Examples of Premise Based Implicative Truth Synthesis

3.1 Applied mathematics

Mathematics introduces the number a-priori, without any proof – within mathematics the number simply exists, it is given. The central property of applied mathematics is the nature of specification of that initial number entering the computation. It’s up to you in many cases what that starting number will be.

Different professions or industry disciplines give name to the applied mathematics field. More preciously, the professionals who pick the initial numbers, as inputs to mathematics, define the field of applied mathematics. Sometimes processes within an academic or industry field generate the starting numbers for mathematical analysis. 
  

For example, for mathematics application in physics, the initial number generating process is the measurement and the discovery of quantitative relationships in nature; in finance, bankers choose an interest rate or a trader specifies the stock price; in economics, economists define initial numbers representing demand and supply or the price of the goods; in psychology, the psychologist specify the number of subjects in a statistical behavioural experiment. 
  

In the fields of applied mathematics, it's actually the inquiries extraneous to mathematics that generate initial, entry point numbers, the initial premises. 
   

Within the field of mathematics application (economics, finance, trading, psychology) there are no new mathematical operations or new kind of numbers - they all come from, and belong to the same, “only one” mathematics.

The fields to which mathematics is “applied” (economics, finance, psychology…) are axiomatic systems because they have their own axioms and inquiry methods and the common logic that supports them. This is important observation for the application of Implicative Truth Synthesis. Since mathematics is also an axiomatic system (where the word axiom comes from) the other systems of its application have postulating power to select the initial numbers for mathematics, which are considered “given”, for further calculations. A whole philosophy of reasoning and decision making takes place, within the discipline extraneous to mathematics, before this first number is chosen.
   

Once you enter the mathematical world it really does not matter where the initial number came from. Mathematics sees only that number and has its own rules to process it.
  

Also, by adding the word “quantitative” to the field of application, we generate a new applied mathematics name. Therefore, we might have quantitative psychology, quantitative sociology, quantitative marketing, quantitative archaeology. “Quantitative” means that there are non-mathematical relationships in the discipline that generate, postulate numbers as starting points for mathematical calculations. Mathematics, then, returns obtained mathematical results back to the original discipline (psychology, archaeology, etc.)
  

Since we consider the first system, one which mathematics is “applied” to (psychology, archaeology, trading…) to be axiomatic, and since mathematics is also axiomatic, by introducing quantitative relations between these two systems we cross axiomatic boundaries between them. 
  

For example, let’s look at the stocks trading. Price is, of course, an influential element in this activity. Certain rules exist that precede the price specification, and these rules can be related, for instance, to weather, political events, or certain consumers’ behaviour. These are, in many cases, non-mathematical relations and laws. Hence, based on the conclusions coming from these domains, a trader will state the price. For instance, “based on such and such consumers’ statistics and current weather, the price will be $21.50.” Once you have the price, that number enters mathematical world and is subject to all those relations and rules that apply to mathematics. Mathematics does not care if number 21.5 comes from trading ($21.50), from physics (speed 21.5 m/s), or from weather (21.5 degrees Celsius). Mathematics deals only with numbers! Many kinds of non-mathematical relationships can generate these numbers, and in the case of our trading example these non-mathematical relationships refer to the weather and consumers’ behaviour.
  

When we state the price of $21.5, we crossed axiomatic boundary between our trading reasoning (weather, consumer’s behaviour, political atmosphere) and mathematical world, by postulating the price of $21.5, thus giving to the mathematical world number 21.5 to work with. Therefore, our trading axiomatic system has a postulating power – it can postulate a starting number for mathematics so that mathematics can process that number further. We synthesized new truth via implication which states “based on consumers’ behaviour and the weather conditions the price will be $21.5 and it implies that number 21.5 will be our entry point (postulated!) to the further mathematical computations”. This is the example of Premise Based Implicative Truth Synthesis.
  

Now, a few notes about how to approach mathematics as a discipline – in school or in your projects. To tackle apparent abstraction and complexity of mathematics it is prudent to consider the following: everything in mathematics is about sets and operations on them. Any mathematical formula, branch of mathematics, or mathematical operation can be traced and explained in terms of sets. The trouble to understand mathematics is in the fact that mathematicians go to the great length in arbitrary naming sets and the sequences of operations on sets. Calculus, probability, measure theory, random numbers are just labelling names for sets and the sequences of operations on them. You don't need to use names given by mathematicians to advance your knowledge in mathematics. Think in terms of sets and use any labels that work for you knowing that in the background it is all about the sets and operations on them. And moreover, you don't even need to use language to think about mathematics – think in terms of sets, and use language to try to convey your results to others. 
  

