You're welcome. I had previously read an account of Peirce's criticism of nominalism, so I simply googled the term 'Peirce, Nominalism', and that review came out at the top!

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Would you agree that we have little doubt in local or everyday contexts? I do of course see a connection to religion and culture here. I personally think it is clear that concepts exist. The first question might be: "In what way do concepts exist?" But the second question is fascinating, too: "What sort of conclusive answer to the first question can we really hope for?" Is there a shared criterion in place that allows us to agree on a correct answer-- assuming one "exists"? — R-13

I have been puzzling over this question a long time, indeed my first post on the old Philosophy Forums, from whence hail many of the contributors here, was along these lines (in 2009!)

Sometime before that I had been struck by an epiphany of sorts, which was that natural numbers are different to phenomenal objects in two principle ways: they are not composed of parts, and they don't begin and end in time. (Later I realised that strictly speaking, this describes prime numbers.) I wondered if this was something that was understood in philosophy, and found that it was characteristic of the Pythagorean-Platonic attitude. I learned that the Platonism generally had the understanding that this enabled the mathematician to grasp a higher order of truth. (This attitude is dismissed as 'the romance of mathematics' by Lakoff and Johnson, in their book 'Where Mathematics Comes From' (see here) and is not well regarded nowadays. However there are always some Platonists around.)

The point I make is fairly simple but has profound consequences: that if numbers are indeed real, but not material, then this contradicts materialism and empiricism, as mathematical objects are precisely not object of experience, or really objects at all in the material sense. Yet they're real, and indeed indispensable for science. It's an interesting fact that this 'inconvenient truth' has been recognized by empiricist philosophers who have devised ingenious arguments to deflate the claims of the 'transcendent reality of numbers' such as The Indispensability Argument:

[Rationalists] claim that we have a special, non-sensory capacity for understanding mathematical truths, a rational insight arising from pure thought. These claims appear incompatible with an understanding of human beings as physical creatures whose capacities for learning are exhausted by our physical bodies.

As indeed they are. However I would rather believe the rationalists.

Now, as to what kind of certainty we can arrive at in this matter, the answer can only be 'intuitive certainty'. But we can't demonstrate that in any empirical way, as it is by nature a metaphysical claim.

Pure theory can be viewed as the quest to construct indestructible tools that never become obsolete — R-13

Beware the 'instrumentalisation of reason' ;-)

The point I make is fairly simple but has profound consequences: that if numbers are indeed real, but not material, then this contradicts materialism and empiricism, as mathematical objects are precisely not object of experience, or really objects at all in the material sense. — Wayfarer

I think we start with what might be called "ordinary" experience. We live in a world where there are numbers, people, ideas, chairs, germs, atoms, etc. For "instrumental reasons," some people describe chairs or even people in terms of atoms. For me the mistake would be shifting from this reframing as a useful, temporary perspective to the position that chairs or peoples or even numbers are "really" atoms or waves or what have you. So there's a way to view the instrumental perspective as a transcendence of materialism, for instance. If we are building a cell-phones, it's useful to think reality in terms of electrons. But the poet dwells on reality as the place where people meet and feel and think. I don't think we have to choose. If we do choose, we can choose a sort of higher instrumentalism that doesn't ignore value or the intense "subjective" presence of concepts.

However I would rather believe the rationalists. — Wayfarer

I think the rationalists got something important right. I like Hegel. I generally think in terms of assimilation --an increasingly complex synthesis --rather than in terms of refutation. The natural numbers are just about the paradigm of objectivity. I think that 31 is prime whether anyone wants it to be or not. It's "there" in an important sense for anyone who cares to look. And of course arguments against the presence or value of concepts depend on this presence and value. "Does matter somehow begin to think?" Yes and no, depending on one's investments in the words. Thinking happens, certainly, and most of us believe in the kind of non-thinking stuff that that thinking creatures manipulate. Again, we agree more or less on what's going on in a practical sense, so it's seems largely of matter of taste as to how we frame this all up metaphysically.

