Just for the record, here is Peirce's conclusion about the rock-dropping example (CP 5.100-101, EP 2:183; 1903, emphases in original):

"With overwhelming uniformity, in our past experience, direct and indirect, stones left free to fall have fallen. Thereupon two hypotheses only are open to us. Either: first, the uniformity with which those stones have fallen has been due to mere chance and affords no ground whatever, not the slightest, for any expectation that the next stone that shall be let go will fall; or, second, the uniformity with which stones have fallen has been due to some active general principle, in which case it would be a strange coincidence that it should cease to act at the moment my prediction was based upon it.

"That position, gentlemen, will sustain criticism. It is irrefragable.

"Of course, every sane man will adopt the latter hypothesis. If he could doubt it in the case of the stone, - which he can't, - and I may as well drop the stone once for all, - I told you so! - if anybody doubts this still, a thousand other such inductive predictions are getting verified every day, and he will have to suppose every one of them to be merely fortuitous in order reasonably to escape the conclusion that general principles are really operative in nature. That is the doctrine of scholastic realism."



Before you complain about the words "inductive" and "verified" in that passage - it is clear from Peirce's other writings, including the other lectures in the same series, that this was shorthand. What he meant was that deductively explicated predictions based on retroductively conjectured hypotheses are constantly being inductively corroborated through experimental testing (and everyday life). Again, there is no significant disagreement between Peirce and Popper about this overall process of scientific inquiry, even though they clearly had different views about some of the details.

They're regularities of those particulars. We're not positing something other. — Terrapin Station

Nominalism vs realism is a pretty archaic metaphysics on both sides of the debate these days. Science has moved the conversation on.

In particular, a pan-semiotic approach based on hierarchy theory accounts for the way that particularities have regularities due to downward acting constraints - downward acting constraints being the modern version of formal/final causes, and thus the modern version of a realism that believes in universals.

The key idea is that global constraints make the particulars - a system's degrees of freedom - what they are. The global regulative action shapes the parts by limiting their possible actions, forcing them to become the "kind of things" that must re-construct the globally-prevailing state of constraint ... the thing that makes them.

So it is a classic cybernetic feedback story. The whole shapes the parts so that the parts make the whole.

The key metaphysical shift is switching from thinking of existence as a mystery of how something appears from nothing to instead an account of how it is inevitable that regularity will arise to simplify variety.

If everything is possible, then everything is also going to have its reaction against everything else. Most of these reactions will cancel each other away, leaving only some simple general form of reaction that dominates as the steady equilibrium actuality.

And this is hardly an esoteric way of thinking. It is central to science from evolutionary theory to thermodynamics and quantum field theory. Variety is self-winnowing. Generic simplity is what the least action principle requires of any natural system.

So the particulars of any system are emergent. They are variety pared down to form a part. The regularity of particulars is due to the higher level fact that to exist means being made to fit.

Why is sand composed of billions of the same tiny grains? Is this really a mystery to anyone?

If everything is particular, then there is no good reason for anything to be regular. — aletheist

It apparently seems intuitively obvious to you that if there are universals, then that is a good reason for particulars to behave regularly, but that doesn't at all seem intuitively obvious to me.

We keep seeking answers in the finite time that each of us has . . . — aletheist

All I was getting at in this part is that we have to accept all sorts of things as more or less brute facts where we don't or where we're not going to worry about how or why the furthest-back-reason we've reached for it works as it does. We do this all the time in both the sciences and in philosophy. (And in fact, in the sciences, the majority of scientists tend to get very annoyed if we ask how/why things work just as they do too much.)

It rather seems dubious to me that there are any scientific theories that are not arrived at via a combination of inductive, abdutive and deductive reasoning, with the first two being more prominent than the latter--after all, a deductively-arrived-at theory would at best only need experimentation to confirm its premises, otherwise it's not deductive at all. — Terrapin Station

Quantum entanglement provides a straight-forward example. What series of observations resulted in the induction of the theory? What was the "surprising observation" that resulted in its abduction?

Given that both induction and abduction are purported by some to be part of the method of science, it doesn't seem unreasonable to ask for an example of them being used?

When do you consider the theory of quantium entanglement to start--with the EPR paper? Schrodinger's response to it?

