But then again, you might not need those – just check my Index post to check which option is best for you. The only drawback could probably be the fact that they have only 1 ribbon and the pages aren’t numbered, which might be an issue for you if you’re planning to follow the original Bullet Journal system. It’s among Amazon’s picks in the Bullet Journal notebooks category and has a solid quality paper. This is one of the cheapest options you can get to start with your bujo, but it doesn’t mean it’s not a good notebook. Please see my Disclosure for more details. They will be of no extra expense for you, but I receive a small credit. I hope by now you have an idea of what you might be looking for in your Bullet Journal notebook, so let’s get on with the list! I’d say anything around 100-120 GSM is pretty solid, but of course, the higher GSM, the better. You definitely don’t want any bleeding or ghosting on your pages, so always make sure you check how thick the paper is. So think if you need those or if you prefer to create all the pages yourself. This really helps to speed up the process. Some journals come with already pre-made pages, such as key and index. So think if you have to have your pages numbered or if it’s ok for you to do it yourself as you go. If you want to follow the original Bullet Journal structure, you’ll need numbered pages. Do you want ivory? Cream? Pure white? Think about it because the color of your paper will influence how the color of your markers and brush pens will look. I’m here to help, though here are a few characteristics you might think about when choosing your perfect notebook. There are so many amazing players on the market, and especially when you’re just starting, it’s hard to understand what exactly you need from your notebooks. How To Choose The Best Notebook For YouĬhoosing the right notebook might be a bit difficult. Let’s look into some characteristics you might consider.Īlso, be sure to scroll until the end to get your free Ultimate Guide To Bullet Journal Supplies and some more recommendations. Lately, I’ve been super in love with my Archer and Olive notebooks, and I use different sizes for different purposes.īut you might find that a different type of notebook is best for you, and that’s totally fine. I also have a few favorites, depending on what it is I use them for. When you talk about Bullet Journaling for beginners, getting the right notebook is one of the first things to do!īefore we dive in and take a look at some fantastic Bullet Journal notebooks, I want to be clear about something – there is no such thing as the best notebook!Įveryone needs something different from their notebooks, so it’s up to you to decide what is the best notebook for you. So before you get your journal, take a look at these 13 dot grid journals to try out for your next bullet journal. So, I did my research to figure out what brands are on the market, which ones are popular and why people love them. Yet, it’s always nice to have the best materials and tools for our hobbies and passions. Of course, always remember that for bullet journaling, you can use any notebook you have lying around in your house. However, please be assured that we are working to get your purchases out to you as soon as possible.When you start your Bullet Journal, or even when you just think of moving to a new notebook, it’s important to find the right journal for yourself since this is probably the most important item out of all possible Bullet Journal supplies. During Peak and Sale - due to the high volume of orders, there may be a shipment despatch delay.delivers to over 190 international destinations.All orders are delivered in discreet outer packaging, smaller stationery orders of $60 or less will be delivered in an envelope.Stationery orders under $60 are despatched via United States Postal Services or International Post and will not require a signature for delivery.You will receive an email when your order is ready to be collected from the store. Orders can be collected from selected standalone Mulberry stores free of charge.
