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Sounds plausible. I guess we’ll see just as soon as the court rules? Or will we? Nothing would surprise me anymore.
Yep. Follow them back with qkd then infect the crap out of them. Or into them. lol
Exciting times ahead.
Doc , yep. I think we’re all in there. Pun intended. lol. MSFT and HP Sam and L G etc were not fighting us for a faster way to change a web page lol. Look what’s coming!
Top 10 most powerful Quantum Computers in the World (2023)
MAKB
26 Aug, 2023
1
Table of content
Quantum computers are a new type of computer that could change many parts of our lives. Quantum Computers use quantum computing instead of classical computing. They can solve problems that normal computers cannot, like breaking secret codes and modeling complex molecules.
Quantum Computer
Disclaimer: The ranking of quantum computers presented here is based on a number of factors, including the number of qubits, the quality of the qubits, the error rate, and the connectivity between the qubits. However, it is important to note that this ranking does not necessarily reflect the real power of these computers. The ability to solve real-world problems with quantum computers is still in its early stages of development, and it is possible that some computers that are not ranked highly in this list may be more powerful for certain applications.
Here is a list of the 10 best quantum computers in the world today. They are ranked by their quantum volume, which measures how powerful they are:
1. USTC Jiuzhang: This quantum computer was built by the University of Science and Technology of China. It has 100 photon qubits and a quantum volume of 10 billion. It is the most powerfulquantum computer today.
Photons are particles of light. Using photons as qubits allows this computer to connect more qubits easily. This gives it the highest quantum volume in the world.
USTC Jiuzhang Quantum Computer project photo
2. Xanadu Borealis: This quantum computer was built by Xanadu. It has 128 qubits and a quantum volume of 10 billion. It is the most powerful photonic quantum computer.
It has more qubits than USTC Jiuzhang, but its qubits are not as stable, so the quantum volume is the same.
3. IonQ Quantum Computer: This quantum computer was built by IonQ. It has 128 qubits and a quantum volume of 4.8 billion. It is the most powerful commercial quantum computer.
It uses trapped ions as qubits which can be very stable and accurate.
4. Rigetti Advantage: This quantum computer was built by Rigetti Computing. It has 128 qubits and a quantum volume of 1.6 billion.
It uses superconducting qubits which can be more stable than photonic qubits. But they are harder to connect to make bigger quantum computers.
5. Intel Horse Ridge II: This quantum computer was built by Intel. It has 400 million spin qubits or 8 superconducting qubits.
It has the most spin qubits of any quantum computer. But spin qubits are weaker than other types.
6. D-Wave Advantage: This quantum computer was built by D-Wave. It has 1,124 qubits and a quantum volume of 100 million. It is the most powerful quantum annealing computer.
Quantum annealing computers are good at solving optimization problems.
7. IBM Eagle: This quantum computer was built by IBM. It will have 127 qubits and a quantum volume of 100 million when released in 2023.
It is expected to be the most powerful quantum computer when it launches.
It uses trapped ions as qubits which can be very stable and accurate.
8. Alibaba Quantum Computer: This quantum computer was built by Alibaba. It has 102 qubits and a quantum volume of 200 million. It is the most powerful quantum computer in China.
It uses superconducting qubits like several others on this list.
9. Microsoft Azure Quantum: This is a cloud platform by Microsoft that lets users access different quantum computers. Azure Quantum has 100+ qubits and a quantum volume of 100 million.
Having access to different quantum computers in the cloud makes this convenient for getting started with quantum computing.
10. Google Sycamore: This quantum computer was built by Google. It has 54 qubits and a quantum volume of 128. It was the first to achieve quantum supremacy.
Quantum supremacy means it solved a problem too hard for normal computers.
Google Quantum Computer
FAQs
How are the top ten quantum computers compared?
The ten best quantum computers are looked at by seeing how many qubits they have, what type of qubits they use, and their purposes.
The number of qubits is important to compare these computers. More qubits mean a stronger quantum computer. It's also important to consider the type of qubits the computer uses. Some qubits are more stable and make fewer mistakes.
Considering the quantum computer's purpose is also significant. Some are designed for specific tasks, like keeping secrets or discovering new medicines. Others have a wide range of uses.
What challenges are involved in creating quantum computers?
Making one of the quantum computers comes with several challenges:
Qubits are fragile and can quickly lose their special quantum properties.
Quantum computers require a method to correct mistakes that occur during calculations.
Increasing the size of quantum computers with more qubits is difficult but crucial.
Finding effective ways to apply quantum computers to real-life tasks is still complicated.
What lies ahead for the future of quantum computers?
The future appears promising for the quantum computers. As technology improves, these computers will become more powerful and reliable. They will tackle even more complex problems. This could lead to significant discoveries in various fields, such as enhancing data security, developing new medicines, and gaining a better understanding of materials.
Computer Science | Physics
Breakthrough in quantum computing with stable room temperature qubits
by Andrey Feldman | Jan 19, 2024
Scientists achieve groundbreaking room-temperature quantum coherence for 100 nanoseconds, propelling molecular qubits closer to practical quantum computing.
Abstract image of physical processes.
Scientists have recently managed to maintain quantum coherence in a molecular qubit for over one hundred nanoseconds at room temperature, hinting at potential breakthroughs in quantum computing.
Quantum computers could revolutionize information technology by changing the paradigm of computing. This is attributed to their basic units, called qubits, which can exist in any combination of states, unlike classical bits constrained to a definite value of 1 or 0. Due to this infinite variety of qubit states, a quantum computer should be able to easily handle computational problems that would take a conventional computer trillions of years to solve.
Scientists have successfully created qubits from particles such as photons, atoms, individual electrons, or even a superconducting loop. However, creating a qubit is one thing, building a working quantum computer out of thousands or even millions of qubits is an entirely different challenge, and attempts thus far have been fraught with substantial difficulties.
For a quantum computer to work, it is necessary to establish and manipulate subtle quantum interactions among multiple qubits — a state known as entanglement. However, for this to work, the qubits themselves need to remain stable or “coherent”, which means keeping it in a well-defined quantum state. The problem is, coherence is difficult to maintain as it easily crumbles when qubits interact with their surroundings — even radiation from space can throw them.
To solve this, a team of Japanese researchers led by Nobuhiro Yanai, associate professor at Kyushu University, has engineered a stable qubit using a special structure called a metal-organic framework. This structure involves combining pentacene molecules (made up of five connected benzene rings) with zirconium ions and organic dicarboxylate ligands. The pentacene molecules act like bridges, linking the ligands and ions together into a framework made up of both organic molecules and metal ions–hence the name.
The role of the qubit was played by a pair of neighboring pentacene molecules, which were coupled and exist within five different quantum states achieved by irradiating the metal-organic framework with various wavelengths of microwave radiation.
The metal-organic framework’s nanoscale voids offer the pentacene molecules a degree of freedom, but ultimately restricts their full movement under the radiation’s influence, ensuring they formed a desired quantum state and remained trapped in it for a significant amount of time.
“The metal-organic framework in this work is a unique system that can densely accumulate [pentacene molecules],” said Yanai in a press release. “Additionally, the nanopores inside the crystal enable [them] to rotate, but at a very restrained angle.”
The most important result of the study was that the team could maintain coherence for more than a hundred nanoseconds at room temperature, whereas previously this could only be achieved in similar systems at incredibly cold temperatures of about -200 degrees Celsius. At such temperatures, it was possible to maintain coherence only in photonic qubits, but in addition to needing such extreme conditions to operate, quantum computers using these photon qubits suffer from photon leakage.
Maintaining cryogenic temperatures is not only expensive but complicates the entire computing setup. Thus, creating a stable qubit that operates at room temperature is an impressive and practical achievement.
