"Find a scientific man who proposes to get along without any metaphysics ... and you have found one whose doctrines are thoroughly vitiated by the crude and uncriticized metaphysics with which they are packed. ... Every man of us has a metaphysics, and has to have one; and it will influence his life greatly. Far better, then, that that metaphysics should be criticized and not be allowed to run loose."
- Charles Sanders Peirce

The OP fails to spell out each of the options and the technical terms that they include, and idealism vs. realism is a false dichotomy. For the sake of clarity, I suggest the following definitions as employed by Charles Sanders Peirce, already mentioned () as an example of a philosopher who was both a (scholastic) realist and an (objective) idealist:

• The real is whatever is as it is regardless of what any individual mind or finite community of minds thinks about it.
• The external is whatever is as it is regardless of what any individual mind or finite community of minds thinks about anything.
• The existent is whatever reacts with other like things in the environment.

Accordingly, a metaphysical idealist like Peirce (matter is a peculiar sort of mind) can still affirm that the external world is real (including everything that exists), as well as logical realism (some generals are real even though they do not exist).

How do you get from “Eveything is mind”, to “Everything is semiosis”? — apokrisis

All thought is in signs, so all mind is semiosis.

Peirce certainly makes idealist sounding statements. Yet he is, in the end, the pragmatist and so all about the epistemology of how we mentally model the ontic structure of the world. — apokrisis

According to Peirce's own testimony, he is above all else a synechist. That is what leads him to be not only a pragmatist, but also an extreme scholastic realist, a tychist, and an objective idealist, which is why he eventually seeks to differentiate his "pragmaticism" from the pragmatism of James and others.

Bare qualities exist for us only within cognitive frames. Thus they don’t actually “exist”. — apokrisis

Like I said, qualities in themselves do not exist, but they are nevertheless real--they are as they are regardless of what anyone thinks about them.

Firstness is primordial - the start of “thingness” - when it comes to his ontology. — apokrisis

No, on my reading of Peirce, 3ns is primordial. In his cosmological diagram, the starting point is a clean blackboard (3ns), then come the aggregated white chalk marks of a Platonic world (1ns), out of one of which our existing universe is actualized as a discontinuous mark (2ns).

If I "do away" with firsts, it would be a ball lacking colour "only"? — Manuel

No, it would be pure matter lacking all qualities whatsoever.

It's difficult to imagine 1sts without concrete instantiations of a quale, as in, I don't know if such things could exist: a quale or phenomenal properties without concrete instantiation. — Manuel

Indeed, 1ns does not exist apart from its concrete instantiations, but it is a real possibility. Peirce carefully distinguishes existence as reaction with other like things in the environment from reality as being such as it is regardless of what anyone thinks about it.

How can I register an impact without a sensation? — Manuel

You can't, but the impact itself is 2ns regardless of whether you "register" it. The sensation as you actually experience it is 2ns, while the quality of that sensation is 1ns. We can only apprehend that quality in itself by prescinding it from the experience.

Surely they have to transcend the phenomenal to avoid a mere reduction to idealism. — apokrisis

That depends on what you mean by "transcend the phenomenal" and "reduction to ideaism." After all, Peirce considered phenomenology to the the first positive science, on which all the others depend for principles, and explicitly affirmed (objective) idealism in the sense that the psychical law is primoridal while the physical law is derived and special, such that matter is a peculiar sort of mind--mere specialized and partially deadened mind.

You're saying that getting hit by a red ball is a firstness, aletheist says it's a 2ndness. — Manuel

No, we are both saying that the redness of the ball is 1ns, while getting hit by it is 2ns.

Firstness for him, as I understand him in this example, would be the sensation of rubber I feel from the ball, but me getting hit would be a second. — Manuel

No, again, the sensation itself is 2ns, but its prescinded quality is 1ns.

I’ve noticed before that if you go looking for references on ‘objective idealism’ that Pierce comes up at the top of the rankings. (He endorses Berkeley but rejects Berkeley’s nominalism.) — Wayfarer

Peirce distinguishes his Schelling-fashioned objective idealism from Berkeley's subjective idealism, as well as Kant's transcendental idealism and Hegel's absolute idealism.