We often hear that some results are obtained by using mathematical logic. But the concept ”mathematical logic” is misleading. It suggests that there are many kinds of logic, one of which is mathematical. However, it is not true. There is only one logic for which we can say it is applied to different disciplines. Logic is not more precise if it is used in mathematics than when it is used in a courtroom or during scientific research in chemistry. Logic is about examining truth values of the statements about world around us. Logic deals with truth values and manipulates truth values in any discipline or discourse of thinking.
  

Any discipline, being it mathematics, physics, jurisprudence, chemistry, architecture deals with truths within that discipline. These truths are related to concepts characteristic to the particular discipline. We use universal logic to discover truths within any discipline – for mathematics we use logic to discover truths about numbers. Mathematics appears to be more complex and alienated from our ways of thinking because mathematicians arbitrary name their steps in discovering the truth and the truth statements. The names can be quite unexpected and exotic, yet they refer only to numbers, truth about numbers, and operations on numbers. Mathematics appear to be more precise than other sciences. Hence, in mathematics we have theorems, lemmas, proofs, definitions. But, they all relate to the efforts to discover truths about numbers. I am sure there are theorems and lemmas in chemistry and architecture, but they may not be called the same name.

3.2 Human behaviour

Perhaps the best example of Premise Based Implicative Truth Synthesis is the human behaviour.
 

For a mind’s given input any course of action (within the physics laws) is possible. Which action will be taken depends on the person's internal analysis of the given information, the person’s emotions, feelings, impressions, perceptions, and rational reasoning.  Implicative Truth Synthesis is the main reason a person can initiate any action based on any kind of reasons. Hence, it is of utmost importance how we, humans, infere information that will motivate, initiate their actions. There is no causative link, in the sense of physics laws, between reasoning, decision making and which action to take. We have free will. We can take any action for any reason whatsoever, therefore we directly form an implication from given information and actions that we take based on that information. Reason A implies that we will choose to take action B. That’s where Implicative Truth Synthesis comes into play.
  

An information can motivates us to do a certain thing. But, we don’t need to do it although we can. A premise is the information we have. This information belongs to the axiomatic system A consisting of all relevant information available to us. Second system, the system B, is the system consisting of all possible actions we can take. These actions may not be based on the information we have. But, if we take information we have into account, and based on it we take an action (selected from all the actions we can take) then we crossed axiomatic boundaries between the systems A and B, and synthesized a new truth: given information from A implied that we chose to take action from B. This exactly illustrates the Premise Based Implicative Truth Synthesis.
  

There may not be more inviting and challenging goals as to structure information in such a fashion as to influence decision making process of humans, as the members of the society, in a desired way. Psychology, politics, economics, marketing, are all great examples! And Implicative Truth Synthesis is in the center of it.

3.3 Physics, engineering, and mathematics

As I mentioned, the trick is that mathematics has its own rules, and is an axiomatic field. The only entrance to mathematical world is by choosing starting numbers, postulating (without proof) initial numbers, initial conditions, and/or choosing a set of initial mathematical operations. Given these inputs you can obtain results in mathematics. 
 

I will quickly repeat what I wrote about physics and mathematics. The relations in physics, say motion, momentum, energy, are quantifiable. This, in other words, means, they can generate numbers, supply numbers that are initial conditions for mathematics. That's the link. Only through a postulate combined with implication, two different axiomatic systems can be functionally linked. So, in physics, non-mathematical events postulate numbers as a-priori inputs (no question asked!) to the mathematical system. Then, inner processes within mathematics,  logic playing the major role, accept this spectrum of initial values and do the job on them. After the computation is finished, mathematics returns results to the world of physics. 
 

The significance of the concept of a premise or a postulate which is the part of the method name, Premise Based Implicative Truth Synthesis, can be further illustrated. 
 