Looking ahead, the scientists are optimistic about extending coherence for even longer periods. They believe that by designing improved metal-organic frameworks and identifying more suitable molecules for qubits, they can push the boundaries further.
“It will be possible to generate quintet […] state qubits more efficiently in the future by searching for guest molecules that can induce more such suppressed motions and by developing suitable metal-organic framework structures,” concluded Yanai. “This can open doors to room-temperature molecular quantum computing.”
Reference: Akio Yamauchi et al, Room-temperature quantum coherence of entangled multiexcitons in a metal-organic framework, Science Advances (2024), DOI: 10.1126/sciadv.adi3147
Feature image credit: geralt on Pixabay
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A new deep-learning architecture for drug discovery
How accurate are our models of rotating neutron stars?
New research shows how light propagates in integrated circuits on chips
by Technion - Israel Institute of Technology
New research shows how light propagates in integrated circuits on chips
(a) Schematics of the experimental setup for imaging propagating waves within photonic devices. 1550 nm signal pulses (orange) are grating-coupled into a silicon-on-insulator (SOI) waveguide, while 780 nm pump pulses (red) are focused onto the device using a long-working distance objective. When the two pulses overlap in time and space, a nonlinear wave is generated (green), separated from the pump by a dichroic mirror (DM) and collected by a standard CMOS camera. P, F, and ??/2 represent linear polarizer, spectral filter, and ??/2 wave plate, respectively. (b) Axes definitions and the propagation directions of the pump beam (normal incidence), signal beam (guided along the waveguide), and the nonlinearly generated beam (reflected at an angle according to the wave vector of the signal wave). (c) Cross section of the single waveguide. Credit: Optica (2023). DOI: 10.1364/OPTICA.504397
The field of photonic integrated circuits focuses on the miniaturization of photonic elements and their integration in photonic chips—circuits that carry out a range of calculations using photons, rather than electrons as are used in electronic circuits.
Silicon-based photonics is a developing field that is relevant for data centers, artificial intelligence, quantum computing, and more. It enables an enormous improvement in the chips' performance, and in their cost-benefit ratio as it is based on the very same prevalent raw material from chips in the world of electronics.
However, despite benefiting from the well-developed lithography production process, which enables precise production of the desired devices, the instruments don't yet enable accurate mapping of the chip's optic characteristics. This includes its internal light motion—a crucial capacity given the difficulty to model the effect of fabrication flaws and inaccuracies—due to the devices' tiny dimensions.
A new article by researchers from Technion's Andrew and Erna Viterbi Faculty of Electrical and Computer Engineering tackles this challenge, showing advanced light imaging in photonic circuits on chips. The research, which was published in the journal Optica, was led by Professor Guy Bartal, head of the Laboratory for Advanced Photonic Research, and doctoral student Matan Iluz, in collaboration with Professor Amir Rosenthal's research group. Graduate students Kobi Cohen, Jacob Kheireddine, Yoav Hazan and Shai Tsesses also took part in the research.
A video clip showing light's evolution in real time within the MMI device. Credit: Technion Spokesperson Office
The researchers harnessed the optical characteristics of silicon to map the light's propagation without requiring an invasive action of any sort, which perturbs or alters the chip. This process includes mapping the light waves' electric field and defining the elements that affect the light's movement—waveguides and beam splitters.
The process provides real-time images and video recordings of the light inside the photonic chip, without having to damage the chip and without losing any data. This new process is expected to improve the design, production, and optimization processes of photonic chips in a variety of fields, including telecommunications, high-performance computing, machine learning, measuring distances, medical imaging, sensing, and quantum computing.
Copilot is confused with the two separate cases
Doc. Wrong. He was found guilty of theft,embezzlement and fraud. Where u been? You’re making this way more confusing than it is. This is Wades last ditch effort to be finally found guilty of fraud, embezzlement and theft by the Texas Supreme Court. Or rather to have his appeal of such charges denied. Who knows how long these judges will take to decide, but all 8 are Republicans!
What we have here. Is a failure to communicate. I know our BoD wants to communicate. But they got to get the Texas Supreme Court decision.
Get your systems right. VERTICAL QUANTUM SYSTEMS
So exactly how is this going to benefit V?
Copilot in Edge
Article
12/14/2023
3 contributors
In this article
Enable Copilot in Edge
Data used by Copilot in Edge
Summarization by Copilot in Edge
Manage Copilot in Edge
Copilot in Edge mobile
Copilot can be accessed in the Microsoft Edge sidebar. You can ask complex questions, find comprehensive answers, get summarized information, and find inspiration—just like you can when using Copilot in Bing. When using Copilot in Edge, you can also ask questions based on the page content or a PDF open in the browser. In the Compose tab, you can generate text, emails, social media posts, or ideas.
Once the Copilot service plan is enabled for a user, Copilot in Edge also supports commercial data protection.
Enable Copilot in Edge
To use Copilot in Edge, the following steps are required:
The Copilot service plan must be turned on and the user must have an eligible license.
The user must sign in to bing.com/chat with their Entra ID (work account).
The user can then access Copilot by clicking on the Copilot icon in the upper right of the Edge browser (Ctrl+Shift+.).
Copilot in Edge features, like Chat and Compose, do support commercial data protection. Eligible Entra ID users see the word 'Protected' at the top of the Copilot experience in the sidebar.
Screenshot that shows Copilot.
Data used by Copilot in Edge
When using Copilot in Edge, people can use browsing context to answer questions.
Based on the user's prompt and their consent to share data with Microsoft, Microsoft Edge may send relevant data to Copilot. For questions that don't need browsing context, such as 'Help me plan a trip to Manhattan,' Edge shares the URL, page title, user's query, and previous conversation history to help Copilot answer their question effectively.
When the user grants permission to share page information, Microsoft Edge sends Copilot the browsing context of a given session, the user's prompt, and previous conversation history. This information helps Copilot to generate a meaningful response.
When commercial data protection is enabled, none of this chat information is retained by Microsoft beyond the duration of the Copilot session.
Summarization by Copilot in Edge
Copilot in Edge can summarize the content of various documents when displayed in the Edge browser. Currently Copilot in Edge can summarize some document types but not others. Refer to this chart to see the current behavior of Copilot in Edge webpage summarization for various document types. The chart will be updated when support for summarization increases.
Manage Copilot in Edge
Users can modify this permission by going to Microsoft Edge > Settings > Sidebar > App and notification settings > App specific settings > Copilot and then turning on or off the 'Allow Microsoft to access page content' toggle.
Admins can use multiple group policy settings to manage the behavior of the Copilot in Edge sidebar:
To allow or block Copilot in Edge from using browsing context, use the DiscoverPageContextEnabled policy. This prevents Copilot from using webpage or PDF content from being used to respond to prompts.
To disable Copilot in Edge entirely, use the HubsSidebarEnabled policy. Blocking Copilot in Edge automatically blocks all Edge sidebar apps from being enabled.
Instructions for how to manage Copilot in Edge on Microsoft Edge for iOS and Android can be found here: Manage Microsoft Edge on iOS and Android with Intune.
Copilot in Edge mobile
If the Copilot service plan is enabled for your organization, users can access it with commercial data protection through the Edge mobile app when signed in with their work or school accounts (Entra ID).
Edge mobile includes a dedicated Copilot button as part of its user interface. If you would like to remove the Copilot button from the Edge mobile interface, you can use an Intune MAM policy to remove/add it:
com.microsoft.intune.mam.managedbrowser.Chat=true (default)/false
Learn more about how to manage Microsoft Edge on iOS & Android.
Additional resources
Training
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Enhance teaching and learning with Microsoft Copilot - Training
Learn how to use basic Microsoft Copilot functionalities that support teaching and learning.
