with?
“I will surely offend just about every reader with the following statement, but (having been raised Catholic but now calling myself a Protestant) I think the great contribution of Catholic scholars was to show just how much we could deduce about God from the gift of reason He gave us, while the great contribution of Protestant scholars was to remind us of divine revelation.”
Indeed and not offended. You hit it right on. I am also a former catholic and now a protestan.