Deductive Reasoning - Science topic

Teaching Mathematical Logic to engineering students can indeed be a challenge due to the abstract and formal nature of the subject. However, with effective pedagogical strategies and a clear connection to practical applications, it can be both rewarding and beneficial for students. Here are some considerations for teaching Mathematical Logic to engineering students:

Didactic Considerations

Connect logic concepts to real-world applications, particularly in engineering domains. For example, Boolean algebra has direct applications in digital circuit design, control systems, and programming logic. Use examples that are relevant to engineering problems, such as logical reasoning in software development, circuit design, and systems analysis.

Utilize visual aids such as truth tables, Venn diagrams, and flow charts to help students grasp abstract concepts. Visualization can make complex ideas more tangible.

Encourage collaborative problem-solving sessions where students can work in groups to solve logical puzzles, reason about real-world scenarios, or translate engineering problems into logical models.

Start with propositional calculus as a foundation since it is generally more intuitive. Then gradually introduce predicate calculus and its applications, ensuring students understand the relevance of each concept.

Incorporate problems that require students to apply logical reasoning to solve engineering-related challenges. This approach helps reinforce the practical utility of logic.

Content to Cover

Fundamental concepts such as logical operators, truth tables, equivalences, implications, and normal forms (CNF and DNF). Applications in Boolean algebra and digital logic design.

Introduction to quantifiers, predicates, and their uses in more complex logical reasoning. Applications in databases, algorithms, and programming languages.

Discuss important formal systems, including axiomatic systems and proof techniques (e.g., natural deduction, sequent calculus). Basic proof strategies and reasoning techniques will enhance deductive capabilities.

Focus Areas

Develop students’ abilities to think abstractly and to recognize the structure of arguments and proofs. Emphasize algorithmic logic as it pertains to computational problems and problem-solving in engineering

Encourage logical reasoning and critical thinking, focusing on constructing valid arguments and recognizing fallacies.

Literature and Resources

Consider using foundational texts on mathematical logic that cater specifically to engineering students, emphasizing practical applications. Look for resources that balance theory and applications to maintain student engagement.

Utilize online lectures, MOOCs, and interactive platforms that provide exercises, quizzes, and additional resources.

Explore literature on educational methodologies in teaching logic, focusing on disciplines that involve engineering.

Teaching Mathematical Logic to engineering students is worth the effort, as it enhances their critical thinking skills and prepares them for the logical reasoning required in their fields. By making the subject relevant, interactive, and accessible, educators can help students master logical concepts and apply them effectively in their professional lives. The key Rey Segundo Guerrero-Proenza lies in contextualizing the material and emphasizing the practical applications of mathematical logic within engineering contexts.

In my view, the most accurate and practical theories in any scientific field, particularly gerontology, are heavily influenced by temporal, spatial, and cultural contexts. It is challenging to propose a definitive theory on gerontology, as the perspectives and experiences of elderly individuals vary across different decades.”

Prediction does not belong to the field of Parapsychology. What works here is Dacian vision, perception beyond the ordinary senses. Others fall more into the category of psychology and philosophy

Yes, people may not always be fully rational, but they tend to act within limits of rationality when they are aware of their disincentives and constraints, adjusting their behavior to balance between rationality and irrationality.

The central idea in Jewish philosophy is that God is a singular, indivisible entity beyond human comprehension, distinct from any creation or being. Understanding God as each being's individualized higher self might not be entirely aligned with this. However, Jewish mysticism does talk about the concept of a Divine spark within every living being, indicating a connection and inherent sacredness. Thus, one could think of seeking alignment with their 'higher self' as trying to live in accordance with God's laws and the spark of divine within them. It's important to note that interpretations can vary widely, and other religions or spiritual traditions might have different understandings of the relationship between God and the self.

Rationalism is referring to rational behavior, and it can be based upon many kinds of evidence sources like testimony, history, empirical evidence, etc.. and so on. Critical entails a behavior of carefully analyzing something to the point where it is required. From there we can understand that critical rationalism means that the person is employing a behavior in which they are employing rationality to their thinking using different kinds of evidences as a base for their analysis.