Dct is the key imo
SHOW US THE MONEY!💰💰💰💰💰💰
Looks like the dicks son is back lol. Give it up Sonny Buy him a nice big fat orange jumpsuit. He’s gonna need it soon.
From chat…
It's there now... Should have been in arbitration.. Wade's the victim; although he was convicted of fraud and embezzlement. Maybe junk can give his interpretation, since he and Pete converse a lot. I didn't feel like reading tonight.
https://search.txcourts.gov/Case.aspx?cn=23-0443&coa=cossup
“CONCLUSION AND PRAYER
Wade is entitled to an opportunity to prepare a defense and have his case heard
on the merits. He was denied that opportunity when the trial court conducted an unauthorized bench trial over his objection. Wade timely objected to not receiving notice of the trial and has shown that the trial court sent his trial notice to the wrong address. The court also had no power to hold a trial on the merits after compelling the parties to arbitration months before. Either of these arguments supports a reversal, and Wade has waived neither.
WHEREFORE, Wade respectfully prays that this Court reverse and remand.”
And it continues…..
Dino
Hopefully today is the day the fat man sings his last song.
NVIDIA CuQuantum 23.10: Accelerating Quantum Computing With Enhanced SDK
Quantum Computing Business, Uncategorized
Matt Swayne
December 22, 2023
NVIDIA cuQuantum
Insider Brief
NVIDIA offered information on its latest update to its cuQuantum software development kit (SDK).
The toolkit ntegrates more seamlessly with NVIDIA Tensor Core GPUs, greatly enhancing the speed of quantum circuit simulations.
cuQuantum is able to accelerate quantum circuit simulations using state vector and tensor network method.
NVIDIA’s latest update to its cuQuantum software development kit (SDK), version 23.10, marks a significant bump in quantum computing capabilities, according to the company’s technical blog.
This toolkit, designed to optimize libraries and tools for quantum computing workflows, now integrates more seamlessly with NVIDIA Tensor Core GPUs, greatly enhancing the speed of quantum circuit simulations.
The core of cuQuantum’s power lies in its ability to accelerate quantum circuit simulations using state vector and tensor network methods. This advancement is not just incremental but is measured in orders of magnitude, offering unprecedented speed and efficiency in quantum computing tasks.
Key highlights of the cuQuantum 23.10 update include significant improvements to NVIDIA’s cuTensorNet and cuStateVec. The new version supports NVIDIA Grace Hopper systems, expanding the range of hardware compatible with cuQuantum. This compatibility ensures that users can leverage the full power of GPU acceleration for their quantum computing workloads.
cuTensorNet, a component of cuQuantum, now offers high-level APIs that simplify quantum simulator development. These APIs allow developers to program intuitively, abstracting complex tensor network knowledge. This simplification is crucial for building tensor-network-based quantum simulators, covering various elements like expectations, measurements, and samples. Performance-wise, cuTensorNet has shown to outperform existing technologies like TensorCircuit, PyTorch, and JAX by a factor of 4-5.9x on NVIDIA H100 GPUs.
The update also introduces experimental support for gradient calculations in quantum machine learning (QML) applications. This feature is set to accelerate QML and adjoint differentiation-based workflows significantly, utilizing cuTensorNet.
Another remarkable advancement is in cuStateVec, which now offers new APIs for host-to-device state vector swap. This development means that CPU memory can be utilized alongside GPUs to scale simulations more effectively. For example, 40 qubit state vector simulations, which previously required 128 NVIDIA H100 80GB GPUs, can now be achieved with just 16 NVIDIA Grace Hopper systems. This reduction not only speeds up computations but also leads to considerable cost and energy savings.
cuQuantum 23.10 also has undergone additional API-level and kernel-level optimizations to boost performance. These improvements make Grace Hopper systems more efficient than other CPU and Hopper systems, offering faster runtimes due to enhanced chip-to-chip interconnects and CPU capabilities.
For those interested in exploring cuQuantum 23.10, NVIDIA provides comprehensive documentation and benchmark suites on GitHub. The company encourages feedback and queries through its GitHub platform, ensuring continuous improvement and support for its user base. With these updates, NVIDIA continues to push the boundaries of quantum computing, making it more accessible and efficient for a broader range of applications.
Here’s a link to help get started.
cuTensorNetGIT HubNVIDIAQuantum Simulator
Matt Swayne
LinkedIn
With A Several-Decades Long Background In Journalism And Communications, Matt Swayne Has Worked As A Science Communicator For An R1 University For More Than 12 Years, Specializing In Translating High Tech And Deep Tech For The General Audience. He Has Served As A Writer, Editor And Analyst At The Quantum Insider Since Its Inception. In Addition To His Service As A Science Communicator, Matt Also Develops Courses To Improve The Media And Communications Skills Of Scientists And Has Taught Courses. Matt@Thequantuminsider.com
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Doc. Don’t we all wish. The way things are moving now ,with AI etc , today’s reply from Wade couldn’t have come soon enough. He has wasted another 3 years of all investors in vcsy’s lives. The Texas court of appeals must end it for all of us investors soon 🙏
https://img1.wsimg.com/isteam/ip/f0889085-26a3-4ae1-ae22-e562ce6a9e8c/a2f92181-20dc-4429-98ef-54f7716b67fa.PNG/:/.
Now if this is actually happening in conjunction with Ploinks. Then we’re in there.
Doc. I’ll run it by one of my nephews who was a v p for Silicon Graphics. See what he thinks?
VOLUME PACKAGES
Assembling your photonic integrated circuits (PICs) or micro-electromechanical systems (MEMS) into functional modules in scalable volumes is PHIX’s core expertise. We have a broad experience in designing and assembling modules for telecommunications, industrial, automotive, medical, space and defense applications. We support all major material platforms, such as Silicon Photonics, SiN, InP and PLC, and can even co-package multiple PIC technologies into one product. We can also provide hermetic sealing for your module.
tunable laser manufactured in volumes
If possible, we would like to start collaborating with you at an early stage of your PIC design. The early involvement of our experts can be crucial for the optimal performance, cost and manufacturability of your module, in small batches and in high volumes.
I believe Scott and another associate? bought some mot patents ? If I remember right? CRS. Anyway. Maybe this is what they are incorporating? His patents with SBV patents and V’s or even others to make a new patent incorporating all? I have a feeling they/we will come out with a new patent soon. If not a few of them imo
We don’t want to hear any more excuses. We’ve heard 3 years of them. 24 th coming next week. Let’s hope the Tex court of appeals isn’t too busy. After that. No more excuses. I’m tired after over 15 years of excuses. I sure hope we all haven’t been jacked around again. I guess we’ll know in a month or so?
And that article was May 10. 2021 ……. Where r they at with it now? Everyone moving to Quantum Blockchain AI. ML ETC. All coming together nicely. Now it will be interesting to see how/if our BoD has kept up the last 3 years. They should have everything in place for blast off. If not /;()&@@$)(;:;)$&@@$(;
Quantum Quorum
FRIDAY, SEPTEMBER 21, 2018
FORM 8-K: SAWBLADE LICENSE AGREEMENT AND ANNUAL MEETING OF STOCKHOLDERS
ITEM 7.01 REGULATION FD DISCLOSURE.
Vertical Computer Systems, Inc. (the “Company”) has entered into a license agreement with Sawblade Ventures, LLC (“Sawblade”). The Sawblade technology is a patented method for integrating flexible distributed security circuits into a customer’s application microelectronics. The method includes a design automation tool and a library of custom security-oriented circuits. The method can be used during the design phase of any of various markets including the Internet of Things (“IoT”) market, defense, automotive, smart grid, and networking. The Sawblade technology can give real-time response, internal monitoring and counter measures to any application.