I'll start a thread as others like aletheist might give different answers. — apokrisis

Thanks for the shout-out!

My take is that of someone who sticks pretty closely to Peirce's own writings and terminology. Strictly speaking, his categories are phenomenological rather than metaphysical, the irreducible elements of whatever is or could be present to any mind in any way. As such, they primarily correspond to quality, reaction, and mediation. In mathematics, they correspond to monadic, dyadic, and triadic relations. In normative science, they correspond to feeling, action, and thought. In metaphysics, they correspond to possibility, actuality, and conditional necessity. In cosmology, the constitution of being is a continuum (3ns) of indefinite possibilities (1ns), some of which are actualized (2ns). Time flows from the irrevocable past (2ns) through the nascent present (1ns) toward the indeterminate future (3ns).

For instance seeing the red of a ball is an instance of firstness ... — Manuel

This is a good example of why Peirce's categories can be difficult to grasp without a lot of careful study. Seeing the red of a ball is an instance of 2ns, not 1ns, because the redness is embodied in the ball. The redness in itself, as a qualitative possibility apart from any physical instantiation and without comparison to anything else, is the closest we can get to an idea of pure 1ns.

... me reacting to someone throwing the ball at me and felling the rubber of the ball would be secodness ... — Manuel

Even just the brute impact of the ball on you is 2ns, independent of your sensation of it, although that is also 2ns. Here the quality of the feeling of the rubber is 1ns.

... and me thinking about whom to hit in this game would be thirdness. — Manuel

Sure, anything cognitive is basically 3ns. However, an important principle to keep in mind is that the categories are never really isolated from each other in our experience, only as artifacts of analysis that result from a kind of abstraction. We prescind 2ns from 3ns, and we prescind 1ns from both 2ns and 3ns.

Hope that helps!

The equation of God with being seems odd ... — Janus

Claiming that God is necessary being is not equating God with being.

And God, at least the Abrahamic God, does "react with other individual things" via revelation and prayer. — Janus

Classical theism, even in its Abrahamic versions, maintains that God is simple (not individual) and impassible--God acts on the world, but does not react with it.

Also, the distinction between being and existence seems forced and unnecessary. — Janus

Not when existence is understood as only one mode of being--reaction with other individual things in the environment. Possibility and conditional necessity are other modes of being.

So, the argument looks silly to me from the get-go. — Janus

Like I said, it is really a definition rather than an argument.

But you say theists think God exists of necessity - but they don't, only some do. — Bartricks

No, I said that classical theism maintains that God is necessary being.

I am late to the party, but have read through the thread and would like to offer a few comments on the OP.

God is supposed to be a necessary being. — Banno

As some have already hinted, classical theism maintains that God is necessary being, not that God is a necessary being. In other words, God is not conceived as an individual being who "exists" in the sense of reacting with other individual things.

Something is necessary if it is true in every possible world.
There is a possible world in which god does not exist.
Hence, god is not a necessary being. — Banno

We can reformulate this as a conditional proposition that should be utterly uncontroversial: If there is a possible world in which there is no God, then God is not necessary being. On the other hand, we can also formulate another conditional proposition that should likewise be utterly uncontroversial: If God is necessary being, then there is no possible world in which there is no God. Taken together, what we have here is just a definition of "necessary being" in terms of possible world semantics: God is a necessary being if and only if there is no possible world in which there is no God.

The debate, then, is whether there is any possible world in which there is no God; theists say no, atheists say yes. Deductive logic, classical or modal, cannot settle this question. Charles Sanders Peirce instead turns to retroductive (also called abductive) logic in his 1908 article, "A Neglected Argument for the Reality of God." He suggests that the reality (not existence) of God as necessary being (Ens necessarium) is a plausible (not certain or even probable) hypothesis to explain the origin and order of the universe. I wrote a paper about this if anyone is interested in further details.

As I understand "musement" it is, at first at first at least, a process by which our observations suggest that something is the case, but not as part of an inquiry on our part. — Ciceronianus the White

Right, although it can also serve as the very first stage of scientific inquiry, just pondering the phenomena as they present themselves and relying on instinct to supply plausible explanatory hypotheses about them.