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Accompanying this are the also perennial cross compatibility issues of Roxio burners meaning that projects made in earlier versions, may not work properly when opened in Roxio Toast Titanium. One particularly useful feature in Roxio Toast Titanium is the Data Recover tool which can help recover data from a badly damaged disk although the results can be rather hit and miss apparently. Of course, some of these, especially Adobe Photoshop Elements and SonicFire, take some understanding and you'll need to devote a whole session of learning via the excellent tutorials to get to grips with them to get the most out of them. Simply select the disk type, drag and drop the files you want on the disk and hit the red burning button! The fun really only starts there however because you can really got to work on your creations with Adobe Photoshop Elements, Sonicfire Pro, SoundSoap and FotoMagico. The side panel of Roxio Toast Titanium contains all the simplest functions for choosing which type of disk you want to burn whether it's Data, Music, VCD, DivX, DVD and of course, HD to BluRay. SoundSoap allows you to easily and instantly remove unwanted noise from digital video or audio files while FotoMagico offers creation of spectacular HD slideshows. Sonicfire Pro is a sound mixers dream allowing you to create professional soundtracks for your projects. Toast Titanium also adds some limited yet welcome editing features, in this case, trimming and cropping to clean up your videos.Īs regards the extras in this Pro version of Roxio Toast Titanium, Photoshop Elements is the famous Adobe design suite which needs no introduction. Your EyeTV shows can be streamed from the internet to your Mac or iPhone. Roxio Toast Titanium can still automatically connect to your TiVo and copy shows and movies across to your Mac, ready to watch there, convert for a portable device or burn to disk. Toast 11 High-Def/Blu-ray Disc Plug-in is ONLY compatible with Toast 11 TitaniumĭVDs created with Toast adhere to the official DVD specifications, and are tested with Hollywood standard certification tools to verify DVD player compatibility.In terms of new features compared to version 10, the most significant addition to Roxio Toast Titanium 11 is higher quality export profiles for export to Vimeo, an updated Roku video export profile and audio CD projects now allows up to 199 tracks. Toast 11 High-Def/Blu-ray Disc Plug-in is ONLY compatible with Toast 11 Titanium The High-Def/Blu-ray Disc Plug-in for Toast 11 Titanium lets you author HD video content from AVCHD™ camcorders and EyeTV recordings on to standard DVDs and Blu-ray Discs for playback on any standard Blu-ray set top box or PlayStation® 3 game console. JPG, PDF, PSD, PNG, TIFFĭisc Images: ISO, BIN/CUE, IMG, DMG, CDR, NRG Video: AVCHD, AVCHD Lite, AVI, DivX Plus HD, DV, FLV and F4V for Adobe® Flash®, MJPEG, MOV, MKV, MPEG-1/2/4, VOB, VIDEO_TS folder, shared iMovie® projects, EyeTV recordings, and TiVoToGo™ transfers High definition AVCHD™, AVCHD Lite™, or Flip Video® camcorderīlackBerry® device or other mobile devices with MPEG-4, H.264, or DivX Plus™ HD playbackĮlgato EyeTV tuner, Turbo.264, or Turbo.264 HD video encoding hardwareĪudio: AAC, AIFF, MP3, WAV, M4A, OGG, FLAC and Dolby® Digital AC-3 TiVo® Series2™, Series3™, TiVo HD / HD XL, or TiVo Premiere / Premiere XL DVR Internet connected required for video tutorials, product updates, and other functionality VideoBoost requires a compatible NVIDIA® card and 4 GB of RAM for optimal performance There are just over 100 puzzles included with HuBrix, spanning a tutorial and the 'easy' and 'medium' difficulty settings. New elements are frequently introduced to increase the challenge, such as alleys to let colors wrap from one side of the board to the other, or squares that only let you pass through them in one direction. It sounds simple, but can become deviously clever in a hurry as you struggle to figure out how to best allocate the available space. Players trace outwards from colored blocks, with the goal of filling all empty space with the colors at their disposal. HueBrix is a delightful and refreshing mobile puzzle game. > Download 'Super Hexagon' from the App Store The quick restart allows the micro-game rounds to turn into lengthy play sessions, driven by the compulsion to top your last run. When players do slip up - and they will frequently - a single tap jumps right back into the game. It isn't uncommon for a round of the game to last only a few seconds, with runs lasting 30 seconds or more feeling like monumental achievements. Super Hexagon is perfectly designed for mobile. The game bluntly and honestly calls its lowest difficulty setting "hard", only getting more challenging from there with two additional settings. This core idea is taken to dizzying heights as the entire screen constantly rotates and pulses with the music. Players rotate a tiny arrow around a hexagon in the center of the screen, attempting to dodge sides of the geometric shape flying toward to the middle from all directions. From the creator of VVVVVVV comes the devilishly difficult Super Hexagon. msi file name that matches your Surface model and version of Windows and select Next. If multiple downloads are available and you want to update your Surface with the latest drivers and firmware from the Download Center, select the. Snappy multitasking throughout a number of tabs and apps, with highly effective twelfth Gen Intel Core i5/i7 processors constructed on the Intel Evo platform. On the Download Center details page, select Download. Starting with version 3.5 and going forward, only the 64-bit version and Windows 8 will be. With its beautiful modern and material design, your desktop will complement it perfectly. Select a 13.5 PixelSense touchscreen for ultra-portable productiveness, or a bigger 15 PixelSense touchscreen finest for split-screen multitasking. Download Intel Power Gadget 3. Windows 7 and 32-bit versions of the Intel Power Gadget for Windows has ceased development from 3.0.7. Desktop Gadgets brings back classic gadgets for Windows 10. Lightning-fast Thunderbolt 4 port connects a 4K monitor, expenses your laptop computer, and delivers quicker information switch for big video information. Unplug at any time when and wherever you need to stream a present, play a sport, or meet a deadline with as much as 18 hours of battery. Lightning-fast Thunderbolt 4 port connects a 4K monitor, expenses your laptop computer, and delivers quicker information switch for big video informationīattery life for actual life. Compatible with the Surface Pro (2017) and newer Pro devices, the Dock 2 offers four USB-C ports (with two for video), two USB-A 3.2, Ethernet, 3.5mm audio, and a Kensington lock slot. Snappy multitasking with highly effective twelfth Gen Intel Core i5/i7 processors constructed on the Intel Evo platformĭisplay: 13.5 PixelSense Show Decision: 2256 x 1504 (201 PPI) Side ratio: 3:2 Distinction ratio 1300:1 Colour profile: sRGB, and Vivid Individually color-calibrated show Dolby Imaginative and prescient IQ 7 help Contact: 10-point multi-touch Gorilla Glass 3 show on laptop computer with Alcantara palm relaxation Gorilla Glass 5 show on laptop computer with metallic palm relaxation Brightness: 400 nits most (typical), 5 nits minimalĭisplay: 15 PixelSense Show Decision: 2496 x 1664 (201 PPI) Side ratio: 3:2 Distinction ratio 1300:1 Colour profile: sRGB, and Vivid Individually color-calibrated show Dolby Imaginative and prescient IQ help Contact: 10-point multi-touch Gorilla Glass 5 Brightness: 400 nits most (typical), 5 nits minimal 13.5 PixelSense touchscreen for ultra-portable productiveness, or bigger 15 for split-screen multitasking The Pyrolancer’s total damage goes up by a percentage for every burning hex around them, so you definitely want to lay down as much fire and then strike at your target for massive damage. The Pyrolancer’s passive ability fits perfectly into their role of spreading fire and, in turn, benefitting from it. This class’ preferred stat upgrades are Physique and Mind. Of all the classes in The Iron Oath, this one only has one support ability to buff nearby allies, but most commonly you’ll want the Pyrolancer on the front line burning up the enemy with flaming strikes and spells. The creatively-named Pyrolancer class is a powerful melee damage-dealer and terrain manipulator capable of hitting burn effects on targets, hitting multiple enemies in a row, laying down fire traps, or even creating rows of fire to make movement treacherous for the opponent. Here’s everything you need to know about character classes in The Iron Oath. If you do run out of ability charges or simply don’t want to use them, all classes have a basic attack that has no limit to the number of uses. In addition, all abilities can be further upgraded as you level up, increasing the power of an ability, giving it extra use charges, or layering an extra effect.Īll abilities have a base use limit of three per fight and dungeon crawl and these can only be regenerated while camping and burning the appropriate incense. At a sufficiently high level, each character can equip a maximum of four abilities out of the total six, so there’s enough flexibility for you to experiment with different loadouts and builds to suit your playstyle and needs. These classes define each character’s battlefield role and what they can do in battle.Īll classes have six associated abilities, usually split into damage abilities and support or miscellaneous abilities, though the exact number of each can vary from class to class. In The Iron Oath, players will bring parties of characters into combat with each associated with a specific class. In a thematic matrix, you summarize your codings for the most relevant categories (=codes) for all cases. Thematic MatrixĪ frequently used and helpful way to present results of a thematic analysis is to produce a thematic matrix. (1998) offer an example from their work:Īnother example is the following coding scheme used by Berends & Johnston (2005):Īn insightful and more detailed account of a collaborative and extensive codebook development can be found in the paper by DeCuir-Gunby, Marshall & McCullock (2011). develop a coding scheme / codebook (short/extended code definition, criteria for when (not) to apply it, an anchor example).determine coding rules (when do you code and which code do you use?), and.define your coding unit (what do you want to code: a sentence, a part of a sentence, or an entire paragraph, …),.See in particular the instructions on how to This quick 10-step rundown might be helpful to get to you started with MaxQDA. Coding unit, rules, and schemes (codebook) These methodological reflections by Da Nascimento & Steinbruch (2019) offer some important insights why it is important to be transparent about your approach to transcription. Make sure to disclose the transcription system that you are going to use. This short chapter by Morey Hawkins (2018) provides a quick introduction to the world of transcription systems. The choice of the transcription system should be closely tied to the type of analysis used (if you are not going to analyze the tone of the voice, interruptions, pauses etc., there is no point of transcribing them). Other transcription systems aim to provide very nuanced written accounts of spoken language by using several different markers to stay as close as possible to the actual language used (“verbatim” or “naturalized” transcription). These are generally referred to as “non-verbatim” or “denaturalized” transcription systems. Some transcription systems “smoothen” spoken language in the process of converting it into written words by erasing pauses, correcting grammar, and making other modifications in order to produce a conceptually-written text. There are different approaches to how spoken language can be converted into written words. Interview data needs to be transcribed before it can be made subject to data analysis in MaxQDA. Following this approach, the information on an individual case is always accessible and can be included in a cross-case analysis. The procedure combines qualitative and quantitative data as well as word-based and category-based procedures and is demonstrated by an example of a mixed methods evaluation of a university course with an online survey. The procedure does not consider the open-ended questions in isolation from the other data collected, but rather interlinks this qualitative data with the standardized, quantitative data in the sense of a mixed methods approach. This guide describes a procedure for analyzing responses to open survey questions with MAXQDA. There are some excellent video tutorials that will bring you up to speed. Tipp: check with your supervisor/department if there is a chance to get the costs reimbursed if the university does not offer a QDA license. As a student, you should be able to get a student license for under 50 EUR. On the MaxQDA website there are different license types listed. While some universities offer licenses to their students, most universities don’t yet. MaxQDA is a fairly comprehensive software package for qualitative data analysis. In what follows, I will focus on MaxQDA as the software that I am most familiar and satisfied with. this chart by Berkley or this resource page by George Mason University). If you want to learn more about those different options and how they compare, there are several good overview charts offered by fairly independent entities like university libraries (see e.g. Among the most prominent ones are Atlas.ti, NViVo, Dedoose, and MaxQDA. There are a number of different options on the market. automatic coding, code co-occurence), I highly recommend using a qualitative data analyis software (typically abbreviated as QDA). To analyze comprehensive data sets and run certain analyses (e.g. I will focus here more on the technical/logistical aspects of how to manage your data analysis, specifically the coding process, and will largely disregard the broader methodological questions (see this blog post for a good reader on how to do high-quality qualitative research). On this page I want to summarize some of the advice I usually give to students who want to get started on a thesis project which involves qualitative empirical research. Once you can perform three full sets of eight repetitions with a certain weight, you can increase the weight by five to 10 percent the following week. For each exercise, perform one to two warmup sets as you work your way up to the "working sets." Perform three working sets with 90 seconds of rest between each. Start light at the beginning, and work up to a set that causes failure in that range. In all cases, the first workout you do in the program will usually establish the baseline for the full training program. Generally speaking, I find five to eight reps is a solid sweet spot for building a combination of strength and size within the same workout program. Is TUT something that you should be overly focusing on or worrying. Strength: 1 30 seconds Hypertrophy: 30 -70 seconds Muscular endurance: 70 100 seconds. Other training variables such as volume-load, inter-set rest, and time under tension have negligible effects on RET-induced changes in muscle size or strength. Charles Poliquin states that different training objectives such as muscular strength, hypertrophy (growth) and endurance are achieved optimally by different time under tension ranges. These are "ranges" as opposed to hard and fast rules. In addition, RET-induced muscular hypertrophy is augmented by increasing training volume, but with diminishing returns. Sets The volume of sets can be modified over time as your training progress. The closer you get to a 12-rep max-meaning a weight you can lift for 12 repetitions prior to muscle failure-the more your body will favor hypertrophy. Hypertrophy/Muscular Development training is typically moderate-heavy loading (75-85 1RM),6-12 reps, 2-0-2, 0-60 or 0-30 rests, 3-6 sets (up to 7), 2-4 Strength exercises per body part. As a general rule of thumb, the closer you get to a one-repetition maximum (1RM), the more the workout will favor strength gains. The most important factor if you want a workout that builds both muscle strength and strength is to lift in the five to eight-repetition range with a weight that is challenging or causes failure within that range. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. The cookie is used to store the user consent for the cookies in the category "Performance". This cookie is set by GDPR Cookie Consent plugin. The cookies is used to store the user consent for the cookies in the category "Necessary". Castle of Illusion Starring Mickey Mouse is a 1990 platform game developed by Sega and released for the Mega Drive/Genesis. Gather your courage and traverse enchanted forests, take on hordes of rebellious toys and navigate mazes of living books. The cookie is used to store the user consent for the cookies in the category "Other. When the evil witch Mizrabel kidnaps Minnie, it’s up to Mickey to brave the dangers of the Castle of Illusion to rescue Minnie. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The cookie is used to store the user consent for the cookies in the category "Analytics". These cookies ensure basic functionalities and security features of the website, anonymously. We rollīack to the theater room where the audience stays still, but we hear applause.Necessary cookies are absolutely essential for the website to function properly. Mickey hugs Minnie, mission accomplished, the end. And so they fly away as the Castle of Illusion disintegrates,Īnd Mizrabel is allowed to turn over a new leaf as a good person. Who has had a change of heart, hands brooms to the couple so that they canĮscape with her. With this, the castle crumbles, and Mizrabel, Urgh, I despise vanity as a motive for evil characters. The youth of others to become young and pretty. Castle of Illusion: Starring Mickey Mouse steht wieder auf Steam zum Verkauf. Morphing Mizrabel from a malevolent-looking old witch to a fairly-more-benevolent-looking old witch.Īt least this one doesn't look like the kind who would steal Hey, gotta try everything that can be tried, right? This turns out to work, bringing Minnie back to normal, and Rainbow Gem, which Mickey tosses in the witch’s face. When she’s defeated, the seven Jewels come down, merged into a single Points, and she first has five different patterns, which she combines for the Patterns, and of course it takes place on a 3D battlefield. This green glow is the most evil thing about this Evil Qu-Īs a final boss, she is suitably hard, with various The barrier of fiction! She'll get the game pulled off Steam again! Name is, in fact, not the Evil Queen! She’ll sue us! She’ll find a way through Hoops and telling you that this character who is the Evil Queen in anything but It an homage if you want, we totally have a reason for going through all these To be beautiful again, also ignore that the rejuvenated form of that witch will Mickey Mouse returns to star in Castle of Illusion, a fantastical reimagining of the Sega Genesis classic. Never mind the fact that the old witch looks and acts exactly as the one from that classic Disney movie, ignore that her end goal is White… but I guarantee you, this is a completely different villain character You know, this totally sounds like the evil queen from Snow Activate the CD KEY on your Steam client to download. The witch plans to steal the mouse girl’s youth in order Buy Castle of Illusion starring Mickey Mouse CD KEY Compare Prices. That mouse says that Minnie was kidnapped by theĮvil witch Mizrabel. The game follows Mickey Mouse on a quest to save Minnie Mouse from the evil witch Mizrabel. An 8-bit version of the game was later released for the Master System and Game Gear. The castle, where he meets an old mouse explaining to him the concept of Castle of Illusion Starring Mickey Mouse is a 1990 platform game developed by Sega and released for the Mega Drive/Genesis. Mickey's search brings him to the entrance of Fr some reason, my digital copy of the game was in French Will Lopes, who became Catapult CEO in November 2019, told SportTechie earlier this year that the company had made some “rookie mistakes” with PLAYR, noting its separate branding, high price point and sub-optimal use of its elite athlete data to guide the product. A reduced-price team option for bulk ordering is also available. PLAYR by Catapult is now Catapult One That means you get a more intuitive app, better functionality for teams, and training plans from the pros Get. Catapult One is available as a membership, with a cost of $179 for an annual subscription or about $16 per month (with a $34 kit cost). Find out how PLAYR can improve your game Lorem ipsum dolor sit amet, consectetur adipiscing elit. We don't know when or if this item will be back in stock. The company said those who trialed the product for 90 days saw a 26% increase in sprint distance, an 11.7% increase in total distance per session, and a 3.5% boost in top speed.Ĭatapult’s first foray into the so-called prosumer space was with soccer-focused PLAYR in 2018 at a purchase price of about $265. CATAPULT PLAYR Soccer Fitness Tracker - GPS Vest and App to Track and Improve Your Game - for iPhone and Android (S) Brand: CATAPULT 4.4 353 ratings 62 answered questions Currently unavailable. Player monitoring in indoor team sports: concurrent validity of inertial. Catapult One captures key physical data such as distances, accelerations and other workload metrics 10 times per second, with an accompanying mobile app to monitor trends and access training content.Ĭatapult One seeks to serve athletes in soccer, American football, rugby, field hockey, cricket, lacrosse, tennis, and Australian rules football. Two GPS units (OptimEye S5 Catapult Innovations, Scoresby, Victoria) were used. No questions asked.Elite sports performance leader Catapult has released its latest GPS wearable for the amateur market. You can pause your Catapult One subscription to give you time to recover. PLAN TRAINING LIKE A PRO - Access a library of training plans that are designed by top tier coaches to help you improve, no matter what stage of the season you’re in KNOW YOUR POSITION - View heatmaps from training sessions and games to better understand and improve your on field positioning The Catapult PLAYR GPS tracker is ideal for any soccer player out there who wants to look at their game in a closer more in-depth way. PLAYR by Catapult (playrbycatapult) Instagram photos and videos 23. ANALYZE YOUR PROGRESS - Follow your trends, benchmark against your personal bests, and see your stats The OptimEye player tracking system is designed for teams and sports scientists but the PLAYR tracking system is built to give feedback to individual players. IMPROVE THE METRICS THAT MATTER - Track and improve the core metrics that make you a better player, such as total distance, sprint distance, top speed, intensity, and more Just download the app and log in to your account to start tracking and analyzing your data. Already a member? The Catapult One app is free with your membership. New to Catapult One? Download the Catapult One app to start your membership and receive a Catapult One starter kit that includes a FIFA-approved tracking pod and vest. PLAYR’s Squad feature lets you compare stats within a team. The SmartCoach and Squad system tailors coaching and training to your football, helping transform your preparation, performance and recovery. HOW TO JOIN & ACCESS THE CATAPULT ONE APP: The beautiful game just got smarter - PLAYR is the only system that measures your speed, distance and positional heat map. Use of the Catapult One app requires a Catapult One or Catapult One Team membership. Catapult One works for individual soccer players and coaches of soccer, American football, lacrosse, rugby, and more. Catapult One is a state-of-the-art athlete training solution, combining top of line GPS data, elite level insights and analysis, and training plans, all powered by the technology more than 3,000 pro teams use. Track and analyze important metrics such as total distance, sprint distance, top speed, and more. El Catapult Playr Tracker, es un chaleco equipado con tecnología de análisis de rendimiento deportivo. One of the consequences that have attracted more attention is that if lambda calculus is available to compute LF, grammars can be monostratal, i.e., it is possible to compute 'meaning' directly from 'surface syntax'. In principle, given an LF object O you can 'abstract' ANY component C of O and analyse the remainder as a function F( ) = O. You can take the sense of a DP expression like 'the definition of syntactic categories in English' and analyze it into a function 'the definition of syntactic categories in _' and an argument 'English', just as easily as you can take the function to be 'the' and the argument the rest of that DP (the NP), or the function to be 'the definition of syntactic _ in English' and the argument to be 'categories', etc. That makes lambda calculus an extremely powerful and flexible metalanguage for the representation of the 'factors' that compositionally contribute meaning to NL expressions of any level of complexity. In other words, 'features' (= pairs) or even feature- values can also be analysed as 'arguments' (or functions!) if necessary, although, in practice, most syntactic-semantic theories treat minimal 'signs' as unanalysable atoms and seldom or never perform sub-atomic analysis (the event structure of verbs, mainly, excluded). Actually, since lambda calculus is based on functional analysis and the latter is so powerful a tool, it can in principle be applied even to sub-morphemic units. What's more, since any function can be trivially turned into an argument of a higher order function ('Type Shifting', 'Type Raising', 'Function Composition'), the analyst can recursively 'reanalyse' functions as arguments (and viceversa!) at will, depending on the type of the 'domains' of the functions he may be interested in acknowledging in order to exhaustively analyze E into just two 'factors', an F and its argument.Īnd by 'any non-atomic expression E', I literally mean ' any expression', i.e., not just sentences, words, or intermediate phrases of any level of internal complexity (NPs, VPS, APs, AdvPs, PPs, QPs.) but also STRINGS (continuous or not!) of linguistic material that under other analytical approaches (e.g., phrase structure grammar, with its constituency tests) would not be acknowledged as relevant syntactic constituents and therefore would not be eligible to undergo operations (either in syntax or at LF). The enormous advantage of lambda calculus over elementary logics as a matelanguage for the compositional representation of natural language LF comes from the fact that, assuming the analyst accepts a very rich ontology (e.g.,Frege's, for example, in which entities are either 'functions' or 'objects' of all types it may be analytically convenient to acknowledge!), it is possible to consider any non-atomic expression 'E' of any NL as the 'product' of two 'factors', a function 'F' and its 'argument' 'a', and say that F yields E if 'applied to' 'a'. You can take 'lambda calculus' as a sort of limit, in this respect, since, in principle, due to the properties of functional analysis, it can acknowledge and operate with an infinite number of types of entities. Such formal languages are more or less 'powerful' (and more or less flexible and adequate) to represent the semantic structure of natural languages in a 'compositional' way to the extent that they acknowledge the existence of additional 'entities' (events, time intervals, etc., and new variables that can be quantified over).As you know, the most austere ontologies acknowledge only individuals (and sets) as in first-order Pred Logic, but Russell, Church, Reichembach and others 'enriched' that ontology with 'higher types', then Davidson added 'events', and others even more generously acknowledged 'times' or time 'intervals', modalities, propositions, possible worlds, etc. However, what I suppose you want to understand better is under what assumptions and in what sense can lambda calculus be considered a better representational system for the LF of natural languages than, say, Predicate Logic, or Predicate Logic 'enriched' with events (plus tense logic, modal logic, possible words, etc.). The question "What is the relation between lambda calculus and LF?" is comparable to "What is the relation between F (any formal system of representation with an 'alphabet' and a set of 'formation rules' that can recursively generate the expressions of LF) and LF?, or even to "What is the relation between a natural language L and the LF of L?, and the answer is rather trivial: the relation is usually understood to be 'representational' (basically: one of 'translation'), i.e., the lambda calculus can (among many other things!) represent the Logical Form of natural languages, as you know very well. |
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