The logic-linguistic approach to verisimilitude
Proponents of verisimilitude have argued that all existing scientific theories are false but some, namely those with fewer false consequences than true ones, are closer to the truth than others.
So the story goes: a theory is closer to the truth than another theory if it has more true consequences and fewer false ones than all of its other competitors.
Nearly all of the definitions of verisimilitude come with a formal metric for calculating the distance a theory and its content from the truth. The so-called distance is measured by how many statements of the theory are false in contrast with other theories and their content. If theory A, for example, has more true consequences and fewer false consequences, than theory B, then theory A is said to be closer to the truth than theory B.
All of the theories of versimilitude fail. By that I mean that the measuring device that one uses to calculate the distance any given theory is from the truth doesn't actually measure what it sets out to measure. Notice that in the example given above, it is a measurement that contrasts the two theories from one another, rather than from the theory to the truth. In the example, we measured the number of true and false consequences in theories A and B. The one with fewer false consequences, and, thus, more true consequences, was deemed to be closer to the truth. However, it should be noted that the measurement had little to do with the theory's distance from truth.
There are other reasons why accounts of verisimilitude fail. Why do they fail? The formality of verisimilitude involves a distance metric comparing two or more sets of sentences or sets of structures. The distance metric, however, is a relativized measurement from one theory or one model to another. The accuracy of the measurement depends on whether the set contains propositions that have been well-confirmed (this is a virtue of the verisimilitude debate).
The formalities of verisimilitude measurements fail to capture a normative or evaluative aspect of truthlikeness. The distance between two points does not reveal whether the distance itself is a 'reasonable' distance, a 'long' distance, a 'short' distance, etc., because these evaluative notions depend on lots of factors.
For example, think of travelling between two US cities, Salt Lake City and Denver. Is the distance between the two cities reasonable? It is no doubt that the distance between the two cities is more reasonable than, say, the distance between Juneau, Alaska and Okeechobee, Florida. What accounts for the reasonableness of travel between Salt Lake City and Denver is the relative overall geographic distances between the four cities. It is a shorter distance between Salt Lake City and Denver than it is between Juneau and Okeechobee.
What we use to measure the reasonableness of travel between the two cities matters for our assessment. Think of travel by automobile. Travelling between Salt Lake City and Denver by automobile is 'reasonable' because the total time it takes to go from one city to the other by car is about 6 hours. But, if we had to walk from Salt Lake City to Denver, then the distance would not be 'reasonable'. Walking would take a few days. Despite that the geographic distance is exactly the same between the two cities, taking one form of transportation, a car, over another, walking, matters for how reasonable the distance is between the two cities. Measurement can tell us about the physical distance between the two cities, but it does not convey anything about whether the distance is 'reasonable'.
The distance between Salt Lake and Denver doesn't change just in case you're walking or driving (It would if you were flying). Formal definitions of truthlikeness concern a quantitative distance between two theories or models. Just as in the case of 'reasonableness' above, the formality of truthlikeness doesn't capture the normative dimension of measurement. So, it seems that a distance-from-truth measure may not capture everything we want from truthlikeness.