More traditional forms of reasoning may come into play after that takes place. — Ciceronianus the White

Indeed, Peirce lays out the entire process of scientific inquiry in the article--formulating a hypothesis (retroduction) is followed by explicating what would follow from it if it were true (deduction) and then examining whether those predictions are borne out (induction).

As I said, there is the triadic epistemology that is a model of psychological processes of reasoning. — apokrisis

Except that for Peirce, reasoning (semiosis) as studied within the normative science of logic (semeiotic) is emphatically not a psychological process. Rather, psychology is a special science that studies the actual thinking of individual embodied human minds. In other words, psychology depends on logic (and metaphysics), not the other way around.

The Cosmos could be understood the growth of universal reasonableness - an ontological strength application of the trichotomy. — apokrisis

Except that for Peirce, the growth of concrete reasonableness is discovered within the normative science of esthetics (not metaphysics) as the only aim that is admirable in itself. Ethics depends on it for this principle in ascertaining what constitutes good conduct, and logic depends on both esthetics and ethics in ascertaining what constitutes good reasoning--again, regardless of any facts of psychology.

Is that article available somewhere? — Ciceronianus the White

Richard Robin catalogued Peirce's 500-plus handwritten pages of multiple drafts for "Pragmatism" under manuscript numbers 317-322 and 324. The five major variants that came chronologically last and have their first nine pages in common are all under 318, as diagrammed by Priscila Borges for the Peirce Edition Project. He abandoned the second and fourth without finishing them, while the third and fifth appear in Volume 2 of The Essential Peirce (pages 398-433). Surprisingly, the first has never been published, even though it seems likely to be the one that he initially submitted to The Nation because it bears his signature at the end. Fortunately, that is about to change--I have prepared my own annotated transcription, which has been accepted by an online journal and will hopefully appear there soon.

What about your article? — Ciceronianus the White

I provided this link in my previous post.

For quite some time, I've been somewhat fascinated with Pierce's A Neglected Argument for the Reality of God and his concept of "musement." — Ciceronianus the White

I share your fascination with that article, and likewise wrote a paper about it. It is important to recognize the distinction that Peirce makes between an argument as "any process of thought reasonably tending to produce a definite belief" and an argumentation as "an Argument proceeding upon definitely formulated premisses." His "Neglected Argument" is the former, not the latter, and it is retroductive (or abductive) rather than deductive or inductive--careful contemplation of the universe ("musement") prompts the hypothesis of God's reality (not existence, another important distinction for Peirce) as a plausible explanation of its origin and nature, not a certain or even probable conclusion drawn from specific premisses or evidence.

The core idea pragmatism is that the object of an idea equates the sensible effects that the object might have. — Nzomigni

This is a common misconception, or at best an incomplete definition. For Peirce, pragmatism is a theory of meaning, not a theory of truth. The core idea is that the ultimate meaning of a concept consists in the general mental habits and resulting deliberate conduct of its interpreters, not the law-governed behavior of its object.

Pierce came up with more than one version of the pragmatic maxim ... — Ciceronianus the White

This is an important point, although Peirce himself never calls it "the pragmatic maxim"--it is occasionally either "the pragmatistic maxim" or "the pragmaticistic maxim," and much more often either "the maxim of pragmatism" or "the maxim of pragmaticism." His original formulation appeared in 1878, but there are at least 13 variants and 47 restatements or clarifications in Peirce's writings after James began popularizing pragmatism 20 years later, which I present and discuss in a recently published paper.

It's been a long time since I read that essay you mentioned, so I can't recall if he had particular concepts in mind. — Ciceronianus the White

Peirce did not clarify until 1907 that he specifically had intellectual concepts in mind, "those upon the structure of which arguments concerning objective fact may hinge," such as hard vs. soft but not red vs. blue. That year, about the same time that James published his book called Pragmatism, Peirce drafted an article with the same title intended to introduce his version of it to a broad audience. He ended up drafting over 500 handwritten pages, and we can only wonder how the course of philosophy in general and pragmatism in particular would have been different had either The Nation or The Atlantic Monthly published one of the finished texts that he submitted to their editors.