Natural sciences are closely related to the physics and laws of motion. Relations between force, mass, energy, velocity are described the best with partial differential equations (PDEs). Methods for solving these PDEs are well developed and documented. The solutions can have either closed form (analytical solution) or they are numerical solutions. But, the question is, if the methods of solutions are already well defined, what is then left to discover? The answer is related to something that most undergrad and some grad courses mention but miss to emphasise – the initial and boundary conditions for PDEs. 
   

Usually, when solving a PDE, you have a domain of interest for which you have a governing Partial Differential Equation and boundary of that domain. It is this boundary (and/or initial system state in time, called initial condition) that needs to be specified, postulated. It will be given, a-priori, information to solve a PDE. There is no ready-to-use formula to postulate these boundary and initial conditions. It is up to the creative capabilities of the person defining the problem to postulate these conditions. This specification or discovery can be a trial and error process or a follow up on some previous results from related experience, or even using intuition. Even then, there is no guarantee that the solution of PDE, with specified boundary and initial conditions, can be found; it may also take an unspecified amount of time to find it, and, if found, there is no guarantee that the solution will be the one you are looking for!

But, what is important here is that the boundary and initial conditions are the gates for the creativity, the originality; it is a fertile land for genius of the person involved in the problem solution to shine. Postulating these initial conditions explains the word “Premise” in the Premise Based Implicative Truth Synthesis.
  

For instance, the Wright Brothers, when designing the first airplane, were looking for the winning airfoil (wing cross-section) shape. The experimental setup of their wind tunnel and measurement devices established the governing aerodynamics PDE. Their research focus was the winning shape of the wing and its cross-section, airfoil. The airfoil is the boundary condition the Wright Brothers were looking for! After performing a number of experiments, with different wing shapes and cross-sections, they came up with the solution and made their first successful controlled flight. The rest is history. Note that, during their discovery process, not all airfoils (boundary conditions) gave satisfactory results. The Wright Brothers had to come up with numerous airfoils to find the right one in order to get the plane up in the air. Their reasoning was one axiomatic system, say system A. The flying wing was another system, B. By postulating correct wing shape and airfoil, the Wright Brothers crossed axiomatic boundaries between these systems, A and B. The correct airfoil implied the aircraft will take off. The implication synthesised the new truth, “the correct airfoils implies that aircraft will fly”. This is Premise Based Implicative Truth Synthesis.
  

Nikola Tesla postulated design of his asynchronous motor, whose construction, in general view, represents the initial and boundary conditions for the relevant Maxwell’s partial differential equations of electro-magnetism. There is no formula that would tell how to set up these initial and boundary conditions, in this case, how to design and build an asynchronous electric motor. In other words, it is the creative talent of an inventor that will postulate how to bend, wind metal wires, how to specify the size and shape of magnetic core, and how to put them in a functional relation that works.

Let’s now look at the architecture.
  

Where is the connection zone between the physics (engineering) and the art in architecture? 
 

It is exactly in the concept of boundary and initial conditions, which are the “Premise” part of Premise Based Implicative Truth Synthesis. Consider a beam that holds, for instance, a side wall of a building. The static force distribution on the beam is described by governing PDE (Partial Differential Equation). If you put a wall on the beam, the wall will exert force on the beam, and this force’s distribution will depend on the wall’s shape. Given this shape, which is a boundary condition for the beam’s PDE, we can calculate the distribution of final force load on the beam, thus determining whether the beam can withstand the wall’s weight. There is no given formula that will tell us what the shape of the wall should be. It is up to the creative talent of an architect, building the wall, to determine its shape, driven by his or her aesthetics intelligence. Physics can help her to calculate the force on the beam given certain wall’s shape - the wall’s shape is the starting point for this computation. But, physics cannot help her to determine the shape of the wall. In the case of architecture, the shape of the wall is chosen to satisfy human aesthetic criteria.
   
  

From the Premise Based Implicative Truth Synthesis point of view, the wall’s shape, as a boundary condition for PDE, is the premise that enters world of physics from the world of art. The art is the first axiomatic system, say system A. The physics of force distribution on the beam is the second axiomatic system, system B. With the boundary condition (the shape of the wall) we cross the axiomatic boundaries between these two systems, postulating the initial force distribution for the calculation, thus synthesizing the new truth: the chosen wall’s shape implies the beam’s force distribution calculation to determine whether the wall can stand it. With the shape of wall we satisfy the aesthetics criteria and with calculated force distribution we satisfy engineering requirements for function and safety.

