Your concept of science seems too narrow. It encompasses not only the empirical study of physical objects, but also any other form of collaborative human activity that investigates the truth about reality. Mathematics, phenomenology, esthetics, ethics, logic, and metaphysics are all sciences in this sense, along with the physical and psychical sciences. Ascertaining meaning is a matter of retroduction, deduction, and induction just as much as anything else that we can come to know.

Then I can safely disregard anything you say about principles, since they do not exist and are thus irrelevant. — darthbarracuda

You believe that nothing is real unless it exists - i.e., that there are only material/efficient causes and brute facts?

Your concept of logic seems too narrow. It encompasses not only deduction (explication), but also retroduction (conjecture) and induction (evaluation). Intuition (or instinct) and creativity are essential to retroduction, the formulation of explanatory hypotheses; it is the only way that new ideas are generated. We then employ deduction to work out the necessary consequences of each hypothesis, and induction to test experimentally whether those outcomes indeed occur under the appropriate conditions.

So we have to go back to the principles which underlie the application of the mathematics to determine why the very successful mathematics produces an unacceptable model. — Metaphysician Undercover

Right, it is a matter of how we are mapping the (ideal) diagram to the (actual) universe - both in formulating the model, along with its accompanying transformation rules, and in interpreting the results. In other words, like so much of philosophy, it comes down to our assumptions.

I'm an anti-realist on mathematics. — Terrapin Station

Yes, that is what I would have guessed. Just curious, then - how do you explain the element of surprise, the fact that there are genuine discoveries in mathematics?

As I suspected - that is not how either of those words is normally defined, especially within philosophy.

And is understanding itself not useful? Don't we become better people the more we understand? — Agustino

Not necessarily, on both counts.

I will ask again--how are you defining and distinguishing "intelligible" from "intelligent" in this thread?

You deny that we can observe (through experimentation) that force is directly proportional to both mass and acceleration? How else have we ascertained that the equation is an accurate representation of reality?

As for mathematics being observational, I suggest looking into what Peirce called theorematic (as opposed to corollarial) reasoning.

The problem I see with this is that we're not mapping F=ma to F equaling m times a in experience ... — Terrapin Station

We are mapping F=ma to the real relations that we observe in experience among force, mass, and acceleration.

... mathematics isn't an empirical science. — Terrapin Station

This is true, in the sense that mathematics only pertains to ideal states of things. It is false, in the sense that mathematics is an observational science; we manipulate diagrams in accordance with transformation rules and observe what other relations become apparent that were not part of the diagram's original construction.

Since we know that the essence of the object is separable through abstraction, there is nothing inconsistent, nonsensical, or incoherent, about the proposition that the essence of the object has existence separate from the object prior to the object's existence. — Metaphysician Undercover

I still suggest that using the term "existence" in these two different senses is counterproductive. I would say, instead, that the essence of the object has being separate from the object prior to the object's existence--i.e., esse in futuro. This also avoids the objection that the essence of the object must itself be an (existing) object; the mode of its (real) being is not actual, it is potential.

Of course, for someone who denies the reality of abstractions, this particular argument will carry no weight anyway.

F=ma is a diagrammatic representation that embodies the relations among force, mass, and acceleration--all of which are concepts that we have defined in order to facilitate this mapping of an idealized state of things to something in experience. The transformation rules are such that we can rewrite the equation as a=F/m or m=F/a. Analysis in this case is merely a matter of finding the third value when we only know two of them initially.

You need to explain why universals have to exist ... — darthbarracuda

The terminological point that I have been trying to make is that universals do not have to exist in order to be real. It is nominalism that insists on limiting reality to existence.

As I posted in another thread: The hierarchy of Being involves an infinite continuum (Thirdness) of indefinite possibilities (Firstness), only some of which are actualized as determinate individuals (Secondness). The sequence of events in each case consists of spontaneity (Firstness) followed by reaction (Secondness) and then habit-taking (Thirdness). The evolution of states is from complete chaos (Firstness) in the infinite past, through this very process (Thirdness) at any assignable time, to complete regularity (Secondness) in the infinite future.

Saying that all mathematical models would be examples of necessary reasoning seems dubious to me. — Terrapin Station

To clarify--constructing the model requires creativity and imagination (retroduction), but processing the model is entirely a matter of necessary reasoning (deduction). Once the model is created, the results are inevitable, given the transformation rules that govern the analysis.

When else is intelligibility useful? — Agustino

How about when it facilitates understanding? In any case, on what basis is "usefulness" the only criterion for intelligibility (or anything else) to be valuable? How are you defining and distinguishing "intelligible" from "intelligent" in this thread?

What is the source for that being what mathematical models are? — Terrapin Station

As you might have guessed, it is something that I picked up from Peirce. He favorably cited his father Benjamin's definition of mathematics as "the science that reasons necessarily," and added that necessary reasoning only strictly applies to ideal states of things. A diagram is an icon that embodies the significant relations among the parts of its object; both geometrical figures and algebraic equations qualify.

Mathematical models on their own, sans ontological commitments, are taken to be sufficient for explanatory scientific theories. — Terrapin Station

Every mathematical model is a diagrammatic representation of an ideal state of things. As such, any ontological commitments are manifested in the mapping of the model - as well as the accompanying rules for its analytical transformation - to something in experience. The model itself embodies only the relations that the one doing the modeling has judged to be significant, and ignores everything else. The analysis of it is intended to simulate contingent events with necessary reasoning, so its "accuracy" is limited by that of the underlying assumptions.

Further motivation to 'read more Pierce'. — Wayfarer

When I first started getting acquainted with Peirce's thought, several people warned me that it would take a while--and I have found that to be very much the case. If you would like to read his own words, I think that the best place to start is with the two volumes of The Essential Peirce. If you prefer a fairly comprehensive introduction written by someone else, I suggest The Continuity of Peirce's Thought by Kelly Parker. If you are looking for something shorter that focuses primarily on metaphysics, I recommend Charles Peirce's Guess at the Riddle by John K. Sheriff.

The being can't for example just create some another being and try to pass it off as autonomous and pretend that it doesn't know or isn't responsible for what the new being is going to do ... — zookeeper

The OP stipulated that we are talking about an omnipotent being. It sounds like you are suggesting that there is something that such a being cannot do.

For how could anything fall outside the causal control of an omnipotent being? — lambda

What if the omnipotent being chooses not to exercise complete causal control over everything? Surely that power would be among those that such a being would possess.

It looks like Calvinism is right after all. — lambda

Calvinism does not strictly entail theological determinism in the global sense that you describe. It simply holds that God has predestined everyone either to salvation or to damnation. Some Calvinists do go a step farther and attribute everything that happens to the sovereignty of God, but not all.

Peirce called himself an "extreme scholastic realist" and eventually developed a cosmology that, at least from where I sit, explains both similarity and difference. The hierarchy of Being involves an infinite continuum (Thirdness) of indefinite possibilities (Firstness), only some of which are actualized as determinate individuals (Secondness). The sequence of events in each case consists of spontaneity (Firstness) followed by reaction (Secondness) and then habit-taking (Thirdness). The evolution of states is from complete chaos (Firstness) in the infinite past, through this very process (Thirdness) at any assignable time, to complete regularity (Secondness) in the infinite future.

When we talk about whether something is conceivable, we do not usually mean whether a particular person is capable of conceiving it at a particular time; we usually mean whether any person could ever be capable of conceiving it.

I agree and I probably only diverge in that I equate being with existence and that I do not think being exhausts reality. I would say there is also spirit ... — John

Are you suggesting that spirit is somehow not being? Peirce characterized spirit as "disembodied mind," and hence Thirdness; it is real and has being, but (strictly speaking) does not exist.

... and that it is on account of spirit that there can be final and formal causation, and beauty, goodness and truth as well. — John

Peirce held that final and formal causation are also manifestations of Thirdness, while beauty, goodness, and truth are the proper ends of feeling (Firstness), action (Secondness), and thought (Thirdness), respectively; i.e., the subject matter of the normative sciences, which are esthetics, ethics, and logic (semeiotic).

... I would not claim such things are not real. I just want to say that they do not "have being" or exist ... — John

Late in his life (1908), Peirce wrote about "three Universes of Experience." The first "comprises all mere Ideas," everything "whose Being consists in its mere capacity for getting fully represented, regardless of any person's faculty or impotence to represent it," such that "their Being consists in mere capability of getting thought, not in anybody's Actually thinking them." The second "is that of the Brute Actuality of things and facts," whose "Being consists in reactions against Brute forces." The third "comprises everything whose being consists in active power to establish connections between different objects ... its power of serving as intermediary between its Object and a Mind." Elsewhere he also characterized them as (1) ideal possibilities, (2) Matter and physical facts, and (3) Mind and minds, along with habits, laws, and (especially) continua.

For Peirce, the constituents of all three Universes are Real--"having Properties, i.e. characters sufficing to identify their subject, and possessing these whether they be anywise attributed to it by any single man or group of men, or not"--but only those in the second Universe exist. This is why the particular article that I am quoting here described an argument for the Reality of God--Ens necessarium, creator of all three Universes--rather than the existence of God. I continue to find this terminological distinction helpful in these kinds of discussions.

Peirce confined existence to Secondness/particularity/Brute Actuality. Therefore, strictly speaking, Firstness/possibility/Ideas and Thirdness/generality/Mind indeed only exist in their instantiations. However, they nevertheless have Being--they are real--apart from those instantiations. Within our existing universe, all three Categories are involved in anything and everything to varying degrees; but in the cosmological sense, Thirdness is primordial because actualities are determinate individuals in a continuum of indeterminate potentiality.

You are not adhering to the definitions that I am using, which come from Peirce and are well-established in semiotics, so we are just talking past each other. In particular, you seem to have a very narrow concept of representation. If "the portrait signifies primarily by resemblance," then it represents its object by resemblance--it is an icon. The weather vane represents (i.e., indicates) the direction of the wind, regardless of whether anyone interprets it as doing so--it is an index. If the photo "presents certain features which are recognizable as the face," then it represents the face--iconically due to the resemblance, and indexically due to the causal process that placed the image on the film. Now, just about every sign has all three aspects--iconic, indexical, and symbolic; but I am focusing on the predominant relation of the sign to its object.