I've never been much of a fan of Pierce's Firstness, Secondness and Thirdness and his Triadism, though, if that's what's intended by pragmatism's "metaphysical ambition." — Ciceronianus the White

It is another common misconception that Peirce's three universal categories are fundamentally metaphysical. On the contrary, they are primarily phenomenological in a sense that is distinct from that of Hegel or Husserl--1ns as quality, 2ns as reaction, and 3ns as mediation are the irreducible elements of whatever is or could be present to the mind in any way. As for pragmatism, Peirce is adamant that it "is, in itself, no doctrine of metaphysics, no attempt to determine any truth of things. It is merely a method of ascertaining the meanings of hard words and of abstract concepts."

It might help to separate pragmatism as a triadic epistemology from semiosis as a triadic ontology. — apokrisis

Peirce's classification of the sciences is grounded in the idea that the more concrete fields depend on the more abstract fields for their principles. Accordingly, metaphysics as the study of reality depends on logic as the normative science of how we ought to think if our aim is having stable beliefs/habits, which he generalized to semeiotic, the study of all signs and semiosis. Pragmatism falls within its third branch, speculative rhetoric or methodeutic, and thus depends on its second branch, critical logic or logic proper, which in turn depends on its first branch, speculative grammar--loosely aligned with what is commonly (and in Peirce's view mistakenly) called epistemology. Again, his categories come from phenomenology, which is the most basic of the "positive sciences" and depends only on mathematics, the discipline that draws necessary conclusions about strictly hypothetical states of things.

I read Charles Pierce's Guess at the Riddle by John Sheriff, and found that helpful. — Ciceronianus the White

Yes, that is an excellent short introduction. For a more detailed overview, I recommend The Continuity of Peirce's Thought by Kelly A. Parker.

In particular, what is the alleged justification for the premiss that there are no justified basic beliefs?

So, you believe that the earth does not really revolve around the sun? — aletheist

I know that it doesn't. — tim wood

How do you know this? I am not asking how you justify that belief, but on what basis it is (purportedly) true.

But I suspect you have no honest interest in the discussion. — tim wood

I would prefer that you just come out and make whatever point is on your mind.

How do you know what is real? — tim wood

Whether I know that something is real is irrelevant. Again, the real is that which is such as it is regardless of what anyone (including me) thinks about it.

You present as a fact that the earth revolves around the sun. — tim wood

I explicitly stipulated that this is a fact if and only if the earth really revolves around the sun. Like all our beliefs, this one is fallible.

It doesn't. Yours just a convenient fiction - a non-truth. — tim wood

So, you believe that the earth does not really revolve around the sun? Like all beliefs, that one is also fallible. Since they are contradictory, one of us affirms a true proposition and the other affirms a false proposition; but which is true and which is false does not depend on what either of us (or anyone else) thinks about the matter.

On the contrary, it is quite clear to me that a fact is the real state of things that a true proposition signifies.

You seem to be conflating knowledge with truth. The standard philosophical definition of knowledge is justified true belief. I can believe a proposition, and even be justified in believing it, but that is not what makes it true.

What is "a" reality? — tim wood

Whatever is such as it is regardless of what anyone thinks about it.

And can you record here even one fact, any at all, as you describe fact? — tim wood

The earth revolves around the sun--provided that it really does, as I believe to be the case.

On the contrary, within semeiotic the definitions of terms including "object" and "subject" are unambiguous and foster greater understanding. As far as I can tell, your only reason for rejecting them is that they are different from your preferred definitions, which you want to impose on any and every context.

The proposition that the sun - and everything else - revolved around the earth was a proposition propounded by folks who believed and had proofs of it. For them it was a true proposition. But just one not altogether in accord with the facts. — tim wood

Truth or falsity is not a matter of human belief. A proposition that is "not altogether in accord with the facts" is not a true proposition, no matter how many people hold it to be true. A proposition about the world is true if and only if it denotes a reality as its object and signifies a fact as its interpretant.

I know that's what you think, but I disagree. — Metaphysician Undercover

I know that you disagree, and at this point I find that comforting.