4. Electronics and digital circuits

Implicative Truth Synthesis plays an extensive role in the design of logical gates. For given input voltage the specific connection and configuration of active and passive electronic components generate desired output voltage. Or, given the initial voltage as a premise, it is implied, by our circuit design, that certain output voltage will be obtained. Note that we can choose, by design, almost any output voltage for any given input voltage (within the laws of physics). This mimics how the human mind works – we can take any action for any given reason. Hence, the wide presence of electronics and electrical engineering in the world around us.
  

In the design of an electronic logical circuit (logical gate), our premise is input voltage. It is given, postulated information to the circuit. The mechanism that selects this particular input voltage (can originate from our reasoning or from another circuit) is the first axiomatic system, say system A. The digital circuit itself is the axiomatic system B. By stating the input voltage we crossed axiomatic boundaries between these two systems – A and B. System A, our reasoning has postulating power to pick a starting state of the system B – digital circuit.
  

Next step is the design of our logical circuit to produce specific output voltage given the input voltage. We synthesized new truth via implication – given input voltage implied certain output voltage. We created this implication by our circuit design, hence we have all of the components of the method – Premise is input voltage, Implicative is how we linked input and output voltage, and that’s the truth we just synthesized – Implicative Truth Synthesis.

3.5 Music

Consider the acoustic guitar. The selected fret’s position, the string length, will dictate the frequency (pitch) of the tone. There is a number of different frequencies a performer can choose and generate. When playing an instrument, a performer postulates a sequence of tones. For a listener, they are the starting points, the points of departure of the musical piece, and the beginning of the listening experience. Music is a sequence of tonal premises - generated by strings – a melody. Note how the guitar is decoupled from the act of composition. Guitar strings can accept any kind of plucks, but it’s up to a composer to create a work of art. From all possible fret positions, tone sequences, and duration, a composer postulates only the ones that satisfy his or her musical aesthetic criteria. Composer has a postulating power in relation to the guitar strings. During the process of composition, a composer defines initial (allowable, possible) states of the vibrating strings, which originate from the axioms of the guitar.
  

Guitar is an axiomatic system. It is independent of all other systems in its surroundings, like, of composer, performer, orchestra, audience. The guitar axiomatic system can be defined, for instance, by the guitar parts, the head stock, tuning keys, fretboard, body (resonant chamber), but most importantly by its strings and all possible tones that can be produced with them. A music piece is a set of notes which are postulated. Consider one particular guitar. Performers can change. Composers can change, also the audience can change. Yet, the guitar remains the same, an autonomous axiomatic system.

With each plucked string we cross axiomatic boundaries, from composer (or performer) to the guitar. The sound from the guitar is crossing axiomatic boundaries that envelopes guitar and its audience. By plucking a string, a performer synthesised a new truth – new tone. With each tone in the air, a new truth is synthesized – audience just heard that tone.
  

Axiomatic system of an audience member tells us that he or she can hear the music. If there is no guitar, nothing happens. But, if there is a guitar played, it will imply that the listener will enjoy the music. This is Implicative Truth Synthesis. 
 

Compare this guitar axiomatic system discovery, its decoupling and later connection via Implicative Truth Synthesis with the relationship between racing car driver (one axiomatic system) and the car engine (another axiomatic system), or decoupling mathematics from its field of application. The same way mathematics is defined by and enclosed within its axiomatic system, the same can be said about the guitar and the car engine. It is this axioms discovery for a system that admits further linking with other systems via Implicative Truth synthesis. 
 

Decoupling composition from the guitar, along their axiomatic boundaries, allows us to study the performance and guitar construction separately from composition. Decoupling racing car driver from the car and its engine allows us to study and focus separately on the driver’s training and the engine’s performance design at the factory.
  

Hence, with that said, the axiomatic system analysis can also define what your profession could be: a composer, a performer, a mathematician, a physician, a racing car driver, or a car engine designer. Or, you can be more than one – you can cross disciplines. You can be a good musician and skilful racing car driver. Or be a mathematician and a solid guitar player. And all this is seen more clearly through Premise Based Implicative Synthesis lenses.

