As any product, logical truth has two complementary aspects. Primarily, it refers to a class of objects with their natural properties, which are reflected in the subject and communicated to the others (that is, inside a higher-level, collective subject) in the form of objective statements that are deemed to be (objectively) true or false. On the other hand, any subject is not only passively reflecting the world, but also trying to reorganize it in some intentional action. That is, beside the image of the world, a conscious being will necessarily show some active attitude, which is related to the subjective side of any truth. Though subjective truth can also be communicated to the others in the form of apparently verifiable statements, logical judgement is here directed by different criteria, expressing subjective attitudes rather than objective properties of things. A statement will be called true or false depending on whether it properly reflects the personal position or significantly distorts it.
While objective statements are said to be "true" or "false" on themselves, subjective truth always implies a particular subject (individual or collective , real or virtual). However, this difference is not as drastic as it may seem, and as it is often presented by some politically engaged scientists proclaiming the absolute independence of science of any social bias or economic interest. People don't live in the vacuum, and any personality is a product of the current cultural environment. This means that the inner organization of the subject is essentially objective, and the subjective attitudes do not come from nothing, they are virtually explainable on the basis of the objective cultural hierarchy. In this respect, subjective truth is much wider than mere personal opinion; it is an expression of a cultural regularity, which may act sometimes as an objective law. Conversely, the world is always reflected in the subject inasmuch it is involved in people's activity, and hence any object is not only material in the universal sense of the word, but also a matter of personal interest. The very selection of the object is a subjective act, nothing to say about the angle of view and the form of reflection. Objective and subjective logic are hence opposed to each other in a relative way, as a kind of duality rather than segregation. This requires yet another level of logic pertaining to the synthesis of the two poles; in this "productive" logic, truth is objective in the sense of a social necessity, while it is also subjective as a motive for individual activity.
However intricate, this hierarchical structure of truth has long since penetrated the ordinary language. We readily attach the labels 'true' and 'false' to anything we learn, combining all the three levels in a situational manner. The assessment of truth/falsity may refer to a true observation, true person, or true something (which may be a thing, a person, or both). In the latter sense, the word 'real' is also used. Within objective logic, the statement "They always lie, even when they're telling truth" is a contradiction; there is no conceptual problem for a hierarchical vision, admitting that somebody may intentionally lie, while telling truth in the objective sense. True lie is a quite normal occurrence in any culture, giving birth to the ambiguity of the phrase, both expressive and impressive.
Objective logic is the "logic of things"; one does not need to be too smart to guess that subjective logic is the logic of the subject. Using objective logic, we organize our "workbench"; subjective logic organizes our preferences, the selection of instruments and tools. We need both in every particular activity. To be logical, both in the objective and subjective sense, one needs consistency and integrity of action (including thought and feelings). Both kinds of logic apply to anything at all, they are equally universal. And both can be either meaningful, or formal.
For instance, the traditional idea of rationality includes some kind of "logical derivation", grounding our assumptions in the objective necessity. The stability of inter-object relations is due to the character of cultural development in a specific historical epoch: for quite a while, the humanity has to assimilate the already achieved modes of production, gradually accumulating experience and sound out the boundaries of applicability; then a qualitative leap puts us in a different cultural context, which also demands revolutionary changes in our formal schemes (from mere reformulation to an entirely new paradigm). Similarly, during the periods of relative stability, subjective logic becomes a kind of common sense, tradition, prejudice; conscious interference will break this formality to regain the universal flexibility of reason, in order to cope with the next (economic, social, or cultural) revolution; subjective formality then gives way to a creative approach, with its own logic. When the hierarchy of the human activity undergoes a revolutionary change, the very distinction between the object and the subject may need reassessment; in this way, objective and subjective logic penetrate each other and give birth to a new structure of logicality in general.