This is taken from Frege's article titled ‘On Sense and Reference’
Now languages have the fault of containing certain expressions which fail to designate an object (although grammatical form seems to qualify them for that purpose) . . .Comment: Some words refer to a concept, conceived by a human, however they are surreptitiously used in a syntactical grammar AS IF they refer to objects. Understanding HOW to resolve this distinction is of the utmost important when processing communication ESPECIALLY in a study of fundamental physics. Understanding this distinction will also help lead to an ultimate appreciation of objects and their essential role in conception.
Continuing Frege says:
So language brands a concept as an object, since the only way it can fit the designation for a concept into its grammatical structure is as a proper name. But in so doing, strictly speaking it falsifies matters. (Gottlob Frege, 1892a, 168-69)
Comment: I would not say it falsifies matters, since validation/verification of statements is another matter that is subjectively performed by humans. I would say in doing so renders that expression irrational, contradictory or at best figurative. Now we do this all the time and it is fine, but in a rigorous intellectual setting such as physics, these matters must be clarified for the sake of communication, sanity, consistency, honesty, and helping to produce brilliant, rational assumptions, theories, conclusions, etc.
Here are some quotes from a study on Frege:
From Philosophy of Language and Logical Theory by Khatchadourian (p.309-11)
A concept-word, according to Frege, is predicative; it is a possible grammatical predicate of a range of otherwise different sentences. To predicate a concept-word of a grammatical subject is to relate a concept to a logical subject, i.e. to an object. Another way of saying this is that to predicate a concept of an object is to state that the object falls under the concept. The predicative character of concepts is what Frege calls “incompleteness” of concepts. In terms of this the difference between a concept and an object is that an object falls under a concept but that the converse is impossible. “An equation is reversible; an object’s falling under a concept is irreversible
Comment: So concepts are based in objects. Frege never figured out why: objects have form, concepts lack form; they are relations between two or more objects worked out in thought. Concepts are based on objects, but objects are not based on concepts. An object has the referent of Form independent of our conception or even perception. The referent of Form is inseparable from an object. So for example the form of that object across the street named woman does not rely on our seeing it or on our naming it ‘woman’. Now this might sound trite or petty semantics but I assure everyone that understanding how to resolve the ontology of word referent in all contexts can help enable one to accomplish immense intellectual tasks for example:
1. Ability to discern and interpret figures of speech, and perhaps learning how to conceive of one’s own figures
2. Ability to interpret obscure and difficult texts, etc.
3. Ability to understand the roots of all languages. All languages have their roots in objects.
4. Identifying intellectual charlatans who make millions even billions off of concepts that refer to nothing in reality
5. Enabling one to see through intellectual hogwash and acquire a sort of natural wisdom.
6. Initiating intellectual revolutions in self and others
7. Appreciating the great value of existing objects and understanding that a dynamic concept such as love will never happen or even be conceived without that object named woman who grew up down the road from you. Thus one would imagine that this woman is very valuable and should be treated with great care and dignity. Understanding that without the two objects named man and woman and what they have the ability to do continues the human family. Understanding that objects such as food, clothes, water, house are more valuable than concepts such as money.
8. Understanding the great darkness and devolution of Western Civilization as it currently operates. Many are enslaved to, burdened and lost in the concepts they worked.
9. Understand how people manipulate each other via use of concepts.
10. Tracing back to the fundamental object that underlies and connects all existing atoms of the Universe and understanding that this fundamental object cannot possibly rely on a concept called space for its form.
11. Figuring out devishly difficult problems in physics such as what object may mediate gravity and light between stars and planet, how atoms work, what electron, proton, and neutron refer to, what sort of assumptions can we make about the fundamental entity, explaining fundamental interactions, exposing the wave-particle duality, balancing the continuity of all objects with their discontinuity, and so on.
12. Enable one to attain freedom of thought.
Continuing with Frege Study:
It seems to follow from this that “completing” a concept can be regarded as stating that a given object falls or does not fall under the concept. We “complete” ‘() conquered Gaul’ by ‘Julius Caesar’, when we state that Julius Caesar falls under the concept conquered Gaul, i.e. when we make the statement ‘Julius Caesar conquered Gaul’.
Comment. We base the concept ‘conquered Gaul’ on Julius Caesar. Without the referent of Julius Caesar the conquering of Gaul would have never happened. Frege took a sort of . . . how do I want to say this . . . backwards approach to solving these problems.
. . .
Concepts are attributes. Hence what we have said about the “incompleteness” of concepts, put in terms of this notion, is that attributes are “incomplete” in isolation from objects. Another way of saying this is that attributes, in order to be attributes at all, have to be attributes of objects. An attribute is “completed” when it is related to an object, is thought of as attributed to the object [objects precede concepts]. Relations [also concepts], which are in a similar position, are functions with two arguments, i.e. are doubly “incomplete”, and so require two objects to be “completed”. Speaking about concepts Frege says:
"It is clear that a concept cannot be represented independently as an object can but that it can occur only in combination. One can say that a concept can be distinguished out of it. All apparent contradictions which one can come upon here result from treating a concept as an object, contrary to its incomplete nature. (Uber die Grundlagen der Geometrie)"
Black says that this suggests that Frege’s contention that functions (and so concepts) are “incomplete” is that “it is logically impossible to make a function the subject of an assertion” (p. 246).