An object is defined according to the law of identity, as unique, primary substance, but a logical subject is not unique, as secondary substance. — Metaphysician Undercover

There you go again, making stuff up to sound knowledgeable. That is not how "object" and "subject" are defined within semeiotic. I get it, you reject those definitions, so again we can stop wasting each other's time.

So I see your definition as completely misguided because it's not conducive for understanding. — Metaphysician Undercover

It is not "my" definition, it is the well-established definition within the discipline of semeiotic.

I do not agree with the fundamental principles of that proposed field of study. — Metaphysician Undercover

Then we can stop wasting each other's time.

I am not one to dismiss things off hand, without some understanding of the fundamental principles. — Metaphysician Undercover

On the contrary, in my experience you routinely dismiss things out of hand, simply because they fail to conform to your peculiar, narrow, dogmatic definitions of terms.

This appears to involve a fallacy of composition. — Metaphysician Undercover

You also say things like this so that it sounds like you know what you are talking about when you really have no idea.

Sure there is pure signification, in the case of any abstract use, a universal, like "temperature", "big", "good", "beauty" "green", "wet", and the list goes on and on. — Metaphysician Undercover

No, these words are examples of signs whose objects--that which they denote--are general concepts.

We use all these terms as a subject when we say things like "temperature is a measurement", "big is a size", "good is desirable", beauty is what the artist seek", "green is a colour". These are phrases of pure signification — Metaphysician Undercover

No, in each of these propositions there are two or three subjects denoting two or three objects, and the interpretant conveys something about the logical relation between those objects. The interpretant of each individual word is the aggregate of all the different propositions that include it, which we attempt to summarize whenever we write a definition of it.

Because then we lose the capacity to distinguish between a physical object denoted, and a subject of study denoted. If these two are the same, as "object denoted", category mistake will prevail. — Metaphysician Undercover

The category mistake is conflating different definitions of "object" and "subject" that apply in different contexts. An object is not necessarily something physical, and a subject is not necessarily something that we study. In semeiotic, an object is whatever a sign denotes, and a subject is a term within a proposition that denotes one of its objects.

I really can't see how a relation is an object. — Metaphysician Undercover

That is because you evidently have an extremely narrow definition of "object" and refuse to accept how that word is defined as a technical term within the discipline of semeiotic. Anything whatsoever that is denoted by a sign is the object of that sign.

I think you are making things up as you go. — Metaphysician Undercover

Not at all, do some research into semeiotic (also called "semiotic" or "semiotics") and you will learn that what I have been discussing is a well-established field of study. I did not anticipate having to get into this level of detail when I offered the simple observation that "Henry Fonda" and "the father of Peter Fonda" denote the same object, which is utterly uncontroversial within that field.

On top of this you allow that two phrases might signify different things, yet denote the very same thing. This indicates very clearly that there are contradicting interpretations of the same phrases. One interpretation says that they are different, the other that they are the same. Yet you allow that the contradicting interpretations are both correct. — Metaphysician Undercover

There is no contradiction because denotation and signification are not synonymous, they correspond to different functions of a sign. Again, what a sign denotes is its object and what a sign signifies its interpretant. The object of a term is whatever it stands for, while the object of a proposition is the collection of objects denoted by the terms that serve as its subjects. The interpretant of a sign is whatever it conveys about its object, and thus is usually what we have in mind when we talk about the meaning of that sign.

What is true or false of a fictional universe is only dependent on what its creator thinks about it. — aletheist

No. What he says about it. — tim wood

Fair enough, but the point is that it does not depend on what anyone else thinks (or says) about it.

Indeed, if it's a fictional universe, then no proposition about it is true - except the proposition that it is a fictional universe. — tim wood

No proposition about it is true of the real universe, but certain propositions about that fictional universe are true within that fictional universe. The proposition "Hamlet was the prince of Denmark" is false in the real universe, but true in the fictional universe of Shakespeare's play.

But you have evaded the point. Truth and falsity are assigned to propositions. If no propositions, or, if no one to assign truth or falsity, then no truth or falsity. You need the assigner. — tim wood

I did not realize that this was the point, and in any case I disagree. Truth and falsity are not assigned to propositions, they are properties of propositions. The proposition "the earth revolves around the sun" was true before there were any humans around to express that proposition or to assign truth to it.

