Is there a general form to determine if a tautology in classical propositional logic is a tautology in Lukasiewicz propositional logic?

Soumendra Nath Thakur

May 19, 2025

When a scientifically consistent alternative framework challenges a well-established theory—such as relativity—the focus of scrutiny too often falls disproportionately on the individual proposing the alternative, rather than prompting a balanced and critical re-evaluation of the dominant theory itself. This asymmetry is not only counterproductive but also historically recurrent in the development of science.

Established theories typically enjoy strong institutional backing, extensive historical development, and widespread acceptance due to their practical applications. As a result, questioning them can appear to undermine the collective efforts and intellectual investments of generations of scientists. This psychological and social inertia frequently leads to resistance, not necessarily on scientific grounds, but due to deeply embedded paradigm commitments—as famously described by Thomas Kuhn.

Moreover, scientists, being human, are not immune to confirmation bias. They may more readily accept evidence that supports prevailing theories while dismissing or demanding higher proof from alternative proposals. This leads to a double standard: new frameworks must endure intense scrutiny and carry a heavy burden of proof, while traditional models are often granted undue leniency, even when empirical anomalies or conceptual flaws emerge.

A key concern arises when this imbalance allows potentially flawed assumptions to remain unchallenged, thereby obstructing scientific progress. Instead of testing both the new and old ideas with equal rigor, the scientific community may prioritize defending the established view—sometimes to the detriment of discovery.

To foster genuine advancement, scientific evaluation must adhere to objective standards. This includes:

• Rigorous examination of the alternative theory’s internal consistency and mathematical foundation.

• Careful assessment of empirical evidence supporting the new framework.

• A critical reappraisal of the traditional theory in light of the challenge.

• Open, respectful, and evidence-based debate that prioritizes ideas over authority.

Skepticism is a healthy and necessary part of scientific inquiry, but it must be evenly applied. Disproportionate skepticism directed only at new ideas, while shielding established theories from equivalent critique, creates a pseudo-authoritative environment contrary to the principles of science itself.

Science, unlike legal or political institutions, should not be governed by authoritative consensus. Scientific knowledge is inherently provisional, always subject to refinement or replacement as better explanations arise. Theories are not meant to be preserved as immutable truths but must remain open to falsification—a core tenet emphasized by Karl Popper.

Treating scientific premises as unquestionable dogma suppresses critical inquiry and innovation. Progress depends on the freedom to explore unconventional ideas and to challenge prevailing models without fear of institutional or reputational reprisal. Authority and tradition must never replace evidence and logical coherence as the basis for scientific judgment.

While consensus may reflect accumulated knowledge, it should never be mistaken for finality. A single, well-supported piece of empirical evidence—or a more comprehensive theoretical model—has the power to overturn a widely accepted view. Scientific consensus, therefore, must remain responsive to dissent and open to re-evaluation.

Unfortunately, the current structure of scientific publishing, peer review, and institutional hierarchy can unintentionally reinforce gatekeeping. Textbooks and public science communication often present dominant theories as settled facts, reinforcing the perception of unchallengeable authority—especially for those outside the research community.

In conclusion, the health of science depends on its commitment to intellectual humility, openness, and methodological rigor. When a scientifically coherent challenge arises, the response should not be one of dismissal or deference to tradition, but of balanced and critical engagement with all premises—old and new alike. Only by adhering to these principles can science fulfil its role as a truly progressive, self-correcting endeavour.

We, humans, couldn't have abstracted the identity of indiscernibles and self-identity from our sense perception; the existence of space precludes the possibility of two objects (a,b) being identical--no two objects can possibly occupy the same space. On the other hand, the existence of time precludes the possibility of a single object (a) being identical with itself-- no object can maintain the same properties (mass, volume, color, the coordinates of its electrons orbiting the nuclei .etc...) over time. Still, we hold that a=a and a=b ,with certainty.

Where do we get this apparently a priori knowledge of identity then, if not from experience?

Dear RG colleagues

What is the scientific/logical concept and relationship of Life, Death and Life after Death with Hell and Heaven?