Quantum entanglement provides a straight-forward example. What series of observations resulted in the induction of the theory? What was the "surprising observation" that resulted in its abduction? — tom

It is a puzzle that you don't see this as an exemplar of the Peircean account of scientific reasoning.

Schrodinger cites the surprising fact that demands an abductive leap - the EPR paper:

Attention has recently* been called to the obvious but very disconcerting fact
that even though we restrict the disentangling measurements to one system, the
representative obtained for the other system is by no means independent of the
particular choice of observations which we select for that purpose...

And then he offers "entanglement" as his abductive leap to the best retroductive explanation. As Schrodinger says, his hypothesis is based on a holistic or constraints-based take on reality, as opposed to EPR's more conventional deterministic (and nominalistic) metaphysics.

Another way of expressing the peculiar situation is: the best possible knowledge
of a whole does not necessarily include the best possible knowledge of all its parts,
even though they may be entirely separated and therefore virtually capable of
being " best possibly known ", i.e. of possessing, each of them, a representative of
its own. The lack of knowledge is by no means due to the interaction being insufficiently
known—at least not in the way that it could possibly be known more
completely—it is due to the interaction itself.

And then from this abductive leap to a different viewpoint, Schrodinger fleshes out the deductive consequences that might allow inductive corroboration of his position.

So what we have here is a classic example of the scientific imagination at work - there were none better at this than Einstein and Schrodinger.

But there maybe a "mystery" about abduction itself when it is seen in a typical reductionist light as a constructive, and non-creative, mental exercise.

It is indeed a problem how "induction" - of the bit by bit, step by step, variety - could ever get started. But that computational view of generalisation is simply wrong because it depends on a reductionist view of epistemology.

Actual brains work differently - naturally. They operate using a holistic Peircean logic.

So it is no surprise that abduction is not induction in any simple sense. It is instead all about the ability to relax states of constraint, ease up on existing habits of conception, so as to enter a suitable state of vagueness - a state in which the whole of a different story can pop out as a hierarchical symmetry breaking.

Creative thought starts with an inkling that this new generic principle could explain these particular kinds of observable particulars. You suddenly have the right kind of whole in mind. And the test of that is whether it has sturdy enough deductive structure to produce the right kind of inductive measurables.

So - ironically given the OP - Schrodinger's abductive leap regarding entanglement as a hypothesis was a break with the old nomimalistic order.

Einstein was all for retaining local determinism or nominalistic realism at all costs. (Not because he lacked imagination but because it was a principle that had served physics so well for so long - so inductively it ought to hold.)

But Schrodinger was willing to imagine a reality in which wholes are more than their parts because wholes shape their parts. Reality is at base indeterministic or vague. Existence is only crisply actual to the degree it has been collapsed or decohered by the universality of some global form.

Since the shock of quantum mechanics, the whole of physics has got used to thinking about existence in terms of this kind of top-down constraints logic. It is the new normal. Which is why Peirce has really started to catch on as the guy who pretty much got it all before the 20th century got going.

It apparently seems intuitively obvious to you that if there are universals, then that is a good reason for particulars to behave regularly, but that doesn't at all seem intuitively obvious to me. — Terrapin Station

Yes, and as is often the case in such circumstances, I have a hard time even imagining what it is like not to find it intuitively obvious. In my mind, a universal or general is a real type of relation (vs. token) that transcends the individuality of particulars as something that they can (and often do) have in common. To say that something has a property means that if certain conditions were to obtain, then certain results would follow. To say that a rock has weight means (among other things) that if we were to let go of it, then it would fall to the ground; and this is the way things really are, not only regardless of whether anyone thinks so, but also regardless of whether we ever actually let go of the rock.

Are you saying that you see no distinction between treating predictable regularities as a brute fact vs. explaining them as the logical consequence of there being real laws of nature that really govern actual (and counterfactual) events? — aletheist

If I may interject, I find it hard to distinguish between "predictable regularities" and "real laws of nature." In other words, I don't see how "real laws of nature" explain rather than differently refer to the same predictable regularities. Do we not experience the order we find as a "brute fact"?

In my mind, predictable regularities are what we experience and observe, while real laws of nature are what we hypothesize to explain them. In other words, there must be something about reality that results in things and events exhibiting those predictable regularities.

I think that the order we find in the universe calls for an explanation. Why should we just accept it as a brute fact? If we did, why would we engage in philosophical and scientific inquiry at all?

