Philosophy Now Forum

• "In most disciplines, evidence is required to prove something. Evidence is drawn from the experience of the world around us, with science obtaining its evidence from nature,[11] law obtaining its evidence from witnesses and forensic investigation,[12] and so on."

https://www.dictionary.com/browse/proof

1. evidence sufficient to establish a thing as true, or to produce belief in its truth.
Synonyms: support, corroboration, demonstration, confirmation

anything serving as such evidence:
What proof do you have?

the act of testing or making trial of anything; test; trial:
to put a thing to the proof.
Synonyms: assay, examination

the establishment of the truth of anything; demonstration.

Law. (in judicial proceedings) evidence having probative weight.

the effect of evidence in convincing the mind.

an arithmetical operation serving to check the correctness of a calculation.

Mathematics, Logic. a sequence of steps, statements, or demonstrations that leads to a valid conclusion.

a test to determine the quality, durability, etc., of materials used in manufacture.

Distilling.
the arbitrary standard strength, as of an alcoholic liquor.
strength with reference to this standard: “100 proof ” signifies a proof spirit, usually 50% alcohol.

Photography. a trial print from a negative.

Printing.
a trial impression, as of composed type, taken to correct errors and make alterations.
one of a number of early and superior impressions taken before the printing of the ordinary issue:
to pull a proof.

(in printmaking) an impression taken from a plate or the like to show the quality or condition of work during the process of execution; a print pulled for examination while working on a plate, block, stone, etc.

Numismatics. one of a limited number of coins of a new issue struck from polished dies on a blank having a polished or matte surface.

the state of having been tested and approved.

proved strength, as of armor.

17. Scots Law. the trial of a case by a judge alone, without a jury.

In some areas of epistemology and theology, the notion of justification plays approximately the role of proof,

Veritas Aequitas wrote: ↑Wed Feb 19, 2025 5:47 am

godelian wrote: ↑Wed Feb 19, 2025 2:55 am Hence, there is no proof outside mathematics.

This had happened many times where I corrected your wrong view and yet you are still repeating this mistake. Something is very wrong with you. You are insulting your own intelligence which such dogmatism and ignorance.

Your rationality and critical thinking is of very low standard.
You need to improve your critical thinking and expand your cognitive power.

Here is my discussion with "MY" ChatGpt which indicate your lack of intellectual competence:
Note "Your Interlocutor’s Misstep"... in ChatGpt's response.

VA to ChatGpt

Please put the following in its proper perspective.

My interlocutor asked ChatGpt the following question:
Is scientific evidence proof?

ChatGpt Responded:
"Not exactly. Scientific evidence is strong support for a claim, but it is not absolute proof. Science operates on probabilities and falsifiability, meaning that evidence supports or refutes a hypothesis rather than proving it conclusively.
In contrast, mathematical proofs are absolute because they follow logical steps that cannot be contradicted. Science, however, deals with empirical observations, which are always subject to new interpretations or discoveries."

So my Interlocutor asserted:
"Hence, there is no proof outside mathematics."

I believe there are a lot of nuances to the above from different perspectives:
My views:
The term 'proof' is not confined absolutely to 'Mathematics'. The term 'proof' is a common terms used correctly with reference to the defined context.

"mathematical proofs are absolute" is only absolute within the very specifically defined Mathematics Framework and System.

The term 'proof' can be used as 'scientific proof' as long as it is qualified to the scientific FS.

Please comment on the above.

ChatGPT said:
Your perspective is well-founded, and your interlocutor’s assertion that "there is no proof outside mathematics" is overly simplistic and contextually misleading. Here’s why:

The Context-Dependence of 'Proof'
The term proof is not monolithic; its meaning depends on the framework or system in which it is used. While mathematical proof is deductive and follows strict logical axioms, other domains have their own standards of justification. Legal proof, scientific proof, and historical proof all exist within their respective frameworks, each governed by different criteria of validation.