Sometime before that I had been struck by an epiphany of sorts, which was that natural numbers are different to phenomenal objects in two principle ways: they are not composed of parts, and they don't begin and end in time. (Later I realised that strictly speaking, this describes prime numbers.) I wondered if this was something that was understood in philosophy, and found that it was characteristic of the Pythagorean-Platonic attitude. I learned that the Platonism generally had the understanding that this enabled the mathematician to grasp a higher order of truth. — Wayfarer

My own affinity to universals stems from belief in those that are, at least to some extent, experiential: the Good, the Aesthetic, etc. (all of which in more ancient philosophies tend to be different facets of the same given—or else different facets derived from the same given). I’m still fumbling, through this affinity, with mathematical universals. In this respect:

I’m very comfortable with the universals of rudimentary geometric figures, but I don’t take these to be numbers. Numbers, on the other hand, to me are cognitive models, or representations, of quantity. Geometric points then seem to naturally be the core root of all mathematical universals: via multiplicity of geometric points one attains quantity (numbers) and geometric forms, dimensions, etc. Yet geometric points as well are a human model, or construct. This leads me to believe that they too represent some universal that is independent of human models—such as, for example, can be stated of quantity and its relations being independent of human models.

I’d much appreciate your comments on this perspective. Disagreements are always welcomed.

Nominalism can be falsified: simply show evidence for a real universal. — Terrapin Station

What would you count as evidence for a real universal?

On the other hand, is realism is falsifiable?

That's the rub, no amount of evidence is ever enough.

Nominalism can be falsified: simply show evidence for a real universal.

Of course that's not so simple as there are no real universals, but if there were, one would just have to show evidence of one, and that would falsify nominalism. — Terrapin Station

I admit I’ve little hope of succeeding, but I’ll give it a try:

The innate notion of good--i.e., of what is beneficial--is, I argue, a universal. By this shouldn’t be interpreted concrete examples of what is good—be these either presumed relative to context or independent of context. Nor do I intend issues regarding good for whom. Instead, I merely intend that the innate awareness of what is beneficial is universal and stands apart from any sentience in and of itself: good is a property that can be divorced from the properties of an individual sentient being. Yes, what is good to you is not always likewise good to me (sometimes), yet despite this there is yet the universal awareness of there being something which we cognize and label “good”. For one extreme example, ameba won’t cognize the concept of good but will yet be endowed with awareness of what is good, i.e. beneficial.

In what manner would you then disagree with good being a universal?

How do you circumvent "the problem of abduction" - i.e. that it's just another name for induction, which never happens in reality, because it can't. — tom

Abduction is not another name for induction, and induction can and does happen in reality. The scientific method employs both of them routinely. It seems like you may not be familiar at all with what Peirce meant by these terms.

I roughly believe that the human being is "essentially" an engineer and that thinking is usefully conceived of in terms of engineering. — R-13

I would probably not go quite that far. However, I do think that Peirce's characterization of inquiry as the struggle prompted by doubt, which has the fixation of belief as its goal, is analogous to ingenuity as the struggle prompted by uncertainty, which has the fixation of decision as its goal.

I would probably not go quite that far. However, I do think that Peirce's characterization of inquiry as the struggle prompted by doubt, which has the fixation of belief as its goal, is analogous to ingenuity as the struggle prompted by uncertainty, which has the fixation of decision as its goal. — aletheist

I suppose it's just a metaphor that I find useful. Problem solving! Yes, the fixation of belief in response to doubt. Also the fixation of decision is crucial. We might even reduce the fixation of belief to the fixation of belief. That's why beliefs matter, right? We act on beliefs, and nothing manifests genuine belief as convincingly as action that involves risk. One might describe doubt as a sort of pain. Then we could look at metaphysical systems that address the problem of evil, for instance, as relief of pain or even as sources of ecstasy (rational "mysticism"). I like the trinity of prediction, control, and morale --but perhaps this boils down to control or power. We only want to predict so that we can be in the right place at the right time or not be in the wrong place at the wrong time --something like that. And we want to control or convert suffering so that it ceases or becomes pleasure.

Abduction is not another name for induction, and induction can and does happen in reality. The scientific method employs both of them routinely. It seems like you may not be familiar at all with what Peirce meant by these terms. — aletheist

Both abduction and induction are supposed methods of inference from data to a theory. That doesn't happen, it's invalid, and is certainly not part of the scientific method as expounded by Popper.

There is no method of inference from data to an explanatory theory. That's just a story we tell kids. The histories of quantum mechanics and relativity for example bear no traces of tales of abduction or induction, but then how could they?

We act on beliefs, and nothing manifests genuine belief as convincingly as action that involves risk. — R-13

Right - Peirce once described pragmatism as "scarce more than a corollary" of Alexander Bain's definition of a belief as "that upon which a man is prepared to act."