Right, but the question is how we can know that a counterfactual claim is true, if - as the nominalist asserts - there are no real laws of nature, just individual things and events. — aletheist

Under real deterministic natural law, counter-factuals can be regarded as meaningless. In the block-universe of general relativity, there is no room for them it seems.

We have been testing counterfactuals for centuries - that is what experimentation is, and this is precisely what Peirce called "induction." It is not the same thing that Popper rejected, since both men affirmed that theories are never verified, only corroborated (or falsified). — aletheist

If general relativity is wrong, and we don't inhabit a block space-time, then perhaps, but have we really been testing counter-factuals? We have been reasoning about them, but if we had tested them, they wouldn't be counter-factual.

Peirce committed the error of seeking to justify a theory, or render it more probably via "induction". Didn't he claim:

The true guarantee of the validity of induction is that it is a method of reaching conclusions which, if it be persisted in long enough, will assuredly correct any error concerning future experience into which it may temporarily lead us

If I may interject, I find it hard to distinguish between "predictable regularities" and "real laws of nature." In other words, I don't see how "real laws of nature" explain rather than differently refer to the same predictable regularities. Do we not experience the order we find as a "brute fact"? — R-13

Why don't you propose a principle of "Predictable Regularity", then we can use it to describe the universe from the big-bang to the heat-death, with a brief interlude for life on earth? All so predictable and regular after all!

When do you consider the theory of quantium entanglement to start--with the EPR paper? Schrodinger's response to it? — Terrapin Station

Start wherever you want. But remember, we need a set of observations from which to induce the theory an an unexpected observation if you want to abduce the theory. Since these are purported to be part of the methodology of science, I trust you will be able to do both in this case.

To say that something has a property means that if certain conditions were to obtain, then certain results would follow. — aletheist

I wouldn't say that that's what "property" means. That's an upshot of properties, but properties are simply qualities/characteristics.

Anyway, it seems like you keep thinking that I don't believe that properties are real. That's not at all the case. I just don't think that they're something other than particulars.

In my mind, predictable regularities are what we experience and observe, while real laws of nature are what we hypothesize to explain them. In other words, there must be something about reality that results in things and events exhibiting those predictable regularities. — aletheist

The problem is that it's no explanation, and it just adds other things to have to explain.

The reason I'm asking is that we could argue that the EPR paper isn't actually a scientific theory, for example.

I think that the order we find in the universe calls for an explanation. Why should we just accept it as a brute fact? If we did, why would we engage in philosophical and scientific inquiry at all — aletheist

Do you accept the real laws of nature as a brute fact? Or must they also be explained?

That's not at all the case. I just don't think that they're something other than particulars. — Terrapin Station

What is mathematical proof for then? Given that there are thousands of books and papers on properties of the primes, which have been discovered, you might be forgiven for thinking (as mathematicians do) that they are about something real.

Not all mathematicians are platonists. At any rate, I'm definitely not a realist on mathematics.

I wouldn't say that that's what "property" means. That's an upshot of properties, but properties are simply qualities/characteristics. — Terrapin Station

In that case, how do you define qualities/characteristics? Again, to say that something has a quality/characteristic means that if certain conditions were to obtain, then certain results would follow. To say that a chair is green means (among other things) that if we were to measure the dominant wavelength of light reflected by it, then it would be within a certain range; and this is the way things really are, not only regardless of whether anyone thinks so, but also regardless of whether we ever actually shine light on the chair.

Anyway, it seems like you keep thinking that I don't believe that properties are real. That's not at all the case. I just don't think that they're something other than particulars. — Terrapin Station

No, I get that; I just continue to have trouble understanding how you make sense of common properties and predictable regularities on that view.

The problem is that it's no explanation, and it just adds other things to have to explain. — Terrapin Station

It explains the consistencies among individuals that we observe in the world, rather than settling for treating them as inexplicable.

Do you accept the real laws of nature as a brute fact? Or must they also be explained? — Michael

As I have acknowledged previously, they call for an explanation; and that would presumably come from cosmology.