Share your valuable comments to explore the ultimate truth and success that are everlasting.

With best regards

Ijaz

-Reasoning (logic) consists of truth or falsehood, with possibility which is collided into (statistical) probability as a hinge or 'transitional space' (see Winnicott) between the two: truth or falsehood.

-Can then logic only (in sensu exclusivo) consist of these two concepts, either truth or falsehood? Accordingly, only one?

Please check whether my question is correct. Thanks for all answers. Marc.

It seems to me an atomic condition that is not visited by a test case due to compiler short-circuiting has truth values that are irrelevant to the truth values of the whole predicate. Hence, short-circuiting has no effect in computing the relevant set of test cases for maximum MC/DC. But I am likely to be missing something,

Is it “true” that when anyone is rewriting a “sentence” in Logical Form(LF) by deploying metalinguistic constants and variables, the ultimate output would reveal the ‘true’ meaning of a given sentence? In LF, a major concentration is devoted to describe and understand the ‘real world’. This supposed logical positivist “real” is incorporated in the logical analysis of sentences in the algorithmic chain of LF of S-Structure by deploying sentential calculus. LF mainly follows Fregean compositionality or its derivatives like Katz-Fodorian Model. The following questions may be asked:

1. What is “real” in this real world? (To answer such question, one may take a clue from Russell’s An Inquiry into Meaning and Truth: “We all start from ‘naïve realism,’ i.e., the doctrine the things are what they seem. We think that grass is green, that stones are hard and snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and coldness of snow are not the greenness, hardness and coldness that we know in our own experience, but something very different. The observer, when he(sic) seems to himself (sic) to be observing a stone, is really, if physicist to be believed, observing the effects of the stone upon himself (sic).Thus science seems to be at war with itself: when it most means to be objective, it finds itself plunged into subjectivity against its will. Naïve realism leads to physics, and physics, if true, shows that naïve realism is false. Therefore naïve realism, if true, is false; therefore it is false.” (1940:15)

2. What happens in LF if anyone puts Russell’s paradox (1913) in LF? How do we incorporate Gödel’s theorem to tackle a formal system like LF? According to Goedel’s theorem (1931), no formal system is complete enough to handle all the problems within a formal paradigm. If anyone puts any Goedel’s proposition or Russell’s paradox (“One Calcuttan says that all Calcuttans are liars”) in LF of S-Structure, the total formal as well as mechanical algorithmic system to gauge the meaning may collapse.

3. Katz-Fodorian (1963) system of binary componential analysis ignores the prototypical cognition of meaning by the human being. As some cognitive scientist observed that the meaning as endorsed by human beings, could not be analyzed by the stipulated components as humans understand meaning through prototypical cognition. What should we follow in semantic analysis:technical intelligentsia’s critical discursive habit of paraphrasing or commonsense deployment of prototypes?

4. Let us switch over to another schooling and try to understand semantic problems raised by continental philosophers (under the umbrella o fso-called Post-Formalism/ Structuralism). These Post-Formalists are talking about plural meanings of non-disposable texts as well as something called‘surplus meanings’, which is not at all analyzable or quantifiable .According to them, the meaning-site is too slippery area and any futile endeavor to formalize such site will be ended in vain. Do you think that they are neglecting ‘science’ and its formalism by promoting“un-scientific” non-formalism?

Darwinian theory's survival of fittest is a strong and valid argument but when it is taken to the extreme i.e spevuies develop by trial and error even emerge functioning traits by luck, that is random mutations that "get selected" is far streched if one understand that extreme empirical logic is endorsed.

Empirical logic draws from the functionality in practice of an ideaie chicken foot are shape such way to support walking based on successful empirical tests that survived chicken beared as opposed to non function ing models.

While feedback between genes and environment exist and aids development and survival of species, empirical lohic is just one of possible logics and syllogistic or inferential processes and has limits and weaknesses.

Basing such a big claim of a syllogistic approach (empirical truth) which is, by some, peripheral and non central in its role in general syllogism (or highly limited), might pose problems to the theory in that it omits essential stage of inference and jumps to conclusions based just on empirical logic leaps .