On the other hand, empiricism entails that we are demanding about empirical evidence. Skepticism means that the person is employing a behavior of radically questioning something. So if we join both terms, it will mean that the person is asking simultaneous questions about something while demanding only empirical evidence.

So, from the above mentioned understanding we can conclude that critical rationalism is a concept and empirical skepticism is a type of critical rationalism but the latter employ a bit more strong behavior then the former.

So, I am not an expert on the field, neither do I know what these terms actually mean. But from names, I have derived this meaning which is quite sensible in my view

L.D. Edmonds Indeed. I regard that as an implicit feature since the comparatives (more, less) can apply adverbially to the adjectives "good" and "bad".

this is a good start, you will see how subject to environmental and pseudo-random chaos theory effects of critical systems like the brain, are. the idea that we are masters of our brains and minds, is an illusion to all but probably some very dedicated monks and practices of discipline.

What counts as a bird? If feathers are a sine qua non, then it's not inconceivable that some early featherless flying critters evolved into feathered flying critters, in which case their birdhood evolved after the capacity for flight. Note that I said "some". The evolution of birds might have taken several paths with different sequences from a common nonbird ancestor.

In general, instincts may contribute to some forms of tribal knowledge, such as basic survival instincts, but not all tribal knowledge can be reduced to instincts. The distinction lies in the source and nature of knowledge: instincts are innate biological tendencies, while prior knowledge is independent of sensory experience and can be known through reason alone.

Gerardo Ó. Matía Cubillo

There are also other anomalous cases I didn't mention in my response to Orlando M Lourenço that can be added as qualifications to my claim that empirical premises yield an empirical conclusion. For example, when the premises are contradictory or entail a contradiction. In classical logic that yields a valid argument no matter what the conclusion. Likewise, if the conclusion is a tautology or logical truth, the argument is valid no matter what the premises. Nonclassical logics such as relevance logics were developed in order to avoid such anomalies which many regard as unacceptable or counterintuitive.

So. we need the Holy Spirit, which is the substance of man's soul.

Jeus can give man eternal life and redemption, according to the Scritpure.

Occam's razor is related to free will in the same way that Truth is related to Reality (the “how it should be” is related to the “how it is”).

Wisdom can emerge at any time rather than regurgitation of past knowledge and its deductions. This being said, our limited knowledge of cognitive development has to be based on observations of diverse reality, as per Copernicus. The observer does have an intricate effect upon the observation, so deductive reasoning alone limits and induction takes us beyond the assumptions of neatly packaged compartmentalized thinking, antithetical to the pioneers in thought and cognition. Margaret Mead tried to break through this by her investigations into other diverse culture/paradigmatic views. She said: "Children need to be taught how to think, not what to think." Albert Einstein in Relativity recognized that everything is relative, everything is in relationship with everything else from the microcosmic to the macrocosmic. The analogs in nature he observed led to his own theory inductions, never fully proven by science until years after his death. He stated: "I live my daydreams in music. I see my life in terms of music." Art met Science in his thinking. We need merger of the arts to express cognitions that go beyond our current cognitions/assumptions/compartmentalized thought and observe All inducing in us that which we participate in throughout the cosmos. Then science can deduce new ideas from that inspirational origin with first humility and then heuristic quality. Psychology is still a new science still defending itself by certitude of what cognition is, which limits our understanding. William James, the Father of American Psychology investigated the "Stuff of Consciousness" grounding in the observable, pragmatics of the stuff of the Cosmos.

HOT TAKE ANSWER:

A very tempting statement to make, since neoliberalism could be thereby reduced to a capitalist heresy. Liberalism is all about public goods and the rule of law. Neoliberalism is all about privatizing public goods (aka the commons) and legal institutions; and then eliminating legal powers that protect public interest, through capital's regulatory capture.

To declare that liberalism is divine means that neoliberalism 's regulatory capture and degradation of the rule of law are both heretical. Lovely!

But I think that's a bit too much wishful thinking, for a political philosophy that promotes human reason as the foundation of freedom.

The basic role of human reason is why, for example, the Introduction to John Stuart Mill's On Liberty is about the imminent ability of colonized people to decolonize and live by self-rule, and so the first chapter about how to ensure liberty is through a freedom of thought and expression. Liberalism means that people accomplish their self-governance (or assent to be governed) through dialogue and education. It is not until the final chapter of Mill's little book that finally explains the "harm principle" for guiding the legitimate use of legal power; the limits of personal freedoms.