How can this be when the "true or false of it" is exactly dependent on people and not otherwise? — tim wood

I do not understand the question. What is true or false of a fictional universe is only dependent on what its creator thinks about it. It is such as it is regardless of what anyone else thinks about it.

How do you characterize classical logic? — tim wood

It codifies how we can properly draw necessary conclusions about states of things that are definite, thus conforming to non-contradiction; individual, thus conforming to excluded middle; and real, in the sense that they are such as they are regardless of what we think about them.

Full disclosure, I am not a mathematician, so my ability to address the details of SIA is admittedly limited.

In other words, all functions defined in the system are continuous by definition. Am I correct? — jgill

I believe so, as this seems to be simply what it means for a world to be smooth. As Bell says on p. 276, "If we think of a smooth world as a model of the natural world, then the Principle of Microstraightness guarantees not just the Principle of Continuity--that natural processes occur continuously, but also the Principle of Microuniformity, namely, the assertion that any such process may be considered as taking place at a constant rate over any sufficiently small period of time." For me this is reminiscent of the following passage.

Accepting the common-sense notion [of time], then, I say that it conflicts with that to suppose that there is ever any discontinuity in change. That is to say, between any two instantaneous states there must be a lapse of time during which the change is continuous, not merely in that false continuity which the calculus recognizes but in a much stricter sense. Not only must any given instantaneous value, s, implied in the change be itself either absolutely unchanging or else always changing continuously, but also, denoting an instant of time by t, so likewise must, in the language of the calculus, ds/dt, d^2s/dt^2, d^3s/dt^3, and so on endlessly, be, each and all of them, either absolutely unchanging or always changing continuously. — C. S. Peirce

A step function obviously has a discontinuity that violates this requirement. Of course, the "false continuity which the calculus recognizes" is that of the real numbers, which Peirce elsewhere calls a "pseudo-continuum."

Consequently, classical logic is strictly applicable only where "a recognized universe [of discourse] is ... real (so that what is true or false of it is independent of any judgment of man or men, unless it be that of the creator of the universe, in case this is fictive)." — aletheist

This is strange. Do you understand it? Because I do not. Try reading it closely and see if it doesn't begin to seem to you that the writer is confused about his subject. — tim wood

It makes perfect sense to me. Again, the basic definition of real is being such as it is regardless of what anyone thinks about it. If we are talking about a fictional universe, then what is true or false of it depends entirely on what its creator decides about it, but not on what anyone else thinks about it. In Shakespeare's "Hamlet," the title character is the prince of Denmark and kills Claudius because Shakespeare says so; but no one can now truthfully claim that within the universe of that play, Hamlet is the king of Spain and spares Claudius. That is why there are objectively right and wrong answers on tests that students of English literature have to take after reading it.

And I see "logic requires us." Logic does no such thing, nor can. Hmm. — tim wood

This strikes me as merely shorthand for your own characterization of logic as a game with certain rules. In the case of classical logic, one of those rules is excluded middle--every constituent of the universe of discourse must be treated as "individual (so that any assertion is either true or false of it)," which "amounts to saying that the universe [of discourse] has a perfect reality."

I can see how "I did X", and "I did Y", both refer to the same object with "I", but each signify something different. — Metaphysician Undercover

Good, and they also both denote the same object with "did," which is the relation of doing. However, they presumably denote different objects with "X" and "Y," although since these are variables it is conceivable that they could also denote the same object--for example, the activity of exercise.

How do you come up with this idea that two phrases which signify something completely different actually denote the same object. — Metaphysician Undercover

We already went over this with "Henry Fonda" and "the father of Peter Fonda." These signs both denote the same object despite signifying different interpretants because it happens to be a fact that Henry Fonda is the father of Peter Fonda.

Clearly, in our use of mathematics there is signification without denotation. — Metaphysician Undercover

As someone once said ...

Do you understand the fallacy of "begging the question", assuming the conclusion? — Metaphysician Undercover

Why then did you insist on a distinction between "signification" and "denotation" in the other thread, when here you want any signification to be a denotation? — Metaphysician Undercover

This question just confirms an ongoing failure (or refusal) to understand the technical definitions of denotation and signification within semeiotic.