3.5.1 From composing music to selling concert tickets

Tone by tone, music can evoke pleasant feelings; each tone carefully initiates response in our musical minds, creating musical experience that we share with others. 
 

We can observe that our musical emotional, reactive response disappears after music stops. However, music can change our mood, and this change can last long after the music stops. We are all aware of this when attending a concert.

This whole positive experience is the reason why good music sells! Captivating, pleasant, inspiring music implies that the orchestra or the band will sell tickets. One truth (music is good) implies another truth (we are going to buy tickets). Hence, the new truth is synthesised: when the music is good we are buying the tickets. Good music (system A) has a postulating power in relation to us (system B) – it motivates us to buy tickets. This Implicative Truth Synthesis is the core of profitable music industry. Note that, because we have free will, we can take any action yet we decide to buy tickets.

3.5.2 Mathematics and music

The most prevalent, if not the only, connection between mathematics and music is in the sequential selection of the duration and of the frequency (pitch) of the tones, in order to form a melody. (We also can quantify dynamics of a music piece, crescendo, forte, fortissimo, etc. as well, but let’s stay only with tone’s pitch and duration, for clarity.)
  

This tone’s selection process corresponds to postulating sets and number of elements in them in mathematics. Hence, no arithmetic, no quantitative investigation of numbers flow from music to math; only a sequence of numbers. It is because what matters in music is the relationship between successive tones which we are capable to perceive and how these relationships evoke certain feelings and emotions, and not the numerical relations between tone’s pitches and duration. 
 

On the other hand, feelings are not a priority in the mathematical operations on sequentially selected sets. In mathematics, you don’t get too much of a thrill from stating one number after another or one set after another. Of course, you can investigate convergence or divergence of a sequence of numbers – but, that’s the different step from only stating the sequence, and in music we are interested how long a tone will be and not in the convergence or divergence of the series of tones’ duration.
  

There is one additional, important association in this comparison. Musical piece, in general, consists of a melody and a harmony. With melody and harmony we are simultaneously generating and passing more than one number to the mathematical world. How many numbers can we pass, then, at the same time? Let’s see. In melody, we have the tone duration and the pitch - that’s two numbers. In harmony we have a number of different instruments and instruments groups. A modern full-scale symphony orchestra consists of approximately one hundred permanent musicians, most often distributed as follows: 16–18 1st violins, 16 2nd violins, 12 violas, 12 cellos, 8 double basses, 4 flutes (one with piccolo as a specialty), 4 oboes (one with English horn as a specialty), 4 clarinets (one with bass clarinet as a specialty, another specializing in high clarinets), 4 bassoons (one with double bassoon as a specialty.)¹ This means that a composer and a conductor can keep in their heads 148 variables - 18(1^st violins) x 2(pitch and duration) + 16(2^nd violins) x 2(pitch and duration) + 12(violas) x 2(pitch and duration) + 12 (cellos) x 2((pitch and duration) + 8(double basses) x 2(pitch and duration) and so on, which equals to around 74 pairs of different pitches and durations adding up to 148. This is equivalent to the function of 148 variables in mathematics! And instruments are distributed into four different sets - woodwinds, brass, percussion, and strings type. This relates to the mathematical definition of a distribution!
  

Only the functions of one variable are almost exclusively thought in high schools and some college mathematics courses. Functions of two or more variables are usually introduced in calculus or pre-calculus courses. While musicians may not be so good in arithmetic (they don’t need to, it might be as well boring too!) they are quite capable abstract mathematicians, even if they don’t know that – they can deal with functions of 148 variables distributed in four sets! Impressive indeed!
  

Of course, postulating such a big number of variables when, say, composing a symphony, put emphasis on the premise generation. These tones, for various groups of instruments, are actual premises and as such they contribute to the premise part of the Premise Based Implicative Truth Synthesis method.

Back to the sets and music. It is often in your advantage to manipulate abstract concepts quickly. While you will get speed over time, with training, the very process of remembering abstract concepts can be a difficult task – you may feel that you are missing their context and therefore cannot just remember and recall any arbitrary idea or object that floats in your mind. The concepts need to be linked to something!
  