If liberalism was a form of freedom that emanated from the Holy Trinity, then liberalism wouldn't be about the testing of ideas, but rather about divine revelation and hierarchy. Something like Mill's "harm principle" could be articulated by scripture or revelation or even dogma. Something like it, but not the same thing.

I think anyone who wants to follow your aphorism will be vexed to find that liberalism is based on (essays concerning*) human understanding.

But what a relief if neoliberalism is a heresy! Neoliberalism can't abide freedom of thought and expression, because the marketplace of ideas is axiomatically the "public" part of the rule of law. Thought and expression can't be free when regulatory capture gets around to capturing the means of talking to each other.

HOWEVER, your aphorism is probably valid from the point of view of a person of faith who wants to use a faith-based institution (like a mosque, a convent, a hermitage) as part of civil society. From inside that institution, looking outward at the local neighbourhood or at the international order, it makes sense.

___

*I am making a reference to Kant because liberalism, as a rights-based political philosophy, can be easily divided into two general theories: dignitarian and utilitarian foundations for human rights and the legitimate use of power.

Maria, Socrates or Plato then devised particulars to cover your contingency. But, yes, an absolute eliminates other possibilities. within this, the particulars create a whole, such as gods and monotheism. But monotheism eliminates so much!

Yes I agree to a large extent as most political debates produces the surface intent of the problems. The real causative entity of the symptoms are unfolded when diagnostic tests are applied analysed and evidence based prescription applied

Based on the initial review of your book, "The Improbability of and Danger in Believing in Reincarnation," here are some constructive criticisms focusing on text size, formatting, citations, and other observations:

These suggestions aim to enhance the readability, academic rigor, and impact of your work. Tailoring the book to address these areas can significantly contribute to its success and the broader discourse on reincarnation and its implications across various fields of study.

About the study itself. Make sure to include data such as regional locations, and applicability of the paper in a universal manner. Do not just consider humans? Maybe an extremely interesting pooint would be to examine this as if you were from another planet. Now that would be novel.

I hope this helps you in your reseach, and feel free to ask any other questions.

Good morning

You can triangulate the answers and also, compare the cases

Best regards

IM: A wave brings in the amplitude paradigm, important as we see in a simple beach. A particle is a localized vibration. For particles, what is important is the frequency, like in the photoelectric effect..

Experimentally, this and other particle properties of photons win, the wave properties lose. The Maxwell Equations (ME) represent the wave properties, only. Photon spin is the particle description of light polarization, where spin +1 and spin −1 represent two opposite directions of circular polarization. Thus, light of a defined circular polarization consists of photons with the same spin, either all +1 or all −1.

Stimulated emission, and its coherence, are the foundations of the laser, and are not represented in the ME, even when represented by relativistic equations for the field strength tensor, with B and E using the same units. There are other examples, like diamagnetism

Denis Korneev Well, there's "modus morons" 🤔, but that's just another name for affirming the consequent.

Cheers. 🤡

Specifically, what the Nobel people said about the work of Tinbergen and Lorenz :

Quoting LAWRENCE K. ALTMAN on the Nobel Committee's selection in 1973: "The

Nobel Committee's Physiology or Medicine Prize has rewarded three zoologists for teaching man what could be learned from simple observation ..."

I.E. Largely from observation, NOT meddled which involves high quality (well-based) observations and inductive reasoning (very high inter-observer agreement and these can often be MUCH more reliable that the findings of experiments).

Also, interesting to note: Tnbergen and Lorenz often had one behavior pattern as a proximate cause for certain behavior pattern(s) that followed. This is what needs to be re learned and abided by or real ethology may be lost. (I.E. DEFINING BEHAVIOR PATTERNS IN TERMS OF OTHER BEHAVIOR PATTERNS -- ALL THESE RELEVANT PATTERNS __THERE__, IF YOU LOOK FOR THEM.)