Again, to say that something has a quality/characteristic means that if certain conditions were to obtain, then certain results would follow. — aletheist

And again, I do not agree with that. I'd agree that it's an interactive upshot of properties, but it's not what they are. Properties/qualities/characteristics are definitions of each other, as they're synonyms. Another way to put it, although I hesitate to state this because I doubt that after I do so folks will be able to remove themselves from a particular groove of misunderstanding, is that properties are simply what something is like (the particular groove of misunderstanding being to read that as necessarily being from the perspective of a sentient being).

I just continue to have trouble understanding how you make sense of common properties — aletheist

Simply by them being similar, not literally identical.

It explains the consistencies among individuals that we observe in the world, rather than settling for treating them as inexplicable. — aletheist

I don't think it does because how the universal "gets into" the particular is left as a complete mystery.

Not all mathematicians are platonists. At any rate, I'm definitely not a realist on mathematics. — Terrapin Station

But there exist necessary truths about the set of primes. Some of these truths have been set out in proofs. So what is going on if the subject of these proofs does not exist?

A proof is a type of computation that models the properties of an abstract entity (e.g. the set of primes) and establishes that the abstract entity has a certain property. So we can grant the abstract entity a list of properties, but not the property of existence?

Are you going to give the cicadas the bad news?

But there exist necessary truths about the set of primes. Some of these truths have been set out in proofs. So what is going on if the subject of these proofs does not exist? — tom

Here's something I wrote just last week in this very thread:

It might be helpful to remind folks that I'm not a realist on mathematics (or mathematical objects etc.), by the way. So I don't think that anything we refer to in mathematical terms pegs anything real. Mathematics on my view is a social and subjective psychological construction, a language we invented for talking, in the most abstract context, about how we think about relations. I do think that on a very rudimentary level that some of the relations we base mathematics on are real relations that we experience empirically, but "based on" doesn't mean "the same as" (think of how The Texas Chain Saw Massacre is "based on" the real-life story of Ed Gein)--the real relations in questions are not actually mathematical relations. Mathematics is our invented language only. And most of mathematics is a thought-based extrapolation of the based-on-but-not-the-same-as rudimentary relations that we experience. — Terrapin Station

So what's going on in the case of a proof about the set of primes? We're playing with the language game we've set up re thinking about relations at a high level of abstraction.

Abstractions, by the way, are strictly mental. Any properties abstractions have is simply properties of the concept we've formulated.

I'd agree that it's an interactive upshot of properties, but it's not what they are. — Terrapin Station

The idea is that the meaning of any concept is the aggregate of its conceivable practical effects - i.e., the pragmatic maxim. If three different words - in this case, property, quality, and characteristic - all pertain to the same set of conceivable practical effects, then they designate the same concept.

Properties/qualities/characteristics are definitions of each other, as they're synonyms. — Terrapin Station

Synonyms are not definitions. I am trying to understand what you mean by a property or a quality or a characteristic. "What something is like" is not really any more helpful.

Simply by them being similar, not literally identical. — Terrapin Station

If everything is particular - i.e., no individual has anything real in common with any other individual - then how can anything be similar to anything else? What exactly does "being similar" mean on your view?

I don't think it does because how the universal "gets into" the particular is left as a complete mystery. — Terrapin Station

The issue here is what it means to say that the universal "gets into" the particular. Again, I am suggesting that meaning has to do with conceivable practical effects, so a property/quality/characteristic is really "in" an individual only in the sense that if certain conditions were to obtain, then certain results would follow. Hardness is "in" a particular diamond only in the sense that if we were to apply a knife-edge to it, it would remain unscratched. It is a real habit/disposition/capacity of every individual diamond, regardless of whether anyone thinks so, and regardless of whether any particular diamond is ever actually tested.

The idea is that the meaning of any concept is the aggregate of its conceivable practical effects - i.e., the pragmatic maxim. If three different words - in this case, property, quality, and characteristic - all pertain to the same set of conceivable practical effects, then they designate the same concept. — aletheist

The more we'd talk about this the more of a mess it would become, because I have very unusual views on what meaning is/how it works, what concepts are, etc. So we should probably just skip that.

Synonyms are not definitions. — aletheist

I coudln't more strongly disagree with this. Insofar as a proposed definition is not a synonym, it fails to capture, or it adds, something to what it's defining. And that's no definition. (Note that I'm not saying that it has to be a single-word synonym--it can be a paragraphs even. But synonyms aren't demarcated by their length.)