Both abduction and induction are ... certainly not part of the scientific method as expounded by Popper. — tom

The Popper who wrote Conjectures and Refutations? Conjectures result from what Peirce called abduction (or retroduction), and refutations (or corroborations) result from what Peirce called induction.

The histories of quantum mechanics and relativity for example bear no traces of tales of abduction or induction ... — tom

Do you really want to claim that quantum mechanics and relativity did not begin as plausible conjectures to explain surprising phenomena (abduction), which had predictable experiential consequences (deduction) that were subsequently evaluated through rigorous experimental testing (induction)?

Right - Peirce once described pragmatism as "scarce more than a corollary" of Alexander Bain's definition of a belief as "that upon which a man is prepared to act." — aletheist

Indeed. This is the point of view I was coming from as a critic of "terminological" disputes or "differences that make no difference." And that's actually what I value most in my exposure to pragmatism, that it shifted my mind away from some earnest wrestling with metaphysics that looked, in retrospect, like a waste of time. I'm currently in a Hegel phase, so I still like metaphysics. But I suppose I'm especially interested in the connection between value and epistemology. How does what we find authoritative, morally and in terms of objective truth, evolve? Clearly self-consciousness is a factor.

This is the point of view I was coming from as a critic of "terminological" disputes or "differences that make no difference." — R-13

Peirce evidently believed that the realism vs. nominalism debate was very consequential, because he waged that battle quite vigorously over the course of almost his entire philosophical career. He contended that nominalism has an inherent tendency to "block the way of inquiry" in various ways, and thus violate what he considered to be "the first rule of logic." I again highly recommend Peirce and the Threat of Nominalism by Paul Forster if you are interested in exploring this further.

The Popper who wrote Conjectures and Refutations? Conjectures result from what Peirce called abduction (or retroduction), and refutations (or corroborations) result from what Peirce called induction. — aletheist

OK, so the scientific method is new to you? Popper wrote the Logic of Scientific Discovery (LSD) first, in which he expounded the scientific method. One pillar of this method is that induction is never employed, because following Hume, Popper shows it is invalid. Later (perhaps even in Conjectures and Refutations) Popper goes a bit further in stating his view that "induction is a myth".

Whatever you think abduction is, its fundamental error is the same as induction - i.e. inference of an explanation from data. This just can't happen. What does happen according to the scientific method is a problem is encountered and a solution is conjectured, and there is no method for this part of problem-solving. Science consists of the method with which these ideas are treated.

Do you really want to claim that quantum mechanics and relativity did not begin as plausible conjectures to explain surprising phenomena (abduction), which had predictable experiential consequences (deduction) that were subsequently evaluated through rigorous experimental testing (induction)? — aletheist

OK, so why don't you list some of the phenomena from which the Schrödinger equation was abduced? Or how about the surprising phenomena from which General Relativity was abduced?

One theory that has struck me as a possible candidate for an example of abduction is the explanation of the photoelectric effect given by Einstein in 1905. I think it's a good one because all the data had been available for some time (it was a well known problem) and even those with a strong aversion to maths can grasp Einstein's conjecture: that light is quantized.

To claim the theory of the photoelectric effect was abduced as part of the scientific method is about as useful and accurate as saying the theory was produced by magic. The scientific method does not concern itself with how theories are come by, but how they are treated.

What does happen according to the scientific method is a problem is encountered and a solution is conjectured, and there is no method for this part of problem-solving. — tom

That was indeed Popper's view, but not Peirce's. The latter suggested - long before Popper wrote anything - that the logical form of abduction looks something like this:

• The surprising fact, C, is observed.
• But if A were true, then C would be a matter of course.
• Hence there is reason to suspect that A is true.

Indeed, this is deductively invalid - reasoning from consequent to antecedent, which is why Peirce also called it retroduction and acknowledged that its outcome is merely plausible at best. However, it furnishes the components of a perfectly valid deductive syllogism in which the conclusion is the surprising fact (C), the minor premiss is the credible conjecture (A), and the major premiss is the reason why C follows necessarily from A. In other words, A explains C in light of other known information, so a well-prepared mind is absolutely essential to the generation of viable hypotheses.

Of course, a plausible explanation does not yet count as a scientific hypothesis. The next step is deductively explicating the conjecture to determine whether it has any necessary consequences that can be experienced, preferably under controlled conditions; this is where Peirce's "pragmatic maxim" comes into play. The third and final step is then inductively evaluating whether the predicted outcomes actually occur, by conducting appropriate experiments. Like Popper much later, Peirce acknowledged that the hypothesis is never confirmed with certainty, only corroborated or falsified. Nevertheless, the logical form of induction is such that if the hypothesis is false, this will eventually come to light - induction is by no means infallible, but it is self-correcting over the long run.