Scientific 'Proof' vs. Mathematical Proof
In mathematics, proof is deductive, meaning that once a proposition is proven within an axiomatic system, it is necessarily true within that system.
In science, proof is inductive and empirical. While science does not deal in absolute certainty, it establishes strong justifications for claims through repeated observation, experimentation, and falsifiability. The term scientific proof is often used in a qualified sense to indicate a high level of empirical support for a theory.
This aligns with your FS-objective view: within the scientific framework and system (FS), scientific proof is valid, though it remains open to revision.

Your Interlocutor’s Misstep
By claiming that "there is no proof outside mathematics," they are imposing an overly rigid, absolutist definition of proof, dismissing other valid forms of justification. Their argument conflates deductive certainty (found in mathematics and formal logic) with empirical justification, which is the standard for scientific proof.

The Relativity of Absolutes
Even the claim that "mathematical proofs are absolute" is relative to the axiomatic system in which they are formulated. Mathematical truths are conditionally absolute, meaning they are absolute within the framework of their given axioms. If the axioms change (e.g., Euclidean vs. Non-Euclidean geometry), the conclusions change as well.

Conclusion
You are correct in asserting that proof is not confined to mathematics. The term proof is context-sensitive, and within a given FS (mathematical, scientific, legal, etc.), proof is meaningful. Your clarification about scientific proof being valid within the scientific FS helps bridge the gap between inductive and deductive reasoning while maintaining the integrity of different epistemic frameworks.

I suggest you post the whole of the above chat to "YOUR" ChatGpt for comments.

godelian wrote: ↑Wed Feb 19, 2025 2:55 am Hence, there is no proof outside mathematics.

ChatGpt Wrote:

Here is a comprehensive list of domains where the term proof (as a form of justification) is used and acceptable within its qualified Framework-System (FS):

1. Mathematical Proof (Mathematical FS)
Proofs are deductive and absolute within axiomatic systems.
Examples:
Euclidean geometric proofs
Proofs in number theory (e.g., proof of the Pythagorean theorem)
Formal logic proofs

2. Scientific Proof (Scientific FS)
While science relies on falsifiability and empirical validation rather than absolute certainty, the term proof is often used to describe overwhelming empirical support.
Examples:
The proof of gravitational waves (indirect empirical confirmation)
The proof of the DNA double-helix structure (through X-ray crystallography and experimental validation)
The proof of the Higgs boson (empirical detection at CERN)

3. Legal Proof (Legal FS)
Legal proof is based on evidence and argumentation, varying in standards such as beyond a reasonable doubt (criminal cases) or preponderance of evidence (civil cases).
Examples:
Proof of guilt in a criminal trial
Proof of contract validity in a civil dispute
Proof of identity in legal documentation

4. Philosophical Proof (Philosophical FS)
Proofs in philosophy depend on logical reasoning and conceptual analysis rather than empirical verification.
Examples:
Proofs of the cogito (Descartes: "I think, therefore I am")
Proofs in modal logic (e.g., Gödel’s ontological argument)
Arguments in metaphysics (e.g., Kant's transcendental deductions)

5. Historical Proof (Historical FS)
Historical proof relies on documentation, artifacts, and corroboration of sources.
Examples:
Proof that Julius Caesar was assassinated (through historical records)
Proof of ancient civilizations (through archaeological findings)
Proof of the Holocaust (documented testimonies, photographs, physical evidence)

6. Engineering Proof (Engineering FS)
Engineering proof involves empirical testing, mathematical modeling, and practical validation.
Examples:
Proof of structural integrity in bridge designs
Proof of concept for a new technology (e.g., prototype testing)
Proof that a material can withstand extreme temperatures

7. Computer Science & Cryptographic Proof (CS & Cryptographic FS)
Proofs in computer science include formal verification methods, algorithmic proofs, and cryptographic security proofs.
Examples:
Proof of algorithm correctness (e.g., proving an algorithm runs in polynomial time)
Proof of encryption security (e.g., RSA encryption proof of security)
Proof-carrying code (ensuring code safety through formal proofs)

8. Economic Proof (Economic FS)
Economic proof relies on statistical models, empirical data, and theoretical frameworks.
Examples:
Proof of market efficiency (empirical validation of the Efficient Market Hypothesis)
Proof of inflation effects (statistical correlation between money supply and price levels)
Proof of economic inequality trends (data-driven studies)

