{"id":74876,"date":"2024-11-14T14:46:08","date_gmt":"2024-11-14T19:46:08","guid":{"rendered":"https:\/\/world.edu\/?p=74876"},"modified":"2024-11-15T00:01:41","modified_gmt":"2024-11-15T05:01:41","slug":"researchers-have-invented-a-new-system-of-logic-that-could-boost-critical-thinking-and-ai","status":"publish","type":"post","link":"https:\/\/world.edu\/researchers-have-invented-a-new-system-of-logic-that-could-boost-critical-thinking-and-ai\/","title":{"rendered":"Researchers have invented a new system of logic that could boost critical thinking and AI"},"content":{"rendered":"

\"\"<\/p>\n

The rigid structures of language we once clung to with certainty are cracking. Take gender, nationality or religion: these concepts no longer sit comfortably in the stiff linguistic boxes of the last century. Simultaneously, the rise of AI presses upon us the need to understand how words relate to meaning and reasoning.<\/p>\n

A global group of philosophers, mathematicians and computer scientists have\u00a0come up with a new understanding of logic<\/a>\u00a0that addresses these concerns, dubbed \u201cinferentialism\u201d.<\/p>\n

One standard intuition of logic,\u00a0dating back at least to Aristotle<\/a>\u00a0, is that a logical consequence ought to hold by virtue of the content of the propositions involved, not simply by virtue of being \u201ctrue\u201d or \u201cfalse\u201d. Recently, the Swedish logician Dag Prawitz\u00a0observed that<\/a>, perhaps surprisingly, the traditional treatment of logic entirely fails to capture this intuition.<\/p>\n

The modern discipline of logic, the sturdy backbone of science, engineering, and technology, has a fundamental problem. For the last two millennia, the philosophical and mathematical foundation of logic has been the view that meaning derives from what words refer to. It assumes the existence of abstract categories of objects floating around the universe, such as the concept of \u201cfox\u201d or \u201cfemale\u201d and defines the notion \u201ctruth\u201d in terms of facts about these categories.<\/p>\n

For example, consider the statement, \u201cTammy is a vixen\u201d. What does it mean? The traditional answer is that there exists a category of creatures called \u201cvixens\u201d and the name \u201cTammy\u201d refers to one of them. The proposition is true just in the case that \u201cTammy\u201d really is in the category of \u201cvixen\u201d. If she isn\u2019t a vixen, but identifies as one, the statement would be false according to standard logic.<\/p>\n

Logical consequence is therefore obtained purely by facts of truth and not by process of reasoning. Consequently, it can\u2019t tell the difference between, say, the equations 4=4 and 4=((2 x 52<\/sup>\u00a0) -10)\/10 simply because they are both true, but most of us would notice a difference.<\/p>\n

If our theory of logic can\u2019t handle this, what hope do we have to teach more refined, more subtle thinking to AI? What hope do we have of figuring our what is right and what is wrong in the age of post-truth?<\/p>\n

Language and meaning<\/strong><\/h4>\n

Our new logic better represents modern speech. The roots of it can be traced to the radical philosophy of the eccentric Austrian philosopher Ludwig Wittgenstein, who in his 1953 book,\u00a0Philosophical Investigations<\/a>, wrote the following:<\/p>\n

\u201cFor a large class of cases of the employment of the word \u2018meaning\u2019 \u2013though not for all \u2013 this word can be explained in this way: the meaning of a word is its use in the language.\u201d<\/p>\n

This notion makes meaning more about context and function. In the 1990s, the US philosopher Robert Brandom\u00a0refined \u201cuse\u201d to mean \u201cinferential behaviour\u201d<\/a>, laying the groundwork for inferentialism.<\/p>\n

Suppose a friend, or a curious child, were to ask us what it means to say \u201cTammy is a vixen\u201d. How we would you answer them? Probably not by talking about categories of objects. We would more probably say it means, \u201cTammy is a female fox\u201d.<\/p>\n