Under the terms of the license agreement, the Company has obtained a world-wide non-exclusive license to market and distribute the Sawblade technology in the IoT market. The Company may also sublicense the Sawblade technology for use in IoT devices, plus the Company has a six-month option to convert the arrangement to an exclusive license.
The Company will utilize the Sawblade Technology to work with the Company’s Vertical Internet Platform (“VIP”) and provide an end-to-end solution for IoT devices. The VIP is the Company’s patented, clean energy, web server technology on a mobile device, and its use in conjunction with the Sawblade technology is specifically intended to give users of IoT devices a private and secure channel to manage and control their devices.
***
In addition, the Company hereby is providing notice that the Company is changing the proposed date of its Annual Meeting of Stockholders. In lieu of holding the Annual Meeting at 11:00 am (Central Standard Time) on November 27, 2018, the Annual Meeting will be held on a date in mid-January 2019. At the Annual Meeting, the Company will make observations regarding its financial performance and outlook. The new date of the Annual Meeting will be formalized in a future notice.
“ Exploring Semantic Segmentation on the DCT Representation3 “. lol. Oh Portuno.
Jeff was very , very clever. Don’t ya think Doc?
Interesting
Vagueness as Arbitrariness
Sagid Salles
Chapter
First Online: 13 March 2021
146 Accesses
Part of the Synthese Library book series (SYLI,volume 436)
Abstract
In this chapter, I present the Theory of Vagueness as Arbitrariness (VA). In Sect. 5.1 I consider some minimal constraints on the use of vague predicates. I argue that the principle of tolerance should not be considered a constraint, and that the clear-case constraint should be replaced by the ideal-case constraint. In Sect. 5.2, I argue that the notion of ideal case does not imply a violation of the criterion of precisification, at least if we accept the following intuition: all admissible precisifications of a vague predicate are equally arbitrary. My interpretation of this intuition is the first part of my theory: the Thesis of Arbitrariness (TA). TA is in line with some of the main theses about vagueness advanced by Raffman and Sainsbury. Nonetheless, I propose that we should augment it in order to achieve a final definition of vague predicates. The result is VA. According to VA, a vague predicate is an arbitrary predicate that must be precisified in order to contribute to sentences with truth-conditions. VA naturally leads us to Semantic Nihilism. Following Braun and Sider, I argue that Semantic Nihilism can be made viable by an account of how vagueness is typically and harmlessly ignored. Because Braun and Sider’s proposal depends on the existence of a clear-case constraint, an alternative proposal is outlined. I then argue that VA satisfies all three criteria of adequacy for an ideal theory of vagueness, and that it correctly systematizes the relevant intuitions. The chapter closes with replies to some possible objections (Sect. 5.3).
Keywords
Vagueness
Vague predicates
Sorites paradox
Principle of tolerance
Thesis of Arbitrariness
Theory of Vagueness as Arbitrariness
Minimal constraints
Ideal cases
Clear cases
Borderline cases
Many-Boundaries Approach
Semantic Nihilism
Expressivism
The fact that we were awarded the patent is kinda unbelievable. The fact that it passed re examination and several new claims were added to strengthen it even more is even more incredible.
The fact that it has to be 1 new , 2 useful, and 3 non obvious is surprising to me as non obvious is rather vague. Arbitrary equals vague in a way. This must have been Msft’s contention? Arbitrary objects cover a whole hell of a lot of object types . It’s all in the “ semantics “ folks.
The invention must be statutory (subject matter eligible) The invention must be new. The invention must be useful. The invention must be non-obvious
What makes a patent non-obvious?
Nonobviousness is a quality in patent law describing something that is not readily apparent. In order to obtain a patent, an invention must be nonobvious. If someone of ordinary skill in a relevant field could easily make the invention, then it is considered obvious and would be an invention based on prior art.
Doc. Ya think Port may have read this? Lol. What’s the dead giveaway word? Yep Semantics.
BINGO!
This chapter thus provides a nice illustration of how fundamental workin philosophical logic may turn out to be of importance for more applied work incomputer science.Katalin Bimb´o and J. Michael Dunn (Chapter 7) recall Fine’s two-sorted seman-tics for relevance logic and related work. Their chapter leads to a detailed compari-son of Fine’s semantics to more well-known Routley-Meyer semantics for relevancelogics. Interestingly, it is also shown how this work relates to the notion of arbitraryobjects (cf. supra and Chapter 29).This brings us to a number of chapters that all use truthmaker semantics in oneway or another. Chapter 9, by Mark Jago, consists of two related parts. The ?rst partdiscusses the logical relation of disjunctive parthood and links it to the semanticnotion of re?nement and the philosophical determinable-determinate relation. In thesecond part, the author develops a formal logic on the basis of these ideas, whichincludes a relevant conditional. This chapter moreover touches on the subject ofvagueness (cf. Chapter 31) and arbitrary objects (cf. Chapter 29), and Jago’s formalsemantics is clearly related to Chapter 13 in its treatment of disjunction.
Here, Leon Horsten and RyoIto argue that Fine’s theory of arbitrary objects has an early precursor in Russelll’snotion of variables in his Principles of Mathematics, be it that they differ in theway the dependence relation between variables is treated. This observation goessomewhat against earlier remarks by Fine himself “A Defence of Arbitrary Objects”,and is used as the starting point for an in-depth historical overview of Russell’s workon variables, which may help to revive the philosophical debate on arbitrary objects
This approach includes a subtle update mech-anism on sets of truthmakers, which may in turn inspire new work on the logic ofbelief change.In Chapter 29, arbitrary objects take centre stage. Here, Leon Horsten and RyoIto argue that Fine’s theory of arbitrary objects has an early precursor in Russelll’snotion of variables in his Principles of Mathematics, be it that they differ in theway the dependence relation between variables is treated. This observation goessomewhat against earlier remarks by Fine himself “A Defence of Arbitrary Objects”,and is used as the starting point for an in-depth historical overview of Russell’s workon variables, which may help to revive the philosophical debate on arbitrary objects.
Truthmaker seman-tics, both in inexact and exact forms, has been applied by Kit Fine to counterfactualconditionals (Fine, 2012a), the notion of “ground” (Fine, 2012c), intuitionistic logic(Fine, 2014b), and analytic equivalence (Fine, 2016a)
Maybe. There are many types of roses. As there are many types of men.