WE HAVE TO LOOK FOR DIFFERENT key FOUNDATIONAL BEHAVIOR PATTERNS (e.g. during ontogeny ) :

Paraphrasing Lorenz (from some text): "This means that to predict behavior in natural conditions it is necessary to know what the animal’s innate perceptual and behavioral instructions are (as in Uexküll). In the same spirit, he claimed that without the notion of innate blueprint it would be impossible to study learning (Lorenz, 1965; Lorenz in Schaffner, 1955, p. 144). His argument is that stimulus association nee ds a releaser to which a conditional stimulus can be associated, and that random response variation alone is improbable because learning almost always results in adaptedness."

Yes, statement 1 supposes there exists a certain cultural phenomenon and proposes to study reasons for it; statement 2 proposes to determine whether such a cultural phenomenon exists at all. But in what sense is existence "due to literature"? Is the cultural phenomenon in question a literary phenomenon? Or are you referring to research articles (the research literature) that alleges there is a cultural phenomenon? In the latter case, the existence may not be "due to literature" unless the research literature has become like a self-fulfilling prophecy.

We use two basic kinds of logic, inductive and deductive, in scientific arguments. When the major premise of an argument is based on observation or experience, it is an inductive argument. On the contrary, a deductive argument is one in which the major premise is based on a theory, rule, law, principle, or general understanding. Deductive method contributed much for the development of primitive science. This method was highly successful in mathematics, but the problem was that it did not succeed well in exploring the universe, and it was not all useful for arriving at new facts. For this, we have to use the inductive methods.

Induction involves generalization from the behaviour of a few samples to that of a population. For example, after smelling a number of jasmine flowers, you could make an inductive statement: “All jasmine flowers are scented”. According to inductive logic, if a situation or condition is true in all observed cases, then the situation or condition must be true in all cases. Therefore, after completing a series of experiments that support the inductive proposition, you can affirm that the proposition holds good in all cases.

Both inductive and deductive methods should be considered as different ways of approaching the same objective. In fact, a combination of induction and deduction is practiced in science now. The observations made through induction are further verified deductively through applications to new situations. The scientist proposes a hypothesis through induction and then tries to deduce the probability that it is false through empirical evidences. This is what is commonly known as the hypothetico-deductive method or inductive-deductive method.

We humans make use of both types of reasoning, and this seems to function rather in the cognitive unconscious. Deductive reasoning works from the more general to the more specific, usually starting from a theory, which is then narrowed down to more specific hypotheses to test. Inductive reasoning works the other way, usually beginning with specific observations, detecting patterns and regularities, formulating some tentative hypotheses to test, and ending up developing some conclusions or theory.

As you see, if your concern is with developing a theory, you will find yourself using more inductive reasoning. If, however, you are concerned with a topic, as I suspect you are at the doctoral level, you are more likely to start from a theory, develop your hypotheses, and test them. In this case, you are more likely to use deductive reasoning. However, there is no quantification of either. If you try to bring all this to consciousness, you will realize that you are doing both, but with more leaning to the deductive one. Unless this distinction is crucial in your area of investigation, I suggest that you should not worry about that since the direction of your argument will guide you where you should be.

Dear Gerry Leisman

For me, I insist on finding ways to relate the types of learning and not just cite "many forms" based on indirect evidence. We need direct observational evidence of overt behavior patterns initiating (at least in their inception) the different related kinds of learning -- the many ill-defined "sub-fields" you note certainly notwithstanding.

It is important to realize that almost all findings in brain science are NOT clearly related to behavior (behavior patterns), and certainly we should not be satisfied with "behavior as you simply want to conceive or imagine it" -- which results when one is not clear on the limits to the meaning of neuroscience findings . THUS:

You simply "snip off" pieces of an imaginary "pie" and find "many things". There IS (or can be) a psychology of behavior patterns (ALL key aspects initiated in directly observable overt behavior) and as responses to corresponding environmental aspects -- those two types of things being the elements of a self contained, and coherent system, which can be discovered. If you cannot believe that, then you literally are lost. (Though, Psychology began with such a definition, no one has been able to actualize it because they do not insist on seeing behavior patterns as ALWAYS AND CLEARLY AS BIOLOGICAL FUNCTIONING -- YET this IS something that can be done.

Lack of present clarity OR "complexity" is no reason or excuse for not starting the field correctly, and keeping fidelity to biology.