I am trying to understand what you mean by a property or a quality or a characteristic. "What something is like" is not really any more helpful. — aletheist

My reaction to comments like that is always, "How could this person not know what property and/or quality and/or characteristic refer to"? I can't understand how you'd not be able to understand that.

If everything is particular - i.e., no individual has anything real in common with any other individual - then how can anything be similar to anything else? What exactly does "being similar" mean on your view? — aletheist

It's not at all a difficult concept. It's simply relative degree of resemblance (at least in respects considered). ( is more like < than it is # in terms of there being a single line in both cases, in terms of the orientation of the curve/angle, etc. But ( isn't the same as < obviously. It's just relatively similar.

a property/quality/characteristic is really "in" an individual only in the sense that if certain conditions were to obtain, then certain results would follow. Hardness is "in" a particular diamond only in the sense that if we were to apply a knife-edge to it, it would remain unscratched. It is a real habit/disposition/capacity of every individual diamond, regardless of whether anyone thinks so, and regardless of whether any particular diamond is ever actually tested. — aletheist

And how is that incompatible with nominalism?

Abstractions, by the way, are strictly mental. Any properties abstractions have is simply properties of the concept we've formulated. — Terrapin Station

So, Information Theory is a complete waste of time, rather than an explicitly counterfactual theory of a type of abstraction, underlying much of technology? Computation doesn't happen, and in particular virtual reality is impossible?

You've got it the wrong way round. What we can know about the necessary truths of abstractions is limited to how closely we can instantiate, or model abstractions physically.

So, Information Theory is a complete waste of time, rather than an explicitly counterfactual theory of a type of abstraction, underlying much of technology? Computation doesn't happen, and in particular virtual reality is impossible? — tom

Why, in your view, (a) would information theory be a waste of time, (b) would technology based on information theory not be possible, (c) would computation not exist, and (d) would virtual reality be impossible just in case concepts/abstractions are purely mental?

Note that I'm not saying that it has to be a single-word synonym--it can be a paragraphs even. — Terrapin Station

We typically call the latter a definition, not a synonym. Besides, you only offered single-word synonyms, plus the multi-word (but not much more helpful) "what something is like."

"How could this person not know what property and/or quality and/or characteristic refer to"? I can't understand how you'd not be able to understand that. — Terrapin Station

I understand the colloquial meaning of the concept, but I am trying to get at the technical meaning that you attribute to the concept from your philosophical standpoint.

But ( isn't the same as < obviously. — Terrapin Station

Yet ( is just as obviously the same as (. They are two different tokens of the same type, just like "the" and "the" are two different instantiations of the same word.

And how is that incompatible with nominalism? — Terrapin Station

As I understand it, nominalism denies the reality of habits/dispositions/capacities, since (in this context) they are general laws of nature distinct from their individual instantiations in particulars. If hardness is merely a particular property of particular objects, rather then a general property that is instantiated in particular objects (such as diamonds) that have something real in common, then I see no warrant for claiming that any particular object (including any particular diamond) would remain unscratched if we were to apply a knife-edge to it.

We typically call the latter a definition, not a synonym. Besides, you only offered single-word synonyms, plus the multi-word (but not much more helpful) "what something is like." — aletheist

There's no restriction that definitions can't be single words. But the idea is that the definiens has to be synonymous with the definiendum, however many words the definiens is.

I understand the colloquial meaning of the concept, but I am trying to get at the technical meaning that you attribute to the concept from your philosophical standpoint. — aletheist

I wouldn't say that I see properties as being anything different than the colloquial senses of those terms.

Yet ( is just as obviously the same as (. They are two different tokens of the same type, just like "the" and "the" are two different instantiations of the same word. — aletheist

First, so do you understand similarity as opposed to identicality from my example?

With ( and ( the idea is that those aren't any more identical than ( and < are. They're rather just more simllar than ( and < are.

Re the last part--Just to review, I had said this:

I don't think it does because how the universal "gets into" the particular is left as a complete mystery. — Terrapin Station

To which you responded:

a property/quality/characteristic is really "in" an individual only in the sense that if certain conditions were to obtain, then certain results would follow. Hardness is "in" a particular diamond only in the sense that if we were to apply a knife-edge to it, it would remain unscratched. It is a real habit/disposition/capacity of every individual diamond, regardless of whether anyone thinks so, and regardless of whether any particular diamond is ever actually tested. — aletheist

That response above is completely compatible with nominalism.