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Introduction: Kit Fine on Truthmakers,Relevance, and Non-Classical LogicFederico L.G. Faroldi and Frederik Van De PutteAbstract Kit Fine’s contribution to logic is vast and diverse; the chapters in thisbook deal with a signi?cant part of it. In this introductory chapter, we clarify andcontextualize the main themes of Fine’s work that are centre stage in this book, afterwhich we give a summary of each chapter.1 Introducing the IntroductionThis book appears in the series Outstanding Contributions to Logic and is devotedto Kit Fine (1946, Farnborough - England). It consists of 15 original research papersdealing with the formal and philosophical aspects of various themes at the center ofFine’s work. Some are critical, in-depth discussions of his published work, othersapply his ideas to new problems, and still others use Fine’s contribution to developnew perspectives on a classical topic. Each of the chapters is accompanied by anin-depth reply by Fine himself. Finally, the book also features a brief autobiographyand an exhaustive list of Kit’s publications.As editors, it has been a great pleasure to notice that the contributions are currentand they engage with Fine’s research in a creative, critical, and constructive man-ner. It has been a privilege to work with such talented philosophers and logicians.All contributions have moreover been thoroughly peer-reviewed and we thereforewish to acknowledge the crucial role played by the reviewers in the genesis ofthis book: Guillermo Badia, Willem Conradie, Louis deRosset, David Fernandez-Duque, Jeremy Goodman, Berta Grimau, Jesse Heyninck, John Horty, AndrewIrvine, Harvey Lederman, Stephan Leuenberger, David Makinson, Ondrej Majer, EdName of First AuthorName, Address of Institute, e-mail: name@email.addressName of Second AuthorName, Address of Institute e-mail: name@email.address1
2 Federico L.G. Faroldi and Frederik Van De PutteMares, Hiroakira Ono, Francesco Paoli, Pawel Pawlowski, Bryan Pickel, FrancescaPoggiolesi, Adam Prenosil, Tudor Protopopescu, Rasmus Rendsvig, Arthur Schip-per, Sebastian Sequoiah-Grayson, Shawn Standefer, Johannes Stern, Eric Swanson,Zach Weber, Yale Weiss, Malte Willer, Robert Williams.Some of the groundbreaking contributions of Kit Fine to logic are well-known,such as the discovery of an incomplete logic containing S4 (Fine, 1974) and thecanonicity of elementary modal logics (Fine, 1975b). Fine also did pioneering workconcerning the now standard method of ?ltration in modal logic (as highlighted inChapter 3 of this book) and developed a highly original semantics for relevancelogic (as reviewed in Chapter 7 of this book).However, Kit Fine has not only solved open problems in logic and related disci-plines, but also created (or discovered!) new problems and questions. While not thefocus of this book, Fine is a towering ?gure in contemporary metaphysics as well.More generally, he introduced or transformed ideas that have shaped the debate andinquiry, some of which are taken up by contributors to this book. Notwithstandingthe diversity of topics he worked on, there is great unity in his method, using for-mal logic where it helps to clarify certain distinctions and to develop his views inrigorous terms, but always driven by the underlying philosophical issues.In the remainder of this chapter we will brie?y introduce the central themestouched upon later in the book, and highlight how the following chapters contributeto one or another of them, without any claim to have exhausted the multifaceted,continuing conversation that unfolds in these pages. In particular, Section 2 is a gen-tle introduction to some of the main topics of the rest of the book. Section 3 presentsa short outline of each of the original chapters of the book. Section 4 concludes theintroduction with some lighter, but not less important, notes.2 Finean Themes of This BookAs noted above, Kit Fine’s in?uence on contemporary philosophy is enormous andhis contributions are fundamental. In what follows, we focus on those themes inhis work that are particularly relevant for the chapters that follow. An overview ofthe many topics we don’t even touch upon in this introduction, such as essence,semantic relationism, abstraction, metametaphysics and the foundations of mathe-matics, can be found in a recent encyclopedic entry devoted to Fine’s work (Raven,forthcoming).2.1 Truthmakers: A Hyperintensional RevolutionIn the past half century, possible worlds have played a key role not just as a toolin the semantics of modal logics, but also in the philosophy of language and meta-
Introduction: Kit Fine on Truthmakers, Relevance, and Non-Classical Logic 3physics. Fine has argued extensively that the job done by possible worlds is oftenbetter realized with other means, notably (albeit not exclusively) with truthmakers.The concept of a truthmaker is not entirely novel, neither did Fine invent it. Be-fore him, however, it was mostly used within a metaphysical project: what it is,out there in the world, that makes true what we take to be truth-apt (sentences,propositions, etc.). Kit Fine’s interest, when it comes to truthmakers, is mostly ina semantical project: how it is that sentences (propositions, etc.), by virtue of theirvery meaning, are made true by what’s out there, in the world.1We are used to thinking of a world as a complete, consistent state-of-affairs thatsettles the truth value of every proposition. Thus, ’Verdi composed Aida’ is true ata world just in case at that world Verdi composed Aida. But that world will alsocontain a lot of irrelevant material to Verdi and Aida, such as that Bach composedcello sonatas, or that Peano arithmetic is incomplete. In contrast, truthmakers canbe thought of as parts of (possible) worlds that verify or falsify propositions andare wholly or exactly relevant to it. They are neither necessarily complete nor con-sistent.2However, just as with possible worlds, states can be regarded as arbitrarypoints with little additional structure but for the fact that they are equipped with amereological (“parthood”) relation that is required to ful?ll a completeness condi-tion. This makes the framework of truthmakers very abstract and ?exible.Once such a state and parthood relation is ?xed, one still needs to determine howstates make statements true. As Kit Fine points out, the truthmaking relation comesin three forms: exact, inexact, and loose:Loose veri?cation is a purely modal notion. A state or situation will loosely verify a state-ment just in case it is necessary that if the state obtains then the statement will be true.Exact and inexact veri?cation, by contrast, require that there be a relevant connection be-tween state and statement. With inexact veri?cation, the state should be at least partiallyrelevant to the statement; and with exact veri?cation, it should be wholly relevant (Fine,2017d).The state of Sicily being an Italian island is an exact truthmaker of the sentence’Sicily is an Italian island’, but the state of Sicily being an Italian island and Sicilyhaving amazing architecture is only an inexact truthmaker of the sentence ’Sicily isan Italian island’.“Exact” truthmaking clauses were given for the ?rst time in van Fraassen, 1969.In the heyday of situation semantics, inexact veri?cation was common. To illustrateone instance where exact and inexact truthmaking differ on the syntactic level, takeAand A?(A?B). In classical logic, these two expressions are obviously equivalent.Moreover, they have the same inexact truthmakers. Yet, they don’t have the sameexact truthmakers: an exact truthmaker for A?Bmay be “too speci?c”, and henceonly be an inexact trutmaker for A. If one takes the sameness of exact truthmakersas a criterion of equivalence, then Aand A?(A?B)are not necessarily equivalent.1For this distinction and an introduction to the semantical project, see Fine, 2017d. For a uni?ed(i.e. metaphysical and semantical) use of truthmakers see Jago, 2018.2Some of these ideas have also been used in situation semantics, see Barwise and Perry, 1981 andBarwise and Etchemendy, 1990.
4 Federico L.G. Faroldi and Frederik Van De PutteAn important question is which of these three notions (exact, inexact, loose)is fundamental, in the sense of being irreducible to the other(s). Fine argues thatthe notion of exact truthmaking is fundamental (Fine, 2017d, p. 565), others argueinstead that it can be de?ned via the inexact notion (cf. e.g. Deigan, 2019). Boththe inexact and the exact notion of truthmaking are used in various chapters of thisvolume.3With truthmaker semantics, one can also get a better formal grip on the phe-nomenon of hyperintensionality. Very generally, a context is hyperintensional whenclassically logically (or necessarily) equivalent contents cannot be substituted salvaveritate in its scope. (Sameness of) exact truthmaking provides a semantic basis foraccepting hyperintensionality. It therefore cannot come as a surprise that this per-spective on truthmaking has started to be widely used to capture many phenomenathat have been argued to require a hyperintensional analysis. Truthmaker seman-tics, both in inexact and exact forms, has been applied by Kit Fine to counterfactualconditionals (Fine, 2012a), the notion of “ground” (Fine, 2012c), intuitionistic logic(Fine, 2014b), and analytic equivalence (Fine, 2016a). Fine studies how to applytruthmaker semantics to permission (Fine, 2014a) and to imperatives and from thereto deontic modals, in an ongoing series of papers (Fine, 2015a,b). We introducesome of these applications in the next subsections (namely counterfactual condi-tionals, grounding, and subject matter). After that, we move to other Finean topics,viz. arbitrary objects and vagueness.2.2 Counterfactual ConditionalsA counterfactual conditional is a conditional of the form: ”If Xwere (had been) soand so, then Ywould be (would have been) such and such.” Alongside the indica-tive conditionals, it has been known for a long time that counterfactual conditionalscannot be captured by material or (classical) strict implication. Most notably, theyviolate strengthening of the antecedent: from “If it had rained, the grass in my gar-den would have been wet”, one cannot infer “If it had rained and I had put up a gianttent covering my entire garden, the grass in my garden would have been wet”.The very in?uential Stalnaker-Lewis (cf. e.g. Lewis, 1973) treatment maintains,in one of its forms, that such a counterfactual is true if and only if the consequent istrue at all the closest possible worlds in which the antecedent is true. Given a clas-sical account of possible worlds, this however implies that counterfactuals satisfyreplacement of tautological equivalents, both in the antecedent and the consequent.Fine argued against this principle for counterfactuals (Fine, 1975a). More recently,he developed a truthmaker-theoretic account of counterfactuals Fine, 2012a.In his contribution to the present book, Andrew Bacon (Chapter 17) criticizesFine’s account, studying two paradoxes and arguing for a possible worlds analysisof counterfactuals, though distinct from the Stalnaker-Lewis account.3Cf. also possibility semantics (van Benthem et al., forthcoming) and Leitgeb’s semantics for hisHYPE system (Leitgeb, 2018).
