 Even on the most cautious way of understanding the modality present in logical truths, a sentence is a logical truth only if no sentence which is a replacement instance of its logical form is false. (This idea is only rejected by those who reject the notion of logical form.) It is a common observation that this property, even if it is necessary, is not clearly sufficient for a sentence to be a logical truth. Perhaps there is a sentence that has this property but is not really logically true, because one could assign some unexpressed meanings to the variables and the schematic letters in its logical form, and under those meanings the form would be a false  sentence.[8]  On the other hand, it is not clearly incorrect to think that a sentence is a logical truth if no collective assignment of meanings to the variables and the schematic letters in its logical form would turn this form into a false sentence. Say that a sentence is universally valid when it has this property. A standard approach to the mathematical characterization of logical truth, alternative to the derivability approach, uses always some version of the property of universal validity, proposing it in each case as both necessary and sufficient for logical truth. Note that if a sentence is universally valid then, even if it's not logically true, it will be true. So all universally valid sentences are correct at least in this sense.