We live in a world where there are numbers, people, ideas, chairs, germs, atoms, etc. — R-13

If you were doing one of those tests where they asked you to identify the anomolous members of a set, then 'numbers' and 'ideas' would certainly jump out, possibly followed by 'germs' and 'atoms'. Why? Because a dog would be able to perceive people and chairs, but would have no hope of perceiving numbers or ideas. Humans are able to perceive numbers, ideas, and rational relationships, because of the power of rationality. It is the distinguishing feature of h. sapiens. Our perceptions and conceptions are inextricably bound up with rational judgement; we see 'through' those judgements, without realising that we're doing it. That is the sense in which the elements of rational judgement inform and underlie our 'meaning-world'.

, we agree more or less on what's going on in a practical sense, so it's seems largely of matter of taste as to how we frame this all up metaphysically. — R-13

Afraid not (but anyhoo.....)

I’m very comfortable with the universals of rudimentary geometric figures, but I don’t take these to be numbers. Numbers, on the other hand, to me are cognitive models, or representations, of quantity. Geometric points then seem to naturally be the core root of all mathematical universals: via multiplicity of geometric points one attains quantity (numbers) and geometric forms, dimensions, etc. Yet geometric points as well are a human model, or construct. This leads me to believe that they too represent some universal that is independent of human models—such as, for example, can be stated of quantity and its relations being independent of human models. — javra

Note I am not offering any theory of the nature of number. Far greater minds than mine have tried and failed. My sole point is that at least some such entities - rules, laws, numbers, universals, and so on - are real but are not materially existent. So if we ask, do geometric forms, scientific laws, and so on, exist, the answer is not obvious; they don't exist as phenomena, although geometric forms can clearly be represented phenomenally. And, even if number is 'the representation of quantity', it is still something that can only be grasped by an intelligence capable of counting. So what intrigues me, is that these are in some sense 'independent of any mind' i.e. they exist independently of anyone thinking about them, but they're still only perceptible to a mind. I think that is very near the meaning of 'objective idealism'.

If you were doing one of those tests where they asked you to identify the anomolous members of a set, then 'numbers' and 'ideas' would certainly jump out, possibly followed by 'germs' and 'atoms'. — Wayfarer

I think I would stress people. So I agree that humans are special, central.

Our perceptions and conceptions are inextricably bound up with rational judgement; we see 'through' those judgements, without realising that we're doing it. That is the sense in which the elements of rational judgement inform and underlie our 'meaning-world'. — Wayfarer

This is very well said, and I agree very much. I associate philosophy with (among other things) becoming more conscious of these judgments that function as lenses. We are free to question and possibly replace such a judgment only after we become aware that we've been taking it for granted all along as a sort of necessity. This is the value, as I see it, in questioning the question. Let's say that we assume that either nominalism or realism is correct. Would we not still need a criterion to establish the correctness of one or the other? And yet philosophy seems largely to be the endless construction, criticism, and refutation of such criteria. The dream or goal seems to be something like a self-founding or self-justifying criterion or authority.

Let's say that we assume that either nominalism or realism is correct. Would we not still need a criterion to establish the correctness of one or the other? And yet philosophy seems largely to be the endless construction, criticism, and refutation of such criteria. The dream or goal seems to be something like a self-founding or self-justifying criterion or authority. — R-13

There was a fork in the road 500 years ago, now we're so far along the road that was taken that the alternative has almost faded from memory. But the dream, or goal, is what it always was: the vision of truth.

But the dream, or goal, is what it always was: the vision of truth. — Wayfarer

I agree. We seek the truth. And this seems to include the truth about truth-seeking. We find ourselves debating about how truth is or should be established. It seems that one aspect of philosophy is particularly concerned with the truth about truth, rather than the truth about life, for instance. It aspires to be meta-knowledge. Religious traditions might have it easier. What assumptions motivate us to defend the truths we are sure of? Philosophy seems to assume that truth is the result of or at least subject to debate. So there's something revolutionary in its essence. It has an anti-truth potential, it seems, since it must seemingly die with the attainment of the truth it seeks. But perhaps this is the philosopher dying into the sage.

Nothing in your post I disagree with, and thank you for it.