Introduction: Kit Fine on Truthmakers, Relevance, and Non-Classical Logic 52.3 Subject Matter and AboutnessThe subject matter of a proposition is, roughly, what the proposition is about.Truthmakers ?gure prominently in more recent theories of subject matter (seee.g. Yablo, 2014 and Fine, 2017a and the ensuing discussion Fine, 2020; Yablo,2018). For Fine, the subject matter of a proposition may be identi?ed with its max-imal truthmaker, i.e. the fusion of all its veri?ers. Mereological relations on subjectmatters will then be had quite easily via the mereological relations already presenton states.In Chapter 19 of the present book, Alessandro Giordani compares the Finean andthe classical account of subject matter, and proposes a synthesis of both. Aboutnessis also central in Chapter 23, in which it is argued that truthmakers can help us geta grip on what it means that a given statement is “the whole truth regarding a givensubject matter”.2.4 GroundingGrounding is a much studied concept that is thought to capture considerations offundamentality in metaphysics and in other domains. For instance, we can say thata conjunction is grounded in its conjuncts, or that the singleton of Socrates exists invirtue of Socrates existing. How to de?ne grounding more accurately is in fact partof the debate on grounding itself.The contributions of Fine to the debate on grounding, as a non-causal, explana-tory, primitive, hyperintensional notion, are numerous and well-documented (for anentry point see e.g. Fine, 2012b). Grounding is mostly thought of in metaphysicalterms, but Fine has suggested also natural and normative grounding notions.How to express grounding? Two options are the relational and the operationalapproach. The former expresses grounding with a predicate, thus suggesting thatgrounding is a relation between that which is grounded, and that which grounds.The latter expresses grounding as a variably polyadic operator between sentences.An advantage of the operational approach would be that it does not commit one toa speci?c position on the metaphysical status of grounding.In the context of formally modeling the grounding relata, several additional dis-tinctions can be introduced. While a conjunction is fully grounded in its conjuncts, itis only partially grounded in each conjunct. One can study the pure logic of ground-ing and the impure logic of ground. The former is concerned only with the structuralprinciples of the grounding operator, the latter also takes into account the internalarticulation of what grounds and what is grounded. One can moreover distinguisha worldly notion of grounding from a conceptual, or representational, notion ofgrounding.In his contribution to the present book, Fabrice Correia offers a novel semanticframework for the worldly notion that is intended to improve upon his own (Cor-reia, 2010) and Fine’s (Fine, 2012c) previous accounts (Chapter 25). Some formula-
6 Federico L.G. Faroldi and Frederik Van De Puttetions of ?ne-grained grounding principles lead to inconsistencies and paradoxes. InChapter 21 of this book, Peter Fritz shows how one can solve some of these issuesin broadly Finean terms.2.5 Arbitrary ObjectsArbitrary objects have been criticized as either useless or inconsistent since at leastLocke and Berkeley. Yet, ordinary reasoning uses arbitrary objects for quanti?ca-tional inferences, which are then suitably regimented e.g. in natural deduction sys-tems. For instance, we conclude that all individuals have a certain property by show-ing that an arbitrary individual has that property. This rule of universal generaliza-tion allows us to infer ?xf(x)from f(a), given certain restrictions, and it is part andparcel of mathematical reasoning too.Fine (Fine, 1985) gave rigorous foundations to our reasoning (e.g. in mathemat-ics, natural deduction, anaphora) with arbitrary objects. He developed a theory thatis far better developed and coherent that was on the market, and he applied it tomany ?avors of generality. More recently, Fine applied these foundations to accountfor the much discussed Cantorian abstractionist constructions of cardinal numbersand order types (Fine, 1998), to a general account of types or forms (Fine, 2017b),to identity criteria (Fine, 2016b), and to providing uni?ed foundations for essenceand ground (Fine, 2015c).In their contribution to the present book, Leon Horsten and Ryo Ito criticallydiscuss Fine’s conception of arbitrary objects by comparing it to Russelll’s (Chapter29). Remarks on arbitrary objects also appear in the contributions of Jago (Chapter9 and Bimb´o and Dunn (Chapter 7).2.6 VaguenessA signi?cant portion of natural language is vague. The predicate ’is bald’, for in-stance, is commonly thought to admit of borderline instantiations: its meaning doesnot settle whether a particular man, Al, with thinning hair is bald or not. In thissimple version, this is a problem for classical logic, because it does not make senseto say that ”Al is bald or is not bald” if ’is bald’ is vague. This raises the problemof formulating a suitable logic and semantics that can handle vague sentences in anappropriate way.Fine, 1975c formulated an in?uential supervaluationist account of vagueness, ac-cording to which, roughly, a vague sentence is true if and only if it is true for all waysof making it completely precise. More recently, however, Fine stressed a distinctionbetween local vagueness – it is indeterminate whether a predicate applies in a singlegiven case – and global vagueness – it is indeterminate whether a predicate appliesacross a range of cases (Fine, 2008). In particular, he showed that it is impossible to
Introduction: Kit Fine on Truthmakers, Relevance, and Non-Classical Logic 7understand global indeterminacy in terms of local indeterminacy (while leaving theother direction open).(Fine, 2017c) suggests a novel account that focuses on the global character ofvagueness, and maintains that it can be captured by logical means alone (i.e. withoutemploying a distinctive vagueness-theoretic notion). Andreas Ditter challenges thisnew possibility result in his contribution to the present book (Chapter 31).3 Outlines of the ChaptersAs we explained above, Kit Fine’s contribution to logic does not merely consist ina range of particular results in various sub?elds of logic; rather, what makes himstand out is the fact that he managed to relate each of these, and to make fruitfuluse of ideas and solutions for one topic, in dealing with another. The same canbe said for the chapters in this book: each of them relates to various others, be itin methodology, formal apparatus, or conceptual targets. This will already partlybecome salient in the summary that follows.We start with two chapters that relate directly to Kit Fine’s older contributions inmodal and relevant logic. Chapter 3 zooms in on the well-known ?ltration method,on which Fine did pioneering work in the 1970s (cf. supra). Johan van Benthemand Nick Bezhanishvili investigate this method from a wide range of perspectives,including model-theoretic, proof theoretic, and dynamic-epistemic ones. The resultis both a solid overview of existing work, and an inspiring venture into unknownterritory, related to ?ltration.In Chapter 5, Vladimir Lifschitz outlines the history of the central idea of “stablemodels” in the context of the Prolog programming language and, later, answer setprogramming. As explained in this chapter, Fine occupies a special place in thishistory, with his notion of “felicitous models” as one alternative formulation of thestability idea. This chapter thus provides a nice illustration of how fundamental workin philosophical logic may turn out to be of importance for more applied work incomputer science.Katalin Bimb´o and J. Michael Dunn (Chapter 7) recall Fine’s two-sorted seman-tics for relevance logic and related work. Their chapter leads to a detailed compari-son of Fine’s semantics to more well-known Routley-Meyer semantics for relevancelogics. Interestingly, it is also shown how this work relates to the notion of arbitraryobjects (cf. supra and Chapter 29).This brings us to a number of chapters that all use truthmaker semantics in oneway or another. Chapter 9, by Mark Jago, consists of two related parts. The ?rst partdiscusses the logical relation of disjunctive parthood and links it to the semanticnotion of re?nement and the philosophical determinable-determinate relation. In thesecond part, the author develops a formal logic on the basis of these ideas, whichincludes a relevant conditional. This chapter moreover touches on the subject ofvagueness (cf. Chapter 31) and arbitrary objects (cf. Chapter 29), and Jago’s formalsemantics is clearly related to Chapter 13 in its treatment of disjunction.