Music can help here, especially getting a sense about sets – and sets are in the center of all the explanations in math. As you listen to the music, you can, at your own pace, imagine the sets in space that contain dots equal in number to the duration or the pitch of the tone you are just listening. With time you will find this quite amusing – while enjoying the music you can see in your mind circles representing sets with dots within them. You may even be able to move them around in an imaginary space, like real objects, in your mind. When you get accustom to the fact that you can manipulate such abstract concepts as sets, embedded in music context, you will feel more confident to manipulate numbers in the similar way, and hence mathematical functions which are, in general, just pairs of numbers – pairs of sets. Remember, everything in mathematics is a set and the operations on them. Enjoy your new math world!

3.6 Software development and computer programming

Here, you specify the “sea of initial conditions” consisting of true and false values to be represented by the bits which are passed to CPU for logical processing in order to get the targeted output result. These bits are called business requirements. Actual software development starts with this “sea of premises”. Business analysts interview subject matter experts and collect information that will be, through the business requirements document, input to the design document for software developers. Business requirements have postulating power – they postulate initial conditions and initial relationships for software developers, who, in turn, assign to bits the initial true and false values based on these requirements or premises. 
 

Business requirements are one axiomatic system. Computer is another. By mapping the business requirement to the bits’ state, in the computer, we cross their axiomatic boundaries by the implication: given this business requirement it implies that the certain bit value will be true (or false). Once a computer has these initial bits’ values, it processes them logically using digital circuits (consisting mostly of logic gates) built around CPU and memory. When finished, the results are, again, computer bits representing values true or false. As the next step, these truth values are mapped back to the business domain by linking them to the concepts who’s truth value they represent (for example, it is true that temperature is 273 degrees Fahrenheit, it is true that the trading price is $10.00, it is false that the auction will take place on June 12^th).

Why are computers so popular and powerful and are successfully used in so many fields? 
 

It is because, once a computer has initial bit states (true or false) it does not care where they came from - computer will do universal logical processing on them for any field.
  

Many concepts in the world around us can be represented by true or false statements.
  

Where Premise Based Implicative Truth Synthesis plays role here? Business domain rules are linked to computer systems via Implicative Truth Synthesis, where, at the start, bits' truth values are postulated by the business domain analysts. At the end of CPU processing, the truth values of bits are mapped back via Implicative Truth Synthesis, to the truth values of the domain of application.

To succeed as a software developer you have to be aware that you have to start with the hundreds of premises represented by truth values of bits (Windows OS can help you input these postulated bits through various windows – text boxes, check-boxes, drop-down boxes…) and, after computer logical processing, you map the obtained truth values of bits, or numbers, to the domain of application. It is an imperative to recognize the central role, importance of premises, design of premises, and premises architecture when designing a software system. Software architecture is architecture of premises which comes from business requirements (finance, medicine, engineering…)
  

We still can ask why computers can be applied to so many diverse fields given that the computers deal only with the binary 0s and 1s? It’s because when you choose the domain where you can claim that something is true or false these true or false values are represented by 0s (false) and 1s (true) within a computer. The domain you chose can be any domain: finance, engineering, medicine, genetics…, and in each of these domains you can form statements that can be true or false. 
 

Let’s analyze the Windows programming (the analysis can be applied not only to the Windows operating system, but also to the Android and the Mac’s iOS or even UNIX). In Windows programming paradigm everything is a window – a functional rectangle. The main purpose of the windows here is to accept input values, premises, and display the end results – the output values. In general, when we look at the windows (functional rectangles) on our computer screen, we are not really concerned with their aesthetic appeal – what matters the most is where in the window we can input our premises (called input data) and, subsequently, in which window, and where on that window, the results will be displayed.
  

Business requirements create premises for our windows! To be a successful Windows programmer you focus to gain massive but structured knowledge how the windows will be displayed on the screen and how they will be manipulated by your code. Windows software libraries can help you with this. Business requirements in general are not of your concern. Why? Because business requirements document will give you your starting points to program windows. That’s all you need. In the same way, business analysts are not interested how you will program the windows! They are focusing on their business data and later on the results from your program.
  

There are two axiomatic systems here. First, say system A, is the world of business requirements. Business analysts have their own axioms, methods, and philosophy to analyze the expert domain to which they seek computer application; often subject matter experts are interviewed to obtain the most accurate business information: a medical doctor or a researcher in medical software application, trader in financial application, or design engineer in electrical engineering application. 
 