A portrait does not represent the person whom it portrays (resemblance)? A weather vane does not represent the direction of the wind (connection)? You do not recognize a familiar face in a photograph (both)?

I have in mind the idea that different statements--in different languages, even--can express the same proposition. I can even express a proposition without using words at all--e.g., holding out a gift-wrapped box is not a statement, but it can indicate (in a certain context) that I am giving you a present.

Fine, we are back to words and their combinations being symbols that represent their objects by arbitrary conventions. Stipulating that we are using contemporary English vocabulary and grammar, the proposition that the moon is made of green cheese cannot represent the fact that Abraham Lincoln was the 16th President of the United States.

Is this a digression, or are you trying to make a relevant point?

Wait a minute--how do you figure that there are any limits on what a proposition is representing, so that we can say that a proposition isn't representing something? — Terrapin Station

Consider the proposition that the moon is made of green cheese. Can we say that this proposition is representing the fact that Abraham Lincoln was the 16th President of the United States? If not, then evidently there are some limits on what a proposition is representing.

The conditional proposition--that if I let go of the rock, then it will fall--is representing the fact that if I let go of the rock, then it will fall. Gravitational attraction is an explanation of this fact, not the fact itself--and it is a habit/necessity/law/regularity, not a mere brute actuality. Furthermore, the conditional proposition is true regardless of whether I ever actually let go of the rock, and would still be true even if no one ever expressed it as a statement.

I am not sure that it makes any sense to talk about "unstated statements." However, a declarative statement expresses a proposition, and a true proposition represents an objective fact, regardless of whether anyone ever expresses that proposition as a declarative statement. Is that what you have in mind?

Yet what else could make a statement justified if not that it is true in virtue of a truthmaker? — darthbarracuda

Given the standard definition of knowledge as justified true belief, there is evidently a distinction between justification and truth; otherwise, one or the other would be redundant. Justification is what warrants someone holding a belief, while truth is what makes that belief count as knowledge. We can be justified in holding a belief even when unaware of its truthmaker(s). We can also be justified (but mistaken) in holding a belief that is not true, and thus has no truthmaker.

So "P" in the t sentence isn't a proposition in your opinion? — Terrapin Station

My understanding is that it is a sentence, not a proposition; which is presumably why this is called the semantic theory of truth, and is not simply (or non-controversially) categorized under either correspondence or deflationary theories.

It's representing gravitational attraction in that case, which is actual. — Terrapin Station

Gravitational attraction occurs whether the antecedent obtains or not, so that cannot be what the conditional proposition is representing. It says what would happen, not why it would happen.

I wouldn't say that the conditional "maps" to a conditional that is actual in the world. — Terrapin Station

Neither would I; rather, I would say that it maps to a habit/necessity/law/regularity that is real, regardless of whether it is actualized. Am I right to perceive that you see no meaningful distinction between reality and existence?

I don't in general buy that the non-linguistic world is structured like language. — Terrapin Station

The idea that I am entertaining is more along the lines that there is an alignment between reality and logic; how we think, in some sense and to some degree, reflects how the universe is--which is why we are able to learn about it at all.

No on my view. — Terrapin Station

That is what I anticipated.

Yes on my view, but it's not representing something (real) that's not actualized. — Terrapin Station

Then what object--if not a real habit, necessity, law, or regularity--is that conditional proposition representing? Given that the antecedent never obtains, it cannot be something actual.

Habits, necessities, laws, regularities--take your pick. Are they real apart from their instantiations? Can a conditional proposition--if I let go of this rock, then it would fall to the ground--represent an objective fact, even if the antecedent is never actualized?

... what is your recommendation ... — Terrapin Station

I just tried to clarify what I meant. A symbol represents its object only because it will be interpreted as doing so, not because of any resemblance or direct connection.

Nominalism is contrasted with realism if we're scholastics talking about universals. — Terrapin Station

Or if we are PF participants talking about whether possibilities and habits are real, not just existents; but that is another thread. I am not sure what we are talking about in this one now.

"Lots of people" make it a convention. Just someone, and not lots of people, make it not a convention. — Terrapin Station

You are missing the point. I am looking at HOW a particular sign represents its object. There are only three options--by resemblance (icon), by direct connection (index), or by convention (symbol). If the word "convention" is what bothers you, then just substitute the notion that a symbol represents its object only because it will be interpreted as doing so. Suppose I designate "glutchski" as a made-up word that represents the moon in my private thoughts. It is a symbol, because I will interpret it as representing the moon, even if no one else ever does.

If your claim that the moon is independent of us doesn't correspond to an objective fact then it isn't realism. — Michael

Of course not--TS has made it quite clear in this and other threads that he is not a realist, he is a nominalist. Again, the usual caveats about labels are hereby acknowledged.