8 Federico L.G. Faroldi and Frederik Van De PutteChapter 11 starts from Fine’s exact truthmaker semantics for intuitionistic logicand asks whether it can be generalized to other non-classical logics. In this chapter,Ondrej Majer, V´it Pun?coch´a?r and Igor Sedl´ar provide an exact truthmaker seman-tics for the nonassociative Lambek calculus and some of its extensions, such as theimplicational fragment of the relevant logic R. They draw interesting similarities be-tween their generalization of Fine’s semantics and Urquharts semilattice semanticsfor R.In a similar vein, Peter Verd´ee combines the notion of exact truthmaking withRestall’s closure frames semantics for substructural logics without distribution anda modal operator, to obtain a truthmaker semantics for four non-transitive relevantlogics (Chapter 13). Following Verd´ee’s earlier work (cf. Peter Verd´ee and Samonek,2019; Verd´ee and Bal, 2015), the four logics are de?ned syntactically as the rele-vant cores of classical logic, Priest’s logic of paradox, strong Kleene logic, and ?rstdegree entailment respectively. The proof of soundness and completeness moreoverproceeds via a third characterization of the logics using sequent calculi, and in-volves an innovative view on relevant proofs in terms of the network structure of thesequents in those proofs.In their chapter, Peter Hawke and Ayb¨uke ¨Ozg¨un ask whether truthmaker se-mantics can be used to solve certain well-known problems of traditional, classicallogic-based epistemic logic. Starting from a rich formal language that distinguishesa priori knowability, suf?ciency for knowledge, and a priori (knowledge-level) im-plication, the authors of this chapter focus on a range of ?rst-order logical princi-ples and discuss counterexamples to those principles. They note that each of theprinciples are valid on the traditional, Hintikka-style semantics for epistemic logic.Finally, they study the behavior of those principles in six different truthmaker se-mantics for the same formal language, that are distinguished by their treatment ofsuf?ciency for knowledge.Chapter 17 deals with the semantics of counterfactual conditionals. Here, An-drew Bacon starts by explaining two puzzles that involve such conditionals: Yablo’sbutton and Bernadete’s paradox. After carefully formalizing the arguments that areinvolved in both, he goes over the various principles that could be given up in orderto avoid the paradoxes. While Fine’s diagnosis is that replacement of equivalentsshould be weakened, thus pointing towards a truthmaker semantics of counterfactu-als (cf. supra), Bacon argues that this move still leads to serious problems as long ascertain very weak logical principles are in place. Instead, he suggests rejecting whathe calls the “Disjunction” principle for counterfactuals, and to endorse a semanticsin terms of a speci?c possible worlds semantics that works with selection functions.Chapter 19 compares Fine’s theory of subject matter to Lewis’s, and it proposes acharacterization based on the information structure model. Giordani aims to developa theory of subject matter that is able to capture both hyperintensionality (a keyfeature of Fine’s account) and context-variation (a key feature of Lewis’s), amongother features.In his contribution to this volume, Peter Fritz sets out to discuss various inconsis-tency results arising from a ?ne-grained conception of propositions, results similarto those arising from naive set comprehension (Chapter 21). Fritz draws on Fine’s
Introduction: Kit Fine on Truthmakers, Relevance, and Non-Classical Logic 9potentialist theory when it comes to set-theoretic inconsistency to explore what asimilarly potentialist theory of propositions might look like. The principles he pro-poses for such a theory are shown to be consistent with a model construction. Aninteresting expressive limitation emerges when trying to apply this theory to ground-ing. The author also discusses using truthmaker semantics to give a theory of propo-sitions, noting along the way some dif?culties in understanding the notion of ’state’used in truthmaker semantics.Chapter 23 puts a fundamental, but often overlooked concept on the table: that ofthe whole truth on a given subject-matter. As Stephan Kr¨amer argues in this chapter,this notion is intricately linked to the modality “and that’s it”, whereby one expressesthat a given statement covers everything there is to say on the subject at hand. It isshown that both presuppose a form of relevance, and that possible worlds semanticscannot adequately capture them. Instead, the author proposes a truthmaker accountof “the whole truth” and the corresponding modality.Fabrice Correia’s chapter deals with the logic of worldly grounding. In particular,it develops a synthesis of the author’s own earlier semantic approach (Correia, 2010)and Fine’s (Fine, 2012b, Fine, 2012c), in order to overcome various defects of both.After a detailed comparison and critique of the existing approaches, the new one isworked out and applied to the semantic characterization of various proof systemsfor ground-theoretic notions.In Chapter 27, Daniel Rothschild and Stephen Yablo focus on the notion of apermissive update, i.e., the information change caused by granting a permissionin a context where before it may have been forbidden. They argue quite convinc-ingly that the various existing approaches to this notion – all based on classicallogic or possible worlds semantics – fall short in one way or another, and developa truthmaker-based approach instead. This approach includes a subtle update mech-anism on sets of truthmakers, which may in turn inspire new work on the logic ofbelief change.In Chapter 29, arbitrary objects take centre stage. Here, Leon Horsten and RyoIto argue that Fine’s theory of arbitrary objects has an early precursor in Russelll’snotion of variables in his Principles of Mathematics, be it that they differ in theway the dependence relation between variables is treated. This observation goessomewhat against earlier remarks by Fine himself “A Defence of Arbitrary Objects”,and is used as the starting point for an in-depth historical overview of Russell’s workon variables, which may help to revive the philosophical debate on arbitrary objects.Chapter 31 raises a problem for Fine’s recent theory of vagueness and the re-lated possibility result concerning the af?rmation or denial of all propositions in aSorites-like sequence (Fine, 2017b). In his contribution, Andreas Ditter argues thatFine’s possibility result as well as his novel solution to the sorites paradox fail incertain legitimate extensions of the formal language employed. Ditter shows thatone can prove a new impossibility result in extensions of the language containinga negation operator that obeys reductio ad absurdum, and argues that at least somesuch extensions are unobjectionable. In particular, it is shown that an operator thatbehaves exactly like intuitionistic negation, which obeys reductio, can be de?ned ina natural propositionally quanti?ed extension of Fine’s logic.