The second axiomatic system is our Windows programming environment, say system B. You, as a software developer, or a software architect, will accept the business requirements through the windows and logically process them giving instructions to CPU via your software code. In the process of programming you can create some errors or business requirements may be logically wrong. Debugging that follows is one example of finding the wrong premises.

Note how these two axiomatic systems can exist without knowing about each other. Business requirements (system A) are created without knowing which software will be used for computation and application. The software development environment is built around Windows libraries and essentially it does not care from which business domain the premises will come. By giving the business requirement document to a software developer, or to a software architect, we crossed axiomatic boundaries between these two systems, A and B. With this crossing we synthesised new truth: given this business requirement from system A it will imply that certain kind of window will be created in system B. Only through this implicative link the two systems can get functionally connected. And this is the Premise Based Implicative Truth Synthesis.

3.7 Famous postulates (premises)

Some of the famous postulates, premises, also called inventions within the corresponding fields, are:

1. The Schrodinger’s equation
2. The Nikola Tesla’s asynchronous electric motor
3. The Wright Brothers’ wing airfoil

Note how it was sufficient to only present a postulate, as a patent for instance, without need to show the proof how the invention has been created. That’s the essential property of a postulate or a premise. It opens up the usage of it in other systems moving forward because it is a starting point that needs no proof within the system it is used in. 
   

Premise Based Implicative Truth Synthesis is the core component of any cross-disciplinary project because of its capability to correctly and efficiently connect inputs and outputs of these fields. The expertise level of a team member in these projects is directly proportional to the number and quality of premises she or he possesses and his or her ability to discover and form implications between different systems thus synthesizing new truths within an interdisciplinary project.
  

You will see that, for success, you will need to have a massive but well structured knowledge in the domain of interest, be it the knowledge of the products you sell, engineering or scientific knowledge, or, for instance, the cooking skills and recipes. But, this massive knowledge requirement does not mean you learn everything without any selection. On the contrary, you will select what matters, what is important, and the volume of this kind of knowledge will be massive. During this process, let’s say you are acquiring knowledge from two thick books, or from a number of research papers, you read sequentially, but the important facts and relations between them you distribute in 3D planes, so you can easier form new relationships, from other books or papers, or experiences. Using Implicative Truth Synthesis to analyze the domain of interest by creating axiomatic boundaries will make your process of gaining knowledge way easier. For instance, for my current projects in engineering and software development I did original research in acoustics and thanks to Implicative Truth Synthesis I just skimmed through tens of scientific papers to extract what is important for my project, in which acoustics meets psychology, and this in turn is linked to sound engineering. Contrast that with approach to spend days reading one thick book trying to extract relevant information.
  

The individual development of disciplines which takes part in a cross-disciplinary project, is possible exactly because they function on the premise-axiomatic principles. Premises define the starting points of inquiry within the field, while axiomatic structure allows solid logical analysis. Cross-disciplinary projects like chemistry and mathematics, social networks and computer science, artificial intelligence, are also possible because the results in one discipline can specify starting premises in another, and within that new discipline the attained results can specify premises to yet another domain of knowledge. Note how premises can be specified in two ways - by discipline itself, and also as an implication from the result in another discipline. This premise specification is a true statement – result from one discipline implies a premise, postulate in another – the Premise Based Implicative Truth Synthesis.
  

As a result of the method application, you will, gradually, be able to recognize abstractions underpinning the systems and concepts you are going to conquer. You will see the relationships between these underlying structures, and you will become accustomed to think in terms of the relationships between these abstractions, gaining benefits of information inferred in this way, the information that can change the real system you are focusing on.

When you start associating different ideas, disciplines, skills, or knowledge domains with Implicative Truth Synthesis, you will awaken many different kind of intelligence you have – emotional, artistic, quantitative, musical, spiritual, physical, analytical…
  

In a number of instances you will stop thinking using ordinary language: instead, you will think in the terms of relationships, possibly existing on several levels, that make up your systems. Language is a way to communicate ideas and their relationships which are often created without the use of language. You will not need to explain your findings and discovered relationships using ordinary language - they will be there, clear and tangible in their own way of existence. 

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