In Frege's view, the question of meaning is ultimately related to logic. The best argument we can make on any subject will not go beyond the logic that constitutes these arguments. We can say that modern logic began with the publication of Begriffschrift by Frege in 1879. This book discusses the concepts of existence and full name in logic for the first time, and discusses the relationship between the following propositions: "There is at least one X, X is Y" and "All X is Y". This simple concept is obvious, but it is completely missing in Aristotle's logic. Before Leibniz made a great contribution, Aristotle's logic always dominated philosophical research in the18th century. In fact, Leibniz kept most of his logical manuscripts in the drawer of his desk, and it was not until the 20th century that they were made public. Many symbols of contemporary symbolic logic come from Leibniz's drafts, but many also come from Frege. )
Frege's next book is Fundamentals of Arithmetic (1884), which states that we need a theory to prove that arithmetic is internally self-consistent (a "consistency proof" is needed). Frege tried to explain that if the basic logic principle is generalized, all basic arithmetic concepts will be produced, so the consistency of arithmetic can be proved from the perspective of pure logic. For example, we can successfully give the definition of "number" from the identity principle of a = a, which means that arithmetic can actually be reduced to logic (the history of reductionism, which started with Socrates, has taken a step forward). If arithmetic originates from logic, then it has the innate identity of pure analysis. If this view holds, it will eliminate Plato's and Descartes' views that mathematics is based on the concept of nature, and will endanger Kant's exposition that mathematics belongs to the category of innate synthesis. You can look up these terms in the glossary of philosophical terms. But it also replaces the argument of empiricists like Mill, who assert that mathematical truth is an empirical generalization, which is unconvincing. ("Yes, whenever we put two things and three things together in the past, we always got five things in the end, so we boldly guessed that' 2+3 = 5' was true, or at least it was extremely possible. But that's not certain. No one knows for sure whether we will get six things next time! " )
The important content of Frege's theory of meaning appears in many contemporary discussions about meaning. This is his distinction between Sinn and Bedeutung, which is usually translated as "sense" and "reference". These two terms should be used in the analysis of proper names (if you are not familiar with this phrase, please refer to the "Philosophical Glossary"). In the past, the view of these two terms was that their meaning lies entirely in their anti-counting function; That is, name functions, or refer to or point to the objects they name. For example, the meaning of the name "George Washington" is the real person represented by this name. This name is his representative, and it has no meaning except indicative function. But Frege pointed out that implication has an important difficulty in this common-sense explanation. Let's name three proper nouns: (a) morning star, (b) evening star and (c) Venus. (a) A celestial body that appeared in the east before sunrise. This name has been used by sailors sailing in the early morning for generations. (b) A celestial body that appears in the west immediately after sunset. This name has been used by sailors sailing at night for generations. (c) The brightest planet in the solar system is the second closest planet to the sun. Now we can find from experience that (A)=(B)=(C), which means that the so-called morning star and the so-called evening star are actually the same planet, and that planet is Venus. Now, assuming that proper names only mean named objects, we call this object "X". In this case, "the morning star is a dim star, but it is actually Venus" means "X=X, actually =X". In other words, this sentence is a repetition of the same language and doesn't convey any information at all. But obviously, the sentences discussed do convey some information. People who know this sentence is true know more than ancient sailors. Therefore, Frege concluded that in these examples, besides the name and the named object, there must be a third meaning element, which he called Sinn (pronounced zinn in German). In each example, it means "casting different lights and shadows" on the object. It is the "representation mode" of an object-a way to represent an object.
Frege's theory can't satisfy all analytical philosophers who follow him, but it points out an important problem that any serious theory of meaning must deal with. Moreover, it set the tone for the whole school of analysis, and analytical philosophy now calls Frege the founder. Although there are great differences among analytical philosophers, all analytical philosophers are influenced by Frege, partly because the two most famous analytical philosophers-Bertrand Russell and ludwig wittgenstein-read Frege's works with great interest, discussed his thoughts with him and were influenced by his theory.
Near the turn of the century-before Frege's works influenced English philosophy-an amazing phenomenon appeared in Britain, and its influence spread to the United States. The British discovered Hegel! Hegelianism has fallen behind in the mainland for a long time. There are many outstanding advocates in the New hegelianism, such as Bradley of Oxford University, J.E. Mactaggart of Cambridge University and josiah Royce of the University of California. However, it is not surprising that the national character of Britain and America (if there is such a thing) is unlikely to feel comfortable with Hegel's idealism, which soon caused a realistic resistance. (Note that "realism" here is used in Locke's sense, and "reality" refers to a real external world, not a Platonic concept like "reality" in the Middle Ages. ) The uprising was led by G.E. Moore and Bertrand Russell.