So if we ask, do geometric forms, scientific laws, and so on, exist, the answer is not obvious; they don't exist as phenomena, although geometric forms can clearly be represented phenomenally. And, even if number is 'the representation of quantity', it is still something that can only be grasped by an intelligence capable of counting. So what intrigues me, is that these are in some sense 'independent of any mind' i.e. they exist independently of anyone thinking about them, but they're still only perceptible to a mind. I think that is very near the meaning of 'objective idealism'. — Wayfarer

This underlined part got me thinking. Other than universals being non-phenomenal, the same could also be said of any physical, phenomenal given. And the greater the sapience of the species, the more cognizance it holds regarding that of which it is aware—again, as applies both to universals and to the realities of the physical world (e.g., though amebas could be innately aware of quantity--say in terms of rudimentary quantity concerning prey or predator--they certainly aren't aware of numbers and their relations). So, I view these attributes underlined within the quote as only part of the picture. Some would say that universals hold constraints upon particulars; else stated, that there is a top-down causation imposed upon particulars by universals. And I’m in agreement with this view. But that might be another story altogether.

Somehow, the more experiential universals (such as that of the good) are easier for me to contemplate, relatively speaking. In thinking of how maths and nature intersect—like fractals in plants—the notions become … well, no longer all that accessible. I know, I’m in long waiting list to have these things finally become easily intelligible, but I'm still somewhere there in that line.

I agree. We seek the truth. And this seems to include the truth about truth-seeking. We find ourselves debating about how truth is or should be established. It seems that one aspect of philosophy is particularly concerned with the truth about truth, rather than the truth about life, for instance. It aspires to be meta-knowledge. Religious traditions might have it easier. What assumptions motivate us to defend the truths we are sure of? Philosophy seems to assume that truth is the result of or at least subject to debate. — R-13

You might say religions make it too easy, that the kind of truth they offer are rather too settled - 'sign here'. That's where the Platonist tradition is so interesting and still so important. Plato was determined not to be taken in by 'mere belief' but to arrive at a greater truth through the exercise of reason, which is still what distinguishes philosophy from religion as such (although there are many overlaps). But your observation of 'knowing how we know' is crucial to that. What motivates that, is something like a religious type of instinct, but again it is more questioning and more critical than what we generally take religion to be. (Have a look the abstract for Katja Vogt's Belief and Truth, I think she's on the money.)

Some would say that universals hold constraints upon particulars; else stated, that there is a top-down causation imposed upon particulars by universals. — javra

I think that is a very widely-accepted view nowadays - you're in good company.

One area of biological research that I think bears that out is the idea of 'convergent evolution' - for instance, if you want to fly, then you have to have a wing, whether it's an insect wing, bat wing, bird wing, or pterosaur wing. So could that be understood in terms of the 'idea' (eidos, form) of a wing? Given that it has to perform a particular function, then it has to assume a certain form - never mind what route it takes to get there. And there you see a nice kind of dynamic between necessity, on the one hand, and freedom, on the other.

(And Happy New Year to all, I'm in Sydney so it's New Years Eve here already, be back later.)

That was indeed Popper's view, but not Peirce's. The latter suggested - long before Popper wrote anything - that the logical form of abduction looks something like this:

The surprising fact, C, is observed.
[*}But if A were true, then C would be a matter of course.
Hence there is reason to suspect that A is true.


Indeed, this is deductively invalid - reasoning from consequent to antecedent, which is why Peirce also called it retroduction and acknowledged that its outcome is merely plausible at best. However, it furnishes the components of a perfectly valid deductive syllogism in which the conclusion is the surprising fact (C), the minor premiss is the credible conjecture (A), and the major premiss is the reason why C follows necessarily from A. In other words, A explains C in light of other known information, so a well-prepared mind is absolutely essential to the generation of viable hypotheses. — aletheist

Sure, and no matter how many times I ask for an example of abduction or induction, I never get one.

So, here are a few surprising facts (C) that have been encountered. Perhaps you could give a rough idea how the best theory may have been abduced to explain one:

Perihelion of Mercury
Quantum Entanglement
The Higgs Boson
Gravitational Waves
The Cosmic Microwave Background?

Abduction doesn't happen, and would be useless if it did. It seems nothing more than an appeal to some sort of justification for an idea.

Nevertheless, the logical form of induction is such that if the hypothesis is false, this will eventually come to light - it is by no means infallible, but it is self-correcting over the long run. — aletheist

There is no "logical form of induction" it is a fallacy.

