Any object has a structure of its own according to the field of knowledge. For instance, in a field of grammar (linguistic), a simple sentence  has a basic structure: subjec and predicate, being "agreetment in number" the structure rule that governs it. Structure has to be with the coherence among parts or features of the objects.

What is meant by sructure?  A chair has a structure, body, limbs, organs have structures, atoms/molecules have structures. Geometrical shapes can be visualized by the mind, are found in mathematics, in the living and inert, in nature.  You also mention the 'structure of a phenomomenon.' Do you mean order?

@Marvin Kirsh

That's the first problem. There are many statements, forming part of the theoretical body of particular sciencies, relating "structure" with several objects, different by nature. Then what "structure" is , considering that different kinds of objects have that "property".

The next question is, how to find structure. Particular sciences have their own methods (or at least, many of them, particularly natural sciences and formal sciences). Is there any general method for obtaining structure?

And, I suppose, structure implies some kind of order, "being ordered" should be one of properties of structure.

I would define structure as relationship that exists between objects. Therefore structure does not appear to be a property of an object, rather it links objects in a more or less ordered  / fuzzy , simple / complex, singular / common, ..,  way. 

To determine the existence of structure you need to be clear about your point of view, since objects can be structured in many ways. An individual can be a father, a teacher, a champion sprinter, i.e. embedded in ( possibly infinitely) many structures. 

If you can quantify objects in respect of specific properties, then you can discover potential structures using factor or cluster analyses. Always assuming that an objective observation of the real world is possible. 

If not, you need to rely on "softer ' methods, such as hermeneutics. 

And yes, I like your question. 

@Leopold A scientist would consider an object to be something that possesses physical features. DNA is determined to have structure = helix. I do not think science would consider the individual chemical elements to be objects, i.e. elements that compose DNA in the example above.

According to the definition posted:

"I would define structure as relationship that exists between objects."

Do you then consider "structure" to refer simultaneously to the 'physical' and to 'motions of the physical', usually titled with a 'function' in the sense of possessing a role according to the way a world structure-(excuse the pun) might be assembled rationally/reflectively by the intellect at the first perspective.

@Marvin Perhaps I should have pointed out first that I am not a natural scientist. My field is the science of education and I am quite aware that some natural scientists do not regard Humanities as 'real' science (Popper for one, although he softened his stance later).

For the sake of argument, let's allow that I am a scientist. In 'my science' objects can be physical, but mostly they are not. As it happens right now I am working on profiling competencies, types of competencies, to be exact. In the network of competencies, that are relevant (to different degrees) for learners as well as for organizations, I regard each competency as an object in that network. At the same time I am trying to profile attitudes towards learning - again each attitude is an object. I am believe 'phenomenon' in the original question refers to objects such as competencies, etc.

In order to be able to map attitude profiles against competency profiles (regarded as networks of objects) I need to discover the structures of the network - it is my underlying assumption, that such structures exist and I 'only' need to unearth them. One of the statistical methods I employ for this purpose is the cluster analysis.

To your question whether I regard 'structure" simultaneously as 'physical'  and  'motions of the physical'. Let's assume that objects like competency, disposition or attitude actually exist in the real world (radical constructivists would disagree), then - with a bit of imagination - we indeed have 'physical' objects. However, unlike most objects / elements of the natural sciences, these objects are not even potentially observable. We therefore need to define constructs of each 'physical' object, operationalized through observable indicators. The observable indicators have a structure (which makes them form the construct), and the structure has properties (such as load factors and causal relationships).  It is the latter that the mind can 'assemble rationally / reflectively' (if I get you correct).  

Following your thoughts - as I understand them - there are indeed inherently two aspects of any 'structure': the physical (if only in an abstract form) and that which gives the structure its very specific nature.

This is why I find the original question pertinent: 'understanding what is structure' - the physical aspect. 'how to find it' - by observing its nature (properties in a wider sense).

Any object has a structure of its own according to the field of knowledge. For instance, in a field of grammar (linguistic), a simple sentence  has a basic structure: subjec and predicate, being "agreetment in number" the structure rule that governs it. Structure has to be with the coherence among parts or features of the objects.

@Luisa "Any object has a structure of its own".

Agreed. In the sentence "I go" the constituent parts (subject, predicate) are connected following a structure, and they (the parts) are objects themselves.

To say the sentence has a structure is the same as saying its parts follow a structure (the latter being the terminology I am using above). 

A high general, wide-ranging  question like this can be answered just in terms of a high general, wide-ranging approach: topology. Indeed, topology talks about the most general features of mathematical, physical and biological systems.  

Good question dear Rey,

A structure is a built up physical,  abstract system or an existing natural phenomena. First, human made objects (built structures) are knowable through their manuals, information that tell what they are and how they function for common users and for experts it is more than that. We can know them using scientific methods  of how they are made and augment/modify them to be better than what they are. Scientific structures are knowable only through the language they are built, starting from the fundamental or basic building axioms, relations defined and substructures created, until we arrive at what indeed the structures are. Natural phenomena, as a natural structures which we can not know exactly what they are, but approximately what they are, as we can not know all natural parameters, visible or invisible, which are reasons for the structures to be formed, exist and its behaviors are, are studied and knowable through mathematics, physics and other natural sciences. Mathematics describes behaviors of natural phenomena and physics and other sciences validate through empirical testings. Mathematics is the sensor and analytical/rational cognition of nature as we presume nature is mathematical. Galileo said: " The laws of nature are written by the hands of God using the language of mathematics" .