So, you insist on a distinction between signification and denotation, then it turns out that there is no such thing as signification in common usage. — Metaphysician Undercover

That is not what I said. There is no such thing as pure signification (without denotation) in common usage. Likewise, there is no such thing as pure denotation (without signification) in common usage. Instead, in practice every sign both denotes its object (what it stands for) and signifies its interpretant (what it conveys about that object). This is most readily evident in a proposition, where the subjects (terms as names) denote the objects and the predicate (embodied as syntax) signifies the interpretant. The fundamental principle of semeiotic (following Peirce) as distinguished from semiology (following Saussure) is that a sign thus stands in an irreducibly triadic relation with its object and its interpretant, rather than there being only a dyadic relation between signifier and signified.

Ordinary mathematics regards '2+1' and '3' as having the same denotation — TonesInDeepFreeze

Indeed, but as the Fonda example has brought to light, @Metaphysician Undercover apparently confuses denotation and signification. The result is wrongly denying that two different expressions signifying different interpretants can nevertheless denote the same object.

That's not true, because the operation signified by "+" is not evident in the group of three apples, so it is not a true representation of "2+1". It is just a representation of "3". — Metaphysician Undercover

I am treating "2+1" and "3" as signs here, and I already acknowledged that their signification is different. At issue is whether their denotation is different. What "+" represents in isolation is irrelevant, all that matters here is that I can point to the same group of items and truthfully say both "that is 2+1 apples" and "that is 3 apples."

If you were teaching children you would not show them a group of three apples and tell them this is 2+1. — Metaphysician Undercover

I actually might do exactly that, if I were teaching them basic addition such as 2+1=3.

We cannot conclude that because the expressions can be substituted, they signify the same thing. — Metaphysician Undercover

Of course not, but we can conclude (in an extensional context) that they denote the same thing.

That's correct in an extensional context, but not in an intensional context: — TonesInDeepFreeze

Fair enough, thanks. Indeed, an extensional context corresponds to denotation (object), which is the same for "Henry Fonda" and "the father of Peter Fonda"; while an intensional context corresponds to signification (interpretant), which is different for the two signs as I have acknowledged all along.

It seems clear that you are using a different definition of "object" than the one rigorously employed within the discipline of semeiotic. Again, anything that is denoted by a sign--real or fictional, existent or imaginary--is an object in that technical sense.

To adhere to the distinction you made for me in the other thread, in much usage of signs, probably the majority actually, the signs have significance without denoting anything. — Metaphysician Undercover

The only signs that theoretically could signify something without denoting anything are pure icons, unembodied qualities that would only convey themselves as they are in themselves. Any sign that stands for something else denotes that other object.

For instance in "I'm going for a walk", the only object denoted is "I". — Metaphysician Undercover

On the contrary, "going for" denotes a certain kind of relation as its object, and "a walk" denotes a certain kind of activity as its object. In fact, as symbols, words and phrases typically denote general concepts like these as their objects. The syntax of the sentence is what signifies the interpretant, which is the relation among the denoted objects that the corresponding proposition conveys.

And in your example of fictional writing, there are no objects denoted. The author simply builds up images of characters without denoting any objects. — Metaphysician Undercover

If this were true, then the author could not create those "images of characters" in the first place, and we could not think or talk or write about them afterwards. Again, the sign "Hamlet" denotes the fictional character in Shakespeare's play as its object.

Then the example is irrelevant to the issue we are discussing, that "2+1" denotes the same object as "3". — Metaphysician Undercover

I have quite deliberately said nothing directly about that issue until now, because I was mainly interested in commenting on the other example that came up. Its relevance has to with the question whether "2+1" and "3" are likewise different signs that denote the same object despite signifying different interpretants. The problem, of course, is that we cannot even in principle point at something and say both "that is 2+1" and "that is 3." However, we can point at a collection of three apples and say both "that is 2+1 apples" and "that is 3 apples." Moreover, we can substitute "2+1" for "3" in any proposition without changing its truth value or in any equation without changing its result. What should we conclude from this?

