Gottlob Frege (1848–1925) is widely regarded as the greatest logician since Aristotle and one of the most significant philosophers of the modern period. His primary contributions to philosophy lie in the areas of logic, mathematics, and language. Frege, a mathematician by training, was principally concerned with establishing mathematics, particularly arithmetic, on a solid scientific foundation, a pressing issue during his time. He believed that if our language were logically perfect, the need for logic might diminish, or logic could be directly read off from the language. Frege's logical inquiries were deeply intertwined with his "logical-arithmetical project," aiming to demonstrate that arithmetic is ultimately a branch of logic. Topics such as Sense and Meaning (Sinn and Bedeutung), object and concept, the context principle, and the nature of definition were all developed as steps towards fulfilling this grand project. While these concepts have gained independent significance in fields like linguistics and philosophy of language, understanding them within their original context—the development of his concept-script for analyzing arithmetic—is crucial. The centerpiece of Frege's logical view is his _Begriffsschrift_ (concept-script) developed in his book of the same name and later in his masterwork, _Grundgesetze_. He also attempted to explain its philosophical aspects in informal introductions that remained incomplete. Frege envisioned concept-script as a "formula language of pure thought modeled upon the formula language of arithmetic". His goal was to create a precise tool to capture and secure the certainty inherent in the laws of thinking and any truths derivable from them, such as those of arithmetic. Frege accepted, in principle, Leibniz’s vision of a unity of science expressed via a _characteristica universalis_, a universal characteristic language, and a _calculus ratiocinator_, a calculus of reasoning. However, Frege adopted a more focused, step-by-step approach, initially developing a logic specifically to capture mathematical content. He aimed to introduce signs for the "things themselves" within this domain, mirroring Leibniz's broader ambition for all areas of knowledge. Frege viewed his concept-script as a "tool for specific scientific purposes," drawing an analogy to the relationship between the eye and the microscope. While ordinary language (the "language of life") possesses greater flexibility and range (like the eye), concept-script (like the microscope) is more precise and suited for the strict requirements of science. Frege clarified that concept-script was not intended as an _organon_, a science extending our knowledge, but as a _canon_, providing rules for "evaluating and correcting our cognitions". He believed that logic could offer an advance in method. One of the stated advantages of Frege's concept-script over other logical symbolisms, such as Boole's, was its ability to develop new, fruitful concepts. Although Frege was modest about the new truths _Begriffsschrift_ proposed, he was ambitious about its future applications in facilitating scientific revolutions through methodological progress. Despite its groundbreaking nature, Frege's concept-script itself did not become the dominant logical calculus; instead, most current logical calculi are descendants of Russell and Whitehead’s _Principia Mathematica_. Nevertheless, other aspects of Frege's work have significantly influenced the philosophy of logic, language, and mathematics. Frege's concept-script was tailored to the epistemological needs of displaying and testing mathematical discourse. This involved several key epistemological aims: first, to demonstrate that arithmetic is a branch of logic, the most secure and general science; second, to create a rigorous testing device for mathematical proofs; third, to provide mathematics with a symbolism that would facilitate the formation of new and fruitful concepts; and fourth, to reveal the nature of numbers with the greatest possible certainty. Frege aimed to show that arithmetical truths, like 2+2=4, are ultimately truths of logic, based on "the laws of thinking alone". Unlike his empiricist predecessors, Frege, similar to Kant, considered logic to be a pure, _a priori_ science whose subject matter and method of finding truth do not rely on experience. He saw logic as dealing with pure thought. Frege believed in the maximal reliability and self-evidence of the laws of thought, providing the "firmest method of proof". This reliability is linked to the objectivity of logic, a crucial aspect of Frege's anti-empiricism. He argued that the aim of all science is to acquire truth, and logic studies the laws of correctly inferring truths from other truths, focusing on the justificatory relation between any truths, thus about truth itself. This distinguishes logic from psychology, which studies mental processes rather than the property of "true" itself. Frege famously stated, "The laws of logic are nothing but the unfolding of the content of the word 'true'". Frege also addressed the normativity of logic, stating that it is analogous to ethics. Just as ethics concerns the property of "good," logic concerns the property of "true". Logic provides the answer to "How must I think in order to reach the goal, truth?" and lays down what holds with the utmost generality for all thinking, regardless of its subject matter. Although Frege viewed the laws of logic as descriptive of the most general truths about judgeable contents/thoughts, he also believed that "from the laws of truth there follow prescriptions about asserting, thinking, judging, inferring". A significant aspect of Frege's view was his opposition to psychologism—the idea that logic is based on or reducible to psychology. He argued that thoughts, unlike ideas or brain processes, are what can be true or false. He pointed out that psychology studies minds and contents of consciousness owned by individual men, whereas logic and mathematics do not have this task. Frege maintained that truth is objective and independent of the judging subject, recognizable by all rational subjects. Frege intended his concept-script to be an instrument that embodies the epistemological status of logical laws and reasoning, characterized by brevity, simplicity, clarity, lack of ambiguity, rigor of demonstration, logical precision, gaplessness, and lack of reliance on intuition. He viewed it as a corrective to ordinary language, which he believed could obscure the relations of concepts and attach unnecessary elements to thought. This critical view of language, while sometimes described as revolutionary, has roots in the history of philosophy. In _Begriffsschrift_, Frege focused on judgeable-content, the content relevant in deductions. His logicist project was fundamentally deductive, aiming to prove the deducibility and reducibility of arithmetic to logic. Frege admitted only two logical operators in his logic: negation and conditionality. His logic was also deeply functional, extending the concept of function from mathematical analysis to the analysis of judgements and their components (objects and concepts). He treated concepts as "unsaturated" entities, fundamentally different from "objects". Frege also made a crucial distinction by dissociating the assertive force from the predicate, introducing the judgement-stroke ($ \vdash $) to indicate assertion and the content-stroke (—) to indicate a judgeable-content. Later in his career, Frege refined his view of logic, particularly with the introduction of the distinction between Sense (Sinn) and Meaning (Bedeutung) in his articles "Funktion und Begriff" (1891) and "Über Sinn und Bedeutung" (1892). He replaced the term "judgeable-content" with a split between "thought" (the Sense of a sentence) and "truth-value" (the Meaning of a sentence). The act of judging remained the acknowledgement of truth, now conceived as an "advancing from a thought to a truth-value". Thoughts, composed of Senses, are the modes of determination of the objects they are about. Frege argued that the thought itself does not contain the objects it refers to, but rather the Senses of the expressions that refer to those objects. Frege considered inferring as a form of judging, specifically "Judging by being cognisant of other truths as providing justification". He emphasized that inferences must be based on true premises or, more precisely, on judgements. All premises and conclusions in his concept-script were to be prefixed by the judgement-stroke, underscoring the foundational role of assertion in his logical system. Despite some philosophical problems and unclarities in the foundations of his concept-script, Frege's logical achievements are undeniable. _Begriffsschrift_ presented a complete and consistent axiomatic system of propositional logic, which, when appropriately interpreted, also provides the basis for predicate logic with identity. Frege introduced higher-order quantification, the concept of scope, and solved the problem of multiple generality, creating a logic capable of displaying inferences of far greater complexity than Aristotelian syllogistic logic. His work laid the groundwork for analytic philosophy, a new approach to philosophy centered on logical analysis and aspiring to mathematical precision. Frege's fundamental insight that logic consists of objective, universal truths, independent of human psychology, had profound implications for philosophy, suggesting that philosophical truths, like those of mathematics, are objective and discoverable.