Comment: Obviously attributes and relations lack form and cannot possibly exist. Attributes and relations refer to our thoughts about objects. Attribute refers to a comparison of objects. What does this thing have or not have in comparison to that thing. What can this thing do that another cannot do.
So, concepts refer to a relation between two or more objects worked out by the brain. A concept is 'incomplete' without a minimum of at least two objects since one of those objects is the man conceiving the relation or two neurons consummating the relation in the brain of the man.
Frege began to understand the hierarchical relation between objects and concepts. Objects precede concepts. Without objects there would be no events (moving relations, syn: phenomena, happening, etc), no perceptions completed by sense organs of humans, animals and possibly plant, no conceptions completed by the brain, no verbs, etc. Verbs refer to what we think objects do. The woman sings . . . stars illumine and gravitate. How they do this is a matter of explanation and we may have to suppose an unperceivable object such as air or invisible mediators so as to explain the action. But it is contradictory to make a verb or a grammatical function the subject of a sentence because then it is treated as an object. Verbs, attributes, or relations CANNOT perform actions or reactions. Objects perform causal relations and undergo change effects via objects and this makes our conception of verbs possible and it is rational to acknowledge this order.
With objects all we can possibly do is name them, assume them, draw them and explain how they work in relation to other objects. Naming refers to a dynamic concept completed by a human and can be traced directly to the object that is named (to that which has Form). We also have the tricky ability to perform the work of naming our conceptions. We name our brain works, to organize, develop and stimulate our brains and also so as to communicate directly with other objects such as humans and animals. Naming concepts modifies objects, describes them, etc. This name can indirectly trace back to the objects of our brains (atoms, electrons, neurons, connectors, etc.) performing causal relations and undergoing change effects in the referred concept or to objects of our environment remembered and used in the conception. The name of our conception serves as a placeholder for the objects of our environment we conceived in a relation via our sensory organ or the objects of our brain performing the work called conception and serves to modify, describe, explain the objects. So we perceive water molecules, remember their locations, think and name that thought wave. Wave is what an object does. Wave does not refer to an object. We can trace back wave to objects even if these objects are no longer perceivable or even unperceivable.
If we conceive an abstract concept such as Universe then we can trace back that abstraction to a nest of all existing objects and the static separation we conceived (space). If we do not at least make note of this, then we may begin to think that our conceptions literally have form and perform causal relations and undergo change effects when clearly this is impossible because our conceptions are already the objects of our brains performing causal relations and undergoing change effects. And bye the bye, we are always conceiving. So naming our conception is sort of a convenient illusion to stimulate our brains and communicate. It is the goal of intellectual life to master this stimulation and not become a slave to this work or use this work to deceive others, lord it over others, or swindle others.
But the reverse is impossible. An object cannot possibly refer to or resolve to a concept.
Our intellectual activities better end on objects that have forms and hopefully exist. In a strict intellectual environment objects should never be used as a concept or vice versa: Concepts should not be treated as objects. When all is said and done, two or more objects induce concepts or make concepts possible. Frege took a sort of negative approach and never completely solved the problem because he failed to understand that Form resolves the ontology of the word referent (does the nominal referent have Form? Yes or No???) Form is the most important name in all philosophy. It is in a category all its own. The Sun, Moon, Stars, atoms, the fundamental object underlying all atoms and the woman or man across the street all had their unique Form and performed their actions before you saw them, remembered them or thought about them.
Frege also wrote an article "On Concept and Object" (1892a) where he struggles with the contradiction that "the concept horse is not a concept". Had he known how to resolve the ontology of the word referent he would have solved some of his own problems.
All names, first and foremost refer to conceptions, verbs, or brain-works performed by a human. Its what we do! These either directly refer to an Object (that which has Form) or indirectly to two or more objects embodied by the brain in a relation with the aim of understanding, communication, praxis, organization, etc, in other words Concept.
Syntax follows this rational order, however for whatever reason, because we are free, i.e. not bound by artificial laws of syntax or of logic, because we are creative, or ? we break these laws all the time and switch the order treating referred concepts AS IF they were objects. Thus we need to parse sentences and discern communication so as to make sense of what the author meant to convey. In other words we resolve the context. If the author is confused we should be able to figure this out rather quickly by using these conceptual tools at our disposal.
From object, form, and concept we can graduate to exist. Exist refers to an object that stands out. Exist implies three dimensions (length, width, height) however these are measurements and whether or not an object exists has nothing to do with our act of measuring. The Sun had Form and existed before any human came along to observe it and measure it. Another possible definition of exist is that which has Form and Location. With this enlightened understanding we can clearly see that 1D, 2D, 4D objects of geometry cannot possibly exist or be used in assumptions, explanations and conclusions in physics. Geometry is a nihilistic religion.
Concept lacks Form and so is automatically disqualified from existence. This does not entail that Concept does not HAPPEN, however these dynamic concepts must ALWAYS be performed or worked by objects that exist.