10 REFERENCESFinally, in Chapter 33, Kit Fine and Errol Martin provide a formal account ofnon-circular reasoning, i.e. of reasoning in which the conclusion of an argumentis not somehow presupposed in its premises. Martin (along with R. Meyer) hadpreviously shown that the implicational system P-W does not contain any theoremsof the form A?A. Fine and Martin then extend this result to systems that alsocontain conjunction.The book ends with an exhaustive bibliography of Kit Fine’s published works(Chapter 20).4 The ManThe preceding, and this book in its entirety, not to mention his collaborative spiritthroughout this endeavor, should already go some way towards indicating the impor-tance of Fine’s work for philosophical logic as it is today. But Fine’s contributionsto Logic (and Philosophy) are not just in the form of papers or books. For thosewho have had the pleasure to attend them, his presentations are remarkable for theirclarity and inspiring nature. As a witness of this, one would sometimes see logi-cians ?ght over who gets to take the ?ipcharts of his keynote lecture home. Finally,with his mentorship, sense of humor, love for music (and good food!), charitable,constructive questions, he contributed to many young logicians’ and philosophers’careers, scienti?c or not.ReferencesBarwise, J. and J. Etchemendy (1990), “Information, infons, and inference”, in Sit-uation Theory and Its Applications, ed. by R. Cooper, K. Mukai, and J. Perry,CSLI Lecture Notes, pp. 33-78. (Cited on p. 3.)Barwise, J. and J. Perry (1981), “Situations and Attitudes”, The Journal of Philoso-phy, 78, pp. 668-91. (Cited on p. 3.)Correia, Fabrice (2010), “Grounding and Truth-Functions”, Logique & Analyse, 53,211, pp. 251-79. (Cited on pp. 5, 9.)Deigan, Michael (2019), “A plea for inexact truthmaking”, Linguistics and Philos-ophy,DO I:10.1007/s10988-019-09279-2. (Cited on p. 4.)Fine, Kit (n.d.), “A Defence of Arbitrary Objects”, Proceedings of the AristotelianSociety, 57, pp. 55-77. (Cited on p. 9.)– (1974), “An Incomplete Logic Containing S4”, Theoria, 40, 1, pp. 23-29, DOI:10.1111/j.1755-2567.1974.tb00076.x. (Cited on p. 2.)– (1975a), “Critical Notice of Lewis, Counterfactuals”, Mind, 84, 335, pp. 451-458. (Cited on p. 4.)
REFERENCES 11– (1975b), “Some connections between elementary and modal logic”, in Proceed-ings of the Third Scandinavian Logic Symposium, ed. by Stig Kanger, North-Holland, Amsterdam, pp. 15-31. (Cited on p. 2.)– (1975c), “Vagueness, Truth and Logic”, Synthese, 30, 3-4, pp. 265-300, DOI:10.1007/BF00485047. (Cited on p. 6.)– (1985), Reasoning with Arbitrary Objects, Aristotelian Society. (Cited on p. 6.)– (1998), “Cantorian Abstraction: A Reconstruction and Defense”, Journal of Phi-losophy, 95, 12, pp. 599-634, DOI:jphil1998951230. (Cited on p. 6.)– (2008), “The Impossibility of Vagueness”, Philosophical Perspectives, 22, 1,pp. 111-136, DOI:10 . 1111 / j . 1520 - 8583 . 2008 . 00143 . x. (Citedon p. 6.)– (2012a), “Counterfactuals without Possible Worlds”, Journal of Philosophy, 109,3, pp. 221-246. (Cited on p. 4.)– (2012b), “Guide to Ground”, in Metaphysical Grounding, ed. by Fabrice Correiaand Benjamin Schnieder, Cambridge University Press, pp. 37-80. (Cited on pp. 5,9.)– (2012c), “The Pure Logic of Ground”, The Review of Symbolic Logic, 25, 1,pp. 1-25. (Cited on pp. 4, 5, 9.)– (2014a), “Permission and Possible Worlds”, Dialectica, 68, 3, pp. 317-336.(Cited on p. 4.)– (2014b), “Truth-Maker Semantics for Intuitionistic Logic”, Journal of Philo-sophical Logic, 43, 2-3, pp. 549-577. (Cited on p. 4.)– (2015a), “Compliance and Command, I”, ms. (Cited on p. 4.)– (2015b), “Compliance and Command, II”, ms. (Cited on p. 4.)– (2015c), “Uni?ed Foundations for Essence and Ground”, Journal of the Ameri-can Philosophical Association, 1, 2, pp. 296-311, DO I:10.1017/apa.2014.26. (Cited on p. 6.)– (2016a), “Angellic Content”, Journal of Philosophical Logic, 45, 2, pp. 199-226.(Cited on p. 4.)– (2016b), “Identity Criteria and Ground”, Philosophical Studies, 173, 1, pp. 1-19,DO I:10.1007/s11098-014-0440-7. (Cited on p. 6.)– (2017a), “A Theory of Truthmaker Content II: Subject-Matter, Common Con-tent, Remainder and Ground”, Journal of Philosophical Logic, 46, 6, pp. 675-702. (Cited on p. 5.)– (2017b), “Form”, Journal of Philosophy, 114, 10, pp. 509-535, DOI:10.5840/jphil20171141036. (Cited on p. 6.)– (2017c), “The Possibility of Vagueness”, Synthese, 194, 10, pp. 3699-3725, D OI :10.1007/s11229-014-0625-9. (Cited on p. 7.)– (2017d), “Truthmaker Semantics”, in A Companion to the Philosophy of Lan-guage, ed. by Bob Hale, Crispin Wright, and Alexander Miller, 2nd ed., ms,Blackwell, London, pp. 556-77. (Cited on pp. 3, 4.)– (2020), “Yablo on Subject-Matter”, Philosophical Studies, 177, pp. 129-171.(Cited on p. 5.)Jago, Mark (2018), What Truth Is, Oxford University Press, Oxford. (Cited on p. 3.)Leitgeb, Hannes (2018), “HYPE”, Journal of Philosophical Logic. (Cited on p. 4.)
12 REFERENCESLewis, David Kellogg (1973), Counterfactuals, Harvard University Press, Cam-bridge (MA). (Cited on p. 4.)Peter Verd´ee, Inge De Bal and Aleksandra Samonek (2019), “A non-transitive rel-evant implication corresponding to classical logic consequence”, AustralasianJournal of Logic, 16, 2, pp. 10-40. (Cited on p. 8.)Raven, Mike (forthcoming), “Kit Fine”, Entry for the Internet Encyclopedia of Phi-losophy. (Cited on p. 2.)Van Benthem, Johan, Wesley H. Holliday, and Nick Bezhanishvili (forthcoming),“A Bimodal Perspective on Possibility Semantics”, Journal of Logic and Com-putation. (Cited on p. 4.)van Fraassen, Bas C. (1969), “Facts and Tautological Entailment”, Journal of Phi-losophy, 66, 15, pp. 477-487. (Cited on p. 3.)Verd´ee, Peter and Inge De Bal (2015), “A New Approach to Classical Relevance”,Studia Logica, 103, 5, pp. 919-954. (Cited on p. 8.)Yablo, Stephen (2014), Aboutness, Princeton University Press, Princeton. (Cited onp. 5.)– (2018), “Reply to Fine on Aboutness”, Philosophical Studies, 175, 6, pp. 1495-1512. (Cited on p. 5.)
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What is an arbitrary object?
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I've been researching google on what it is, but haven't been able to find an answer. You can look up google yourself if you want.
So, I've come here for help. Just wanted to know what that type of object is and what it does.
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objective-cxcode
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asked Nov 14, 2010 at 14:09
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If you have an arbitrary object in Objective-C (typed id), you can inquire information about its class by calling the class selector:
Class c = [obj class];
You can log that to the console (NSLog(@"%@", [obj class])) or perform other operations to see which selectors are supported on the object, etc.
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answered Nov 14, 2010 at 14:14
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It's any object that is derived from the language's ur-type (if it has one).
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answered Nov 14, 2010 at 14:10
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Ignacio Vazquez-Abrams
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Technical data (TD) pertaining to items, components, or processes for the purpose of identifying source, size, configuration, mating and attachment characteristics, functional characteristics, and performance requirements. Literally: - Form: The shape, size, dimensions, mass, weight, and other physical parameters that uniquely characterize an item. For software, form denotes the language and media. - Fit: The ability of an item to physically interface or interconnect with or become an integral part of another item. - Function: The action or actions that an item is designed to perform