Your response to the description above being compatible with nominalism included this:

If hardness is merely a particular property of particular objects, rather then a general property that is instantiated in particular objects (such as diamonds) — aletheist

"A general property that is instantiated in particular objects" is what I was asking about when I said "how the universal 'gets into' the particular is left as a complete mystery." I was saying something about the notion of the universal, the general property, being instantiated in a particular not being explained.

If all there is to "a general property that is instantiated in particular objects" is "that if certain conditions were to obtain, then certain results would follow" and if "Hardness is 'in' a particular diamond only in the sense that if we were to apply a knife-edge to it, it would remain unscratched." then there's a problem:

(1) the latter descriptions are compatible with nominalism: "if certain conditions were to obtain, then certain results would follow" is true of particular properties (which is what particulars are). And "Hardness is 'in' a particular diamond only in the sense that if we were to apply a knife-edge to it, it would remain unscratched" is also consistent with hardness being this particular property of this particular diamond (as well as that particular property of that particular diamond, and so on).

(2) But the first description doesn't make a lot of sense in context. If a general property is something real that isn't identical to the particular properties of the particular objects in question, then how it is instantiated in particular objects remains unexplained, and comments like "Hardness is 'in' a particular diamond only in the sense that if we were to apply a knife-edge to it, it would remain unscratched" do nothing to explain how a non-identical (to the particulars) general property winds up instantiated in particulars.

As I understand it, nominalism denies the reality of habits/dispositions/capacities, — aletheist

That's not actually true. Nominalism just says that we're talking about particular properties there.

since (in this context) they are general laws of nature distinct from their individual instantiations in particulars. — aletheist

That's part of what nominalism denies. But per nominalism, that part isn't necessary for the reality of "habits" etc.

the latter descriptions are compatible with nominalism: "if certain conditions were to obtain, then certain results would follow" is true of particular properties (which is what particulars are). — Terrapin Station

No, because the scope of the subjunctive conditional that represents a general property or law of nature is not limited to one particular object. Any rock - in fact, any object with mass - that is dropped will fall to the ground. Any chair - in fact, any object at all - that is green will primarily reflect light at a wavelength within a certain range. Any diamond - in fact, any object that is hard - will resist scratching.

On the other hand, if all properties and objects are particular, then there is nothing real that the different objects have in common. Hence there is no good reason to expect similar results to follow for different objects, even if those objects and the conditions are similar.

If a general property is something real that isn't identical to the particular properties of the particular objects in question, then how it is instantiated in particular objects remains unexplained ... — Terrapin Station

It is instantiated when particular objects behave in accordance with the law of nature that is the general property. Rather than being "in" those objects in any literal sense, it governs those objects, as well as their relations with other objects. The general property is still real apart from these instantiations, because it is always the case that if certain conditions were to obtain, then certain results would follow - again, regardless of what anyone thinks about it, and regardless of whether those conditions ever actually obtain for any particular object.

No, because the scope of the subjunctive conditional that represents a general property or law of nature is not limited to one particular object. — aletheist

Nominalists are not saying that regularlities of behavior are limited to one particular object. So again, what you wrote there is compatible with nominalism.

It is instantiated when particular objects behave in accordance with the law of nature that is the general property. — aletheist

That is NOT an explanation for WHY or HOW they do that. It's just a claim that they do it.

By the way, it's become increasingly clear that in your view universalism is ONLY about laws of nature. That's not at all what the traditional issue is about.

Universalism is traditionally about types that aren't identical to particulars being instantiated in particulars.

if certain conditions were to obtain, then certain results would follow - again, regardless of what anyone thinks about it, and regardless of whether those conditions ever actually obtain for any particular object. — aletheist

I don't know why you keep stressing this, because no one is denying it.

Well, or wait--actually I do know why you keep stressing it. You see universalism vs. nominalism strictly as being about whether there are "laws of nature," and you see what you're describing there as being a description of laws of nature, where you're not realizing that the way you're describing it is compatible with nominalists saying that with respect to particular properties, if certain conditions were to obtain, then certain results would follow - again, regardless of what anyone thinks about it, and regardless of whether those conditions ever actually obtain for any particular object.