The term "degree of truth" generally refers to a concept in fuzzy logic and multi-valued logic, where truth values are represented not simply as true (1) or false (0), but rather as a continuum between these two extremes. In classical logic, a statement is either true or false, but fuzzy logic allows for statements to have varying degrees of truth, which can be represented by any real number between 0 and 1.
The Vienna Circle was a group of philosophers and scientists active in Vienna, Austria, during the early 20th century, particularly in the 1920s and 1930s. The group is best known for its role in the development of logical positivism, a philosophical movement that emphasized the importance of empirical verification and scientific methodology.
Verificationism is a philosophical theory primarily associated with the logical positivists of the early 20th century, particularly the Vienna Circle. The central tenet of verificationism is the idea that a statement or proposition is meaningful only if it can be empirically verified or is analytically true (i.e., true by definition). According to verificationism: 1. **Empirical Verification**: A statement is meaningful if it can be tested against observable evidence.
Unified Science is an interdisciplinary approach that aims to integrate the various branches of science into a coherent framework. The goal is to find commonalities and connections across different scientific disciplines, facilitating a more holistic understanding of natural phenomena. The concept often emphasizes the interplay between different fields such as physics, chemistry, biology, and social sciences. It can involve the use of mathematical models, theories, and methodologies that can be applied across various scientific domains.
Structural semantics is a branch of linguistic theory that explores the relationships between the meanings of words and their structured connections within a language. It stems from structuralism, a paradigm in various fields, including linguistics, that emphasizes the importance of understanding elements in relation to larger systems or structures.
The "received view" of a theory, particularly in the context of philosophy of science, refers to a dominant or widely accepted perspective on a particular theoretical framework. This term is often used in discussions about scientific theories, emphasizing how certain theories are generally acknowledged and endorsed by a specific community of scholars or practitioners. In the philosophy of science, the received view may encompass a set of beliefs about how scientific theories should be understood, validated, and related to empirical data.
Phenomenalism is a philosophical theory concerning the nature of perception and reality. It posits that physical objects do not exist independently of our perception of them, but rather, they can be understood only through the phenomena they present to us. In other words, what we understand as physical objects are collections of sensory experiences or phenomena rather than things that exist in an objective, mind-independent way.
Otto Neurath (1882–1945) was an Austrian philosopher, sociologist, and graphic designer, known for his contributions to logical positivism and the development of a theory of social science. He was a prominent member of the Vienna Circle, a group of philosophers and scientists that included figures like Moritz Schlick and Rudolf Carnap, who were influential in the early 20th century.
Naïve empiricism is a philosophical viewpoint that emphasizes the role of sensory experience in the acquisition of knowledge, while also suggesting that our experiences provide a direct and unmediated access to reality. Proponents of naïve empiricism tend to believe that knowledge is derived from observation and that the world can be understood solely through the information we gather through our senses.
Moritz Schlick (1882–1936) was a German philosopher and physicist, best known as the founding member and leader of the Vienna Circle, a group of philosophers and scientists who were central to the development of logical positivism and scientific philosophy in the early 20th century.
"Language, Truth, and Logic" is a philosophical work written by A.J. Ayer, first published in 1936. The book is a foundational text in the field of logical positivism, a philosophical movement that emerged in the early 20th century, emphasizing the verification principle—the idea that a statement is only meaningful if it can be empirically verified or is analytically true.
Josef Schächter is not widely recognized in the general context or literature available up until October 2023. It's possible that he could be a private individual, a professional in a specific field, or a fictional character. If you can provide more context or specify the area of interest (such as literature, science, history, etc.
A "coordinative definition" typically refers to a type of definition where a concept is defined by establishing its relationship to other concepts or terms that are considered equivalent or closely related. This method is often used in academic and philosophical contexts to clarify meanings and ensure that the terminology is understood in relation to similar concepts. In essence, a coordinative definition does not just provide a description of a term but also situates it within a network of related terms, helping to create a more comprehensive understanding.
Carl Gustav Hempel (1905–1997) was a German philosopher known for his significant contributions to the philosophy of science. He is best known for his work on the logic behind scientific explanations and the problem of induction. Hempel's most notable contributions include the "deductive-nomological" model of explanation, which stipulates that scientific explanations can be understood as a deductive argument where a phenomenon is derived from general laws and specific initial conditions.
The term "Berlin Circle" typically refers to a philosophical movement or group of philosophers and scientists in the early to mid-20th century who were associated with the Berlin School of Logical Empiricism. This group was influential in the development of logical positivism and scientific philosophy, focusing on the relationships between language, knowledge, and empirical verification. The Berlin Circle sought to promote a scientific worldview that emphasized clarity, logical coherence, and empirical validation.
A. J. Ayer, or Alfred Jules Ayer, was a British philosopher known for his work in the fields of logical positivism and empiricism. Born on October 29, 1910, and passing on June 27, 1989, Ayer is best known for his 1936 book, "Language, Truth and Logic," where he argued that many metaphysical claims are nonsensical because they cannot be empirically verified.
In mathematical logic, a **theory** is a formal system that consists of a set of sentences or propositions in a particular language, along with a set of axioms and inference rules that determine what can be derived or proven within that system. The sentences are typically formulated in first-order logic or another formal logical language, and they can express various mathematical statements or properties.
In mathematics and logic, a theorem is a statement or proposition that has been proven to be true based on previously established statements, such as axioms, definitions, and previously proven theorems. The proof of a theorem typically involves deductive reasoning and follows a logical framework. The process of proving a theorem ensures that it holds under the conditions specified and contributes to the broader body of knowledge within a particular mathematical discipline or logical system.
"Sequent" can refer to different concepts depending on the context. Here are a few possibilities: 1. **Sequent Calculus**: In mathematical logic, a sequent is a formal expression used in sequent calculus, which is a type of proof system.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact