When investigating meaning Frege decided to approach the problem by first determining the properties that meaning necessarily has, whatever it is, and then to use those properties to pin down exactly what meaning was. This method is itself an excellent idea, since it helps separate the essential nature of meanings from our possibly confused intuitions about them . The necessary properties, according to Frege, are that meaning must be universal (the same for everyone), objective (independent of people), and able to be communicated. Again, I cannot find fault with the requirements that something which is to play the role of meaning must meet (although I might want to add a few more). From these Frege concluded that meaning is something that has an independent existence , that it is external to our minds, that we grasp it by coming into a cognitive relation with it, and that multiple people can come into a cognitive relation with the same meaning. It is this conclusion that I would dispute.
Before I examine meaning directly let me first address something simpler, which is in some ways similar to it, color. Like meaning, we consider color to be something that is universal and objective. The color green is green to everybody, although colorblind people cannot see green it is still green, even to them, they simply can’t perceive it, and green is green independently of what people think about it, even if people were to disappear or go blind green things would still be green. However, from these properties we do not conclude that green is something above and beyond the objects, green is simply a way of describing a similarity shared by various objects (specifically similar reflected light). Of course, some philosophers once did think that green was something extra above the object itself (ex: Aristotle), but this view was eventually discarded because there was no role for this extra “greenness” to play, since the similarities that make two different objects both green can be explained by purely physical properties, without any need for “greenness” or a relation to “greenness” to make them green. 
My argument, then, is that Frege is making a mistake similar to that made by philosophers who thought that green somehow existed independently of green things and was related to them. Certainly the properties that meaning must possess, universality, objectivity, and the ability to be communicated, don’t necessitate that it has an independent existence; like color it might be a description of a certain kind of similarity. What would this similarity consist in? Well, we know that the mind has the ability to represent objects and states of affairs, so one possibility is that meaning is simply a similarity between what is being represented by different minds , or in the same mind at different times. If we define meaning in this way it retains all of the necessary properties that were identified earlier. It is universal because by definition it ultimately reduces to representing things in the same way, if two people were representing different things (or the same thing in dissimilar ways) they would no longer be meaning the same thing. It is objective because a similarity in representational content, whether or not we recognize the existence of such a similarity, is an objective fact about what is going on in the mind. And, finally, it can be communicated, since it is possible to trigger a representation (as part of a specific idea or thought) via symbols which themselves have no primary representational powers .
Now the possibility that meaning can be defined in terms of similarity between minds doesn’t rule out the possibility that meaning really is some additional object that we stand in a cognitive relation to, as Frege thought. However, the fact that it can be defined in this way while still meeting Frege’s criteria show that the criteria themselves are not enough to force us to this conclusion. And defining meaning as some kind of similarity between minds certainly seems like the simpler solution, since we aren’t forced to postulate the existence of new kinds of objects, or resolve the problem of epiphenomenalism facing externalist accounts of the mind.
1. In fact I took a similar approach to knowledge here.
2. In other words: that meaning is like a physical object in that it does not depend on anything else to exist.
3. It is this distinction, between a similarity between objects and something existing in addition to those objects, that makes me hate the word transcendental. Some authors employ it to mean one, some the other, some both, and some use it to mean the phenomenological method.
4. Strictly speaking the relation between the mind and an object that it is representing is an external one (see here), meaning that that it can’t properly said to be part of the mind, and if meaning is to be part of the mind it can’t be meaning either. What I really mean by representation, then, is intending, which properly construed is part of the mind. What is intended can be described in terms of what experiences the intender would consider to be the thing that they are intending (satisfaction conditions). Besides being something that can be defined internally, and thus properly speaking part of the mind, intention also has the advantage of being able to be directed at objects that don’t exist, which is essential if we are to be able to connect it to meaning, since we can mean things that don’t, or can’t, exist. So why didn’t I say intend in the main text? Because this explanation was too long to fit.
5. If we say that they represent things it is only because they invoke representations in people, without people they would be deprived of representational powers, while people have the ability to represent an object which is dependant only on them and the object.