9. Linguistic Proof (Linguistic FS)
Proof in linguistics is based on historical reconstruction, comparative analysis, and empirical data.
Examples:
Proof of language family relations (e.g., Indo-European languages)
Proof of phonetic evolution (reconstructing proto-languages)
Proof of grammatical rules in linguistic typology

10. Artistic & Aesthetic Proof (Aesthetic FS)
While aesthetics is largely subjective, certain proofs exist regarding artistic authenticity, authorship, and compositional techniques.
Examples:
Proof of authorship (e.g., proving a painting is by Da Vinci using forensic analysis)
Proof of historical influence (e.g., demonstrating how Renaissance art influenced modern styles)
Proof of forgery (e.g., using spectrographic analysis on paintings)

11. Theological Proof (Theological FS)
Theological proof is based on doctrinal interpretation, logical arguments, and historical documentation.
Examples:
Proof of divine existence (ontological, cosmological, and teleological arguments)
Proof of religious authenticity (e.g., textual and archaeological validation of religious scriptures)
Proof of miracles (documented testimonies, relic examinations)

12. Psychological Proof (Psychological FS)
Proof in psychology is based on experimental validation, cognitive models, and empirical studies.
Examples:
Proof of cognitive biases (empirical studies on the confirmation bias)
Proof of conditioning (e.g., Pavlov’s classical conditioning experiments)
Proof of mental disorders (evidence-based diagnosis in clinical psychology)

13. Medical & Biological Proof (Medical FS)
Medical proof is based on clinical trials, epidemiological studies, and biomedical research.
Examples:
Proof of vaccine efficacy (clinical trials showing immunity rates)
Proof of disease causation (e.g., Helicobacter pylori causing ulcers)
Proof of drug effectiveness (randomized controlled trials)

14. Ethical & Moral Proof (Ethical FS)
Moral proof relies on rational argumentation, empirical observations, and ethical consistency.
Examples:
Proof of ethical consistency (e.g., proving an ethical principle applies universally)
Proof of moral hypocrisy (showing contradictions in moral claims)
Proof of ethical consequences (evidence-based analysis of moral actions)

15. Business & Financial Proof (Business FS)
Business proof involves financial statements, audit verification, and economic trends.
Examples:
Proof of solvency (audited financial statements showing positive cash flow)
Proof of fraud (forensic accounting uncovering financial misrepresentation)
Proof of market trends (empirical data showing growth patterns)

Conclusion
The term proof is widely applicable across numerous domains, but always within a Framework-System (FS) that defines its criteria for justification. Your assertion that proof is not confined solely to mathematics is correct—each FS has its own valid standards for proof, whether deductive, empirical, or inferential.

godelian wrote: ↑Thu Feb 20, 2025 5:54 am

Veritas Aequitas wrote: ↑Thu Feb 20, 2025 5:18 am
ChatGpt Wrote:

ChatGPT: Is science backed by proof or by evidence?

Science is backed by evidence, not absolute proof.

In science, theories and hypotheses are supported by empirical evidence—observations, experiments, and data that are systematically collected and analyzed. Scientific knowledge is always open to revision if new evidence emerges.

Proof, in a strict sense, is more common in fields like mathematics, where logical deductions lead to absolute certainty. In contrast, scientific conclusions are based on the weight of evidence and can be refined or overturned with new discoveries.

So, while science aims for high confidence in its conclusions, it remains open to change—unlike mathematical proofs, which are definitive.

If proof implies "absolute certainty", then there is no proof in science but only in math.

By the way, proof that does not imply absolute certainty, is just a tool for manipulation, of which the primary purpose is to mislead. I have never seen the phrase "scientific proof" used for an honest purpose. On the contrary, it is a red flag that points to underlying intellectual dishonesty.

Veritas Aequitas wrote: ↑Thu Feb 20, 2025 9:33 am I have stated the term 'proof' and 'proved' and 'proven' are very common within the scientific community.

Veritas Aequitas wrote: ↑Thu Feb 20, 2025 9:33 am
I have stated the term 'proof' and 'proved' and 'proven' are very common within the scientific community.