| In this paper, we are trying to cope with three problems. The first problem is to argue that there exists expressions'intension. We construe Alston's and Wittgenstein's argument for intension in which Alston considers that the existence of expressions'intension has an order of priority in epistemology than the synonymity of them, and Wittgenstein considers that it is necessary to presuppose empirical propositions, a kind of intensional entity, in order to describe natural language's semantics. Furthermore, we justify an acknowledged supposition, that is, agent could determine the extension of a concept if the domain in question is fixed, which acts as precondition in JU Shi-er[2004]'s argument for the existence of property. At last, we draw a conclusion that those kinds of intensional entities, such as"proposition"and"property", should be accepted as ontological entities in any certain forms of life, if we admit human's ability of using a language. In order to clarify the concept of"intension"and turn our steps to the existence of expressions'intension, we introduce Frege's distinction of sense and reference. Three kinds of criticism about Frege's semantical theory are introduced, in which the arguments of Kripke and Perry don't launch a material and critical attack to the point in question. This paper discovers the puzzles in Quine's scepticism about intension: Firstly, we point out the problem in the theory of Quine's indivuduating principles and his slogan of"No Entities Without Identity"by Greimann's argument; Secondly, we refute Quine's natural epistemology and his stimulus meaning theory which assert that it is no use to presuppose expressions'intension.The second problem is to argue that Two-Dimensioned semantics is the best method by far to describe expressions'intension. In this paper, five kinds of methods used to describe expressions'intension are mentioned. Two-Dimensioned semantics is the best way among those methods because of (1)its interpretational force to semantical problems and (2)its well-satification for epistemological appeal, in which the former includes that"substitutional failure in intensional context","a coarse-grained view on intensional identity", etc., and the latter includes that"expressions'intension is given in a descriptive way or assigned ad hoc","modal intension and epistemological intension are discovered or not", etc. On the other hand, all kinds of intensional logical systems up to now are sorted according to epistemological and ontological standards. Furthermore, from formal syntax to formal semantics, three kinds of representational intensional logical systems are discussed in detail, which contribute to our understanding to different semantical model for expressions'intension, and some problems occurred in these systems are discovered. Finally, we make a choice in different intensional logic, and Zalta's technique shows its preference than others because it opens out expressions'epistemological intension adequately by introducing"encoding and exemplificating relation".The third problem is to state how to depict expressions'epistemological and modal intension with Zalta's skill. By comparing the theory of abstract objects and Two-Dimensioned semantics, we point that the limitation of Zalta's theory lies on its incapability on modal intension. It is necessary to depict modal intension of expressions for the purpose of fixing objects in discussion and investigate their counterfactual conditions, whether they are abstract objects in fictional context or ordinary object in factual context. We still focus on the same object even if it encodes (loses) a new (old) property. Finally, in order to describe both kinds of intension with Zalta's logical skill, we rectify his theory of possible world.
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