Dear Gentlemen,

I would like to speak about probabilities in Fuzzy systems; I consider as most credible the systems which are related to reality itself.

According to what I mentioned in this discussion, our logical communication is contradictory; this leads to silence. We can brake the silence in a "logical" way through   a claim of minimum contradictions which implies that we decide not to  make mistakes on purpose; however this does not mean that this kind of communication is a pure classikal logic since the contradictions (according to the statement  "A system including logic  Λ   and a statement which is not theorem of  Λ  leads to contradiction"  cannot be vanished. This communication constitutses a kind  of fuzzy logic and more precisely it is a minimum contadictions fuzzy logic.

On this basis new principles (e.g. GRT, QM etc.)  are sources of futher contradictions; therefore we have minimum contradictions when the axioms we use are restricted to the ones of our logical communication.

Taking into account the above mentioned we can reach to the conclution that reality (everything) under the claim for minimum contradictions is described by a stochastic quantum space time  and obeys to the Schroedinger relativistic equation (Gordon Klein); because of this the probability density function P(r,t) has an integral (without any manipulation e.g. renormalization) equal to 1.

 On this basis we use the probabilities of a minimum contradictions Fuzzy system in an absolutely logical way; however P(r,t) of the Schroedinger relativistic equation can be negative which is not understandable; in this point we should remember that contradicions are never vanished. However these negative values can correspond to negative values of mass (quantum space time formation) or to a negative charge (imaginary quantum space time formation). 

Thus,  classical logic might  lead us to entities which seem to be ubnormal but they constitute parts of the whole reality.

describe something  by having as basis the principles of 

Yeah, well. That is a rare case and should be dealt with by the editor-in-chief. What is the opinion of other reviewers? If there aren't any than you should ask for more reviewers. They cannot reject a paper based on 1 referee, unless the editors strongly agree with it, are experts on the subject and also review the paper themselves. That is a very bad thing to do and is also damaging for the credibility of a journal. A review should have 3 referees, and the reason for that is clear in this case. I'd say the journal should have ways of dealing with these situations. If not, then maybe they are not worthy of your research and you should find another journal and take any constructive criticisms you got from the review process...

Hi, 

You can just add the agar. I do it this way with BHI.

I agree with Stephen Joy.  Overall, research has been pretty clear in that the further you separate a practice task from the format and content in which you wish to affect, the less likely the task will improve achievement.  Thus, if the n-back task bears little resemblance to the skill you wish to improve, it is unlikely it will have an affect.  I suggest checking out some of the recent reviews and meta-analyses that have been conducted on the effects of working memory training on academic skills, which I've listed below.  Also check out some recent work by Doug Fuchs at Vanderbilt, who is studying working memory training using tasks that are much more closely connected and relevant to the academic skill being targeted, in which he is finding some evidence of transfer.

Melby-Lervåg, M., Redick, T. S., & Hulme, C. (2016). Working memory training does not improve performance on measures of intelligence or other measures of “far transfer”: Evidence from a meta-analytic review. Perspectives on Psychological Science, 11(4), 512.

Melby-Lervåg, M., & Hulme, C. (2013). Is working memory training effective? A meta-analytic review. Developmental psychology, 49(2), 270.

Shipstead, Z., Redick, T. S., & Engle, R. W. (2012). Is working memory training effective?. Psychological Bulletin, 138(4), 628.

Hitchcock, C., & Westwell, M. S. (2016). A cluster‐randomised, controlled trial of the impact of Cogmed Working Memory Training on both academic performance and regulation of social, emotional and behavioural challenges. Journal of Child Psychology and Psychiatry.

Shipstead, Z., Hicks, K. L., & Engle, R. W. (2012). Cogmed working memory training: Does the evidence support the claims?. Journal of Applied Research in Memory and Cognition, 1(3), 185-193.