More precisely, we would explain that from Tammy being vixen we may infer that she is female and that she is a fox. Conversely, if we knew both those facts about her, then we may indeed assert that she is a vixen. This is the inferentialist account of meaning; rather than assuming abstract categories of objects floating around the universe, we recognise that understanding is given by a rich web of relationship between elements of our language.<\/p>\n

Consider controversial topics today, such as those around gender. We bypass those metaphysical questions blocking constructive discourse, such as about whether the categories of \u201cmale\u201d or \u201cfemale\u201d are real in some sense. Such questions don\u2019t make sense in the new logic because many people don\u2019t believe \u201cfemale\u201d is necessarily one category with one true meaning.<\/p>\n

As an inferentialist, given a proposition such as \u201cTammy is female\u201d, one would only ask what one may infer from the statement: one person might draw conclusions about Tammy\u2019s biological characteristics, another about her psychological makeup, while yet another might consider a completely different facet of her identity.<\/p>\n

Inferentialism made concrete<\/strong><\/h4>\n

So, inferentialism is an intriguing framework, but what does it mean to put it in practice? In a lecture in Stockholm in the 1980s, the German logician Peter Schroeder-Heister baptised a field, based on inferentialism, called \u201cproof-theoretic semantics<\/a>\u201d.<\/p>\n

In short, proof-theoretic semantics is inferentialism made concrete. This has seen substantial development in the last few years. While the results remain technical, they are revolutionising our understanding of logic and comprise a major advancement in our understanding of human and machine reasoning and discourse.<\/p>\n

Large language models (LLMs), for example, work by guessing the next word in a sentence. Their guesses are informed only by the usual patterns of speech and by a long training programme comprising trial and error with rewards. Consequently, they\u00a0\u201challucinate\u201d<\/a>, meaning that they construct sentences that are formed by logical nonsense.<\/p>\n

By leveraging inferentialism, we may be able to give them some understanding of the words they are using. For example, an LLM may hallucinate the historical fact: \u201cThe Treaty of Versailles was signed in 1945 between Germany and France after the second world war\u201d because it sounds reasonable. But armed with inferential understanding, it could realise that \u201cTreaty of Versaille\u201d was after the first world war and 1918, not the second world war and 1945.<\/p>\n

This could also come in handy when it comes to critical thinking and politics. By having a fit for purpose understanding of logical consequence, we may be able to automatically flag and catalogue nonsense arguments in newspapers and debates. For example, a politician may declare: \u201cMy opponent\u2019s plan is terrible because they have a history of making bad decisions.\u201d<\/p>\n

A system equipped with a proper understanding of logical consequence would be able to flag that while it may be true that the opponent has a history of poor decisions, no actually justification has been given for what is wrong with their current plan.<\/p>\n

By removing \u201ctrue\u201d and \u201cfalse\u201d from their pedestals we open the way for discernment in dialogue. It is based on these developments that we can claim that an argument \u2013 whether in the heated arena of political debate, during a spirited disagreement with friends, or within the world of scientific discourse \u2013 is logically valid.<\/p>\n

Author Bio:<\/strong> Alexander V. Gheorghiu is a Research Fellow in Logic or Applied Logic at UCL<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

The rigid structures of language we once clung to with certainty are cracking. Take gender, nationality or religion: these concepts no longer sit comfortably in the stiff linguistic boxes of the last century. Simultaneously, the rise of AI presses upon us the need to understand how words relate to meaning and reasoning. A global group […]\n… learn more→<\/a><\/p>","protected":false},"author":33,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[86115],"tags":[435158],"coauthors":[11733],"class_list":["post-74876","post","type-post","status-publish","format-standard","hentry","category-research","tag-logic"],"acf":[],"yoast_head":"\nResearchers have invented a new system of logic that could boost critical thinking and AI - World leading higher education information and services<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/world.edu\/researchers-have-invented-a-new-system-of-logic-that-could-boost-critical-thinking-and-ai\/\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:locale\" content=\"en_US\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:type\" content=\"article\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:title\" content=\"Researchers have invented a new system of logic that could boost critical thinking and AI - World leading higher education information and services\" class=\"yoast-seo-meta-tag\" \/>\n<meta property=\"og:description\" content=\"The rigid structures of language we once clung to with certainty are cracking. 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