You assume that fictional characters are objects, but you deny that they are real, and you deny that they are existent. How do you validate your claim that they are objects? — Metaphysician Undercover

Simple--in semeiotic, anything that is denoted by a sign is, by definition, its object. Since all thought is in signs, anything that we can think about--real or fictional, existent or imaginary--is an object in this sense.

So, to make the example relevant, we must start with the two expressions, "father of Peter Fonda", and "Henry Fonda", and you need to demonstrate how they necessarily refer to the same object, without begging the question. — Metaphysician Undercover

Good grief, I never said that they necessarily denote the same object, I only said that they actually denote the same object. That is why I kept calling this a fact. If Henry Fonda were not the father of Peter Fonda, then obviously the signs "Henry Fonda" and "the father of Peter Fonda" would not denote the same object. What I mainly wanted to do was simply point out the difference between what a sign denotes (its object) and what a sign signifies (its interpretant).

As you can see, @Meta has gotten into my head over the years. — fishfry

You had me a little worried for a while there. :wink:

Thank you for this clarification. — fishfry

You are welcome, I am glad that it was helpful. :cool:

What Peirce questions is not the LEM, but instead the applicability of it as referenced. To be sure, he calls it the "principle of the excluded middle," and in my opinion the substitution of "principle" for "law" makes all the difference. — tim wood

Indeed, I believe that his use of "principle" rather than "law" for excluded middle is very deliberate. As he wrote elsewhere, "Logic requires us, with reference to each question we have in hand, to hope some definite answer to it may be true. That hope with reference to each case as it comes up is, by a saltus [leap], stated by logicians as a law concerning all cases, namely, the law of excluded middle. This law amounts to saying that the universe has a perfect reality."

Consequently, classical logic is strictly applicable only where "a recognized universe [of discourse] is definite (so that no assertion can be both true and false of it), individual (so that any assertion is either true or false of it), and real (so that what is true or false of it is independent of any judgment of man or men, unless it be that of the creator of the universe, in case this is fictive)."

I do understand Peirce's point that the real line isn't a continuum because it's made up of individual points. — fishfry

I appreciate this and would be content to leave it at that.

How can I agree or disagree with that statement, without sharing your inner visions on the nature of the true continuum? — fishfry

I guess it comes down to the meaning of the concept of continuity. Someone immersed in modern mathematics, where the real numbers are routinely called a continuum, is understandably satisfied with that definition. Someone like Peirce who objects to finding any discrete parts whatsoever in something that is supposed to be continuous can never accept it. He was motivated primarily by logical considerations rather than mathematical ones.

Was Brouwer familiar with Peirce? — fishfry

According to a paper by Conor Mayo-Wilson, "Peirce and Brouwer seemed to have no knowledge of each other's work." However, they were indirectly linked through Lady Victoria Welby, with whom Peirce exchanged a fair amount of correspondence including some of his most important writings about semeiotic, and whose ideas about significs were later adopted by a group of Dutch thinkers that eventually included Brouwer.

Surely Peirce must have been familiar with Dedekind. — fishfry

Yes, Dedekind's name appears in a bunch of his writings, and his most fundamental disagreement with him was about the relationship between mathematics and logic. For Peirce, logic (generalized as semeiotic) depends on mathematics, as does every other positive science; while for Dedekind, mathematics is a branch of logic.

Are you saying Peirce would make sqrt(2) both the largest of the smaller set and the smallest of the larger set? — fishfry

Peirce would not talk about "sets"--or "collections," his usual term--when referring to a continuum at all. By definition, a collection consists of discrete parts, which are ontologically prior to the whole ("bottom-up"); while in a continuum, the whole is ontologically prior to the parts ("top-down").

How can one point become two points? — fishfry

Because the only points at all are the ones that we create by marking them. When we mark a line without separating it, we create one point. When we separate the line, we create two points, one at the discontinuous end of each resulting portion. When we put them back together, we have only one point again. The points are never parts of the line itself, because they are of lower dimensionality. Every part of a line is one-dimensional, but a point is dimensionless. SIA seeks to capture this with its infinitesimal segments that are long enough to have "direction" but too short to be curved.