What would you count as evidence for a real universal? — aletheist

We'd need to be able to somehow "point" (in quotation marks because it wouldn't have to be a literal, direct pointing) at a property that particulars can instantiate, where it's clear that what we're pointing at isn't simply us thinking about the property/formulating a mental concept of the property.

On the other hand, is realism is falsifiable? — aletheist

Asymptotically. The more we look for the above and don't find it, the stronger the falsification is.

The innate notion of good--i.e., of what is beneficial--is, I argue, a universal. By this shouldn’t be interpreted concrete examples of what is good—be these either presumed relative to context or independent of context. Nor do I intend issues regarding good for whom. Instead, I merely intend that the innate awareness of what is beneficial is universal and stands apart from any sentience in and of itself: good is a property that can be divorced from the properties of an individual sentient being. Yes, what is good to you is not always likewise good to me (sometimes), yet despite this there is yet the universal awareness of there being something which we cognize and label “good”. For one extreme example, ameba won’t cognize the concept of good but will yet be endowed with awareness of what is good, i.e. beneficial. — javra

You're explaining what you take a universal to be here. You're not showing evidence that there are real (extramental) universals.

Sure, and no matter how many times I ask for an example of abduction or induction, I never get one. — tom

What would you count as an example of each? Abduction happens every time someone devises a new theory. Induction happens every time someone experimentally tests a proposed theory.

So, here are a few surprising facts (C) that have been encountered. — tom

To take one of your examples: No one "observed" the Higgs boson until they went looking for it (induction) because it was a necessary consequence (deduction) of an explanatory hypothesis (retroduction).

There is no "logical form of induction" it is a fallacy. — tom

Your view of logic seems too narrow. Again, no one is claiming that retroduction or induction is deductively valid.

We'd need to be able to somehow "point" ... at a property that particulars can instantiate, where it's clear that what we're pointing at isn't simply us thinking about the property/formulating a mental concept of the property. — Terrapin Station

Doesn't this requirement effectively beg the question, since realists affirm that our only "contact" with universals is via the mind? In fact, realists usually assert that all of our knowledge is of generals.

Peirce's "proof" of realism was holding a rock and asking his audience whether they knew that it would fall if he let go of it. In other words, our ability to make reliable predictions about the future behavior of individual objects requires the reality of the laws of nature as generals that govern particulars.

The more we look for the above and don't find it, the stronger the falsification is. — Terrapin Station

But that is not falsification in the same decisive sense that "discovery" or "observation" of one real universal would falsify nominalism. As the saying goes, absence of evidence is not evidence of absence. Refuting realism seems to require proving a negative.

What would you count as an example of each? Abduction happens every time someone devises a new theory. Induction happens every time someone experimentally tests a proposed theory. — aletheist

But you can't give a single example of either. Just to point out, you previously claimed testing of a theory was a deductive process. What changed your mind?

For the sake of argument, if we assume that Special Relativity was abduced from surprising observations, then what? How does that affect the status of the theory or what we do with it?

To take one of your examples: No one "observed" the Higgs boson until they went looking for it (induction) because it was a necessary consequence (deduction) of an explanatory hypothesis (retroduction). — aletheist

Could you explain the inductive process of going to look for a particle predicted 50 years previously?

Your view of logic seems too narrow. Again, no one is claiming that retroduction or induction is deductively valid. — aletheist

But you are claiming that they happen, they are useful, and that you can appeal to them for justification. All false!

But you can't give a single example of either. — tom

I mentioned the Higgs boson, since it was one of your own examples. Scientists posited its existence as a plausible explanation of certain surprising observations (retroduction). They predicted certain results if certain tests were undertaken (deduction). They subsequently carried out those tests and compared the actual results with the predictions (induction).

Just to point out, you previously claimed testing of a theory was a deductive process. — tom

I claimed no such thing. Explicating a theory - identifying its experiential consequences - is a deductive process. Evaluating a theory - carrying out experiments in order to ascertain whether those predictions are borne out - is an inductive process.

But you are claiming that they happen, they are useful, and that you can appeal to them for justification. — tom

Retroduction justifies nothing - it merely formulates a plausible hypothesis. Deduction only justifies a hypothesis to the extent of showing that it can produce testable predictions. Induction further justifies a hypothesis to the extent of showing that those predictions are experimentally corroborated. This is the maximum extent to which any scientific theory can be justified - we are always fallible, and thus can never achieve certainty. As Popper maintained, theories can be falsified, but never confirmed.