Hi Michal, cool, I am glad you are interested. Let's first see mental models theory. It was actually introduced in the 80's as an alternative to Euler circles, providing a much better explanatory power. Still, mental models are actually only a graphical variant of Euler circles.  I attached a picture about the denotation of the four main syllogistic statements with mental models and with Euler circles. You can see that they are exactly the same, except that in mental models, we denote the content of the sets, so no need to denote the boundary of the sets, whereas in Euler circles we denote the boundaries, so no need to separately denote the content of the sets. It is well known that traditional Euler circles are not suitable to describe people's syllogistic inferences, and since mental models are the same notation, obviously, they are not suitable either. Consequently, whatever has been told about the explanatory power of mental models is simply rhetorical. I have collected some fun citations do demonstrate this,I can copy & paste them here is you haven't yet lost your interest. 

The really meaningfull term in physics, and more broadly in science, is generality.  But to appreciate generality, one must first know all the cases where it applies, otherwise it can not be recognized as such.

Under the light of generality, opinions may show their limits. The Lagrangian formalism isn't the more general one. It doesn't apply when non conservative forces appear, then new definition of energy must be given, along with sattelite concepts like free energy or enthalpy, so that energy conservation also rules in thermodynamics.  As Noether theorem only applies in the Lagrangian and Hamiltonian formalims, it is useless in this case. Moreover, if a symmetry implies a conservation law, the converse is not true, there are topological invariants for instance.  Of course there is statistical mechanics, but that doesn't include non holonom systems, which need Newtonian mechanics, and which I think will play an important role in physics.

In all that, momentum conservation is the most general, that's why it should not be taught first.  I don't say it should not be taught at all, to the contrary, that is the target of the whole course in physics.  Science developed in the way it did for the same reason, it took the most easy way, and its purpose is generality which is gradually gained.

It is as though one would say that the top of the pyramid is the most important part, since it can be seen from the farthest, then it must by laid first.

Assumption is not an assertive act. Assumption is a directive act and that is why it is performed using an imperative sentence, "Assume/ suppose/ let ...!". "Discharging assumption" is a separate act of returning to the assertive mode.

Dear mr. Tucci,

I am afraid I don't quite understand. In mathematics the axioms are the premises. As I heard a mathematician say "I can define what I want".  The rules of inference are part of them, even if they are not always explicitly stated. Of course, you can define what you want, but you can not prove what you want once you have stated the rules. It is not so common to change the rules of logic (although people do tend to worry a bit about using the axiom of choice), but in the end logic can be considered as just another branch of algebra, and just as in other branches of algebra you can change or relax the rules. E.g. the classic Aristotilean logic allowing proof by contradiction can be replaced by other forms of logic like intuitionistic logic (which tends to be not so intuitive), which then makes some things unprovable although that includes the existence of nasty counterexamples! Computer scientists have used a subtly different form of logic for automatic theorem provers like the coq system and they have used it both for checking the correctness of computer processors and proving the Feith Thomson theorem (a highly non trivial theorem in group theory) from basic axioms. In fact, there is a rather interesting program by Voevodsky for new "Grundlagen" based on these ideas and ideas in algebraic topology. 

In Hilberts time the "Grundlagen" discussions were  raging. You can argue that social, philosophical and economic developments made the time ripe for such discussions, but I believe the most important input in these discussions was the fact that mathematical apparatus had progressed to the point where you run into problems without a formal apparatus. Something as basic and in everyday mathematical use as Lebesgue integration and measure theory simply does not work if you don't know that the cardinality of the real numbers is strictly larger than that of the integers, i.e. the naive and intuitive notion of "infinity" is just not sufficient. Without formalisations like set theory you cannot even express or think about different notions of infinity.  On the other hand once you have the proper formalisation (in this case set and measure theory) and have learned to say things like "the countable union of measurable sets is measurable" without so much as blinking an eye (i.e you have reached the level of a second year undergraduate math student), you can forget about the finer points of set theory and the whole machinery of measure theory just makes it easier to work with integrals and partial differential equations.

So to conclude, the formalisation that the Goettinger school was certainly a leading proponent of, turned out to be a necessity to make progress.  Having said that, one cannot deny that a lot of formalisation has taken place because generalisation and formalisation has become to be viewed as valuable in its own right, sometimes forgetting  (free after Einstein)  "as formal as necessary, but not more formal".

There is a nice discussion (without any formulas) of the issue of rigor and intuition in mathematics by some of the best living mathematicians in 

http://arxiv.org/abs/math/9404229 (reacting to http://arxiv.org/abs/math/9307227 by Jaffe and Quinn). 

Especially noteworthy are the contributions by Michael Atiyah, Renee Thom and Morris Hirsch.

the scopes of taxonomy and logic are fundamentally different. When taxonomy says "look into all details in order to understand how things developed", logic says "forget unessential details and find the most abstract and general principle". However, they are happily interconnected in many ways - and this is good so, because any intellectual activity must be somehow connected to logic, in order to exist. Taxonomy needs a lot of logical thinking in its proofs and argumentation. There are situations which are really difficult to decide, specially in biology, when you really must ask yourself which function could have been more important for this evolution and ao on. Logic needs a very clear taxonomy of its own categories by the definition of every new setting. This happens naturally more at the level of its syntax (related also lexically with Taxa, taxon, taxonomy - and do not forget that syntax was at the beginning a taxonomy of languages.) And only a robust and clear syntax assures a well working semantics. 

But, of course, one should not make logic or even deduction as a particular case of taxonomy. No way. 

I agree with many of the above comments to the effect that Gödel is just a red herring in this context. A supplementary consideration might be to invoke a notion I would assume economists are familiar with, namely "satisficing". An axiomatic system need not attempt to capture everything, not even many things that would be easily capturable if one cared enough to capture them. One may simply want a system that is good enough for the purposes at hand. And such a pragmatic approach can itself be justified on economic grounds.

A hypothesis is a tentative proposition or posit based on insufficient knowlege to be sure that it is factual. A hypothesis is proposed for testing.

If much testing affirms the correctness of a hypothesis, and it is generaly accepted, it then can become accepted as a theory. However, theorys can still be challenged and they may be modified or even discarded altogether, if much contrary knowledge is acquired and presented.

If a theory is rock-solid and apparently is beyond any dispute, it can be accepted as a law. There are laws in physics, for example. However laws are very scarse, or non-exsitent, in other diciplines such as biology.  

Paradigms  are also interesting, if you are keen. They are, very roughly, generaly accepted principles within which research is coducted, but they may be overthrown and replaced by a new paradigm during a scientific revolution.

Note that in non-scientific language, in common speech, even an idea or a train of thought may commonly be referred to as a 'theory', and the word hypothesis is not generaly known or used, and law is usualy used only to refer to the legal system.

I hope this helps Alex,

Regards,

Keith

There is a huge amount of cognitive errors (or cognitive biases) in inductive and deductive reasoning as well as in other types of thinking (e.g. judgement and decision making). Many of them are well demonstrated through the cognitive experiments. 

One of the most important cognitive biases that occurs both in inductive and deductive reasoning is "confirmation bias".  It is tendency for seeking or interpreting of evidence in a ways that are partial to existing beliefs, expectations, or a hypothesis in hand (Nickerson, 1998). Confirmation bias is usually demonstrated in "246 problem" and "Wason selection task". Both problems were invented by British psychologist Peter Wason (1966) and include both deduction and induction.

There are also many other cognitive biases, e.g. belief bias, matching bias, framing effect, anchoring and so on.

The books that might be useful for this topic:

Hope that this helps

Philadelphia, PA

Dear Lewton,

Speaking as one who has often taught logic and published much or related topics, I'd say that general familiarity with a given subject-matter tends to increase facility for logical inferences involving that subject-matter. Since "social content" is a theme of general interest, I think it would be possible to show that logical facility will be sharper in that area of discourse. However, one might also suspect a generalized tendency to go beyond the information actually supplied by particular premises of a syllogism or other argument.

See the opening pages of my paper "Semantic Contextualism and Scientific Pluralism," for illustrations--though I am not specifically concerned with syllogism there.  

H.G. Callaway

There are three main activities involved with the process of theory building:

1. conceiving a theory (abduction)

2. constructing the theory (logical deduction)

3. justifying or evaluating the theory (induction)

So, each of these steps involves a different type of reasoning. However, abduction which initiates this process requires induction so that the theory can be tested via its consequences, which are themselves derived through the process of deductive reasoning;

resource allocation problems are usually ill-solved uising intuition (system I) as people tend to do first the actions which are able to add more value, however these also allocate most resources... so a better reasoning is to use a deliberative optimization model (as Knapsack) to allocate resources.