I agree that an entity without free will will always act the same way in exactly the same environment. I don't know what "without context and environment" means, though. Even the vacuum of space is an environment.
I meant without a context/environment that is changing around the entity. It's isn't that it "always acts the same way" in a static environment. It's that it does not act at all, but rather remains eternally in whatever state it started in. To act is to change in what one was doing before, and that change requires the introduction of some new force upon the entity.
If the context and environment does not change, then the entity will never "act" . IOW, all action is caused by the context external to the acting entity, not just the inherent properties of the entity itself.
Once this is acknowledged, then it follows that the inherent nature of an entity is separate from it's current and past contexts that led to act as it does. Thus, that context could have been otherwise without the nature of the entity being different. Thus, it's actions could have been otherwise, making those actions contingent on context outside of the essential nature of the entity.
Its actions could have been otherwise if the environment was different,
Which means that its actions are
contingent upon what the environment was at that point and time, which is the real definition of contingent truth.
but that's perfectly compatible with my explanation of the law of causality.
No, your definition places all causality within the properties inherent to the object. Only by this untenable assumption are the truths about the current state of an object non-contingent and "neccessary", as you response to the OP claimed. If the action or current state are contingent upon a context, then the truth about that action/state is contingent. Contingent means contingent upon a particular chain of causality. That context in turn could be different, if the even larger context or preceding events had been different, ad infinitum. All that matters is that the events can be conceived of as having occurred differently without changing the definition of the subject and predicate in the assertion. IF so, then it's a contingent truth. If making it untrue requires changing the definition of the subject or predicate (e.g., "Cats are mammals"), then and only then is it a neccessary truth.
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So, to you, there is no improbability involved in your winning the lottery, since it could not have happened other than exactly the way it did? It would seem to also imply that, in fact, there is no such thing as probability. If so, how does your model account for the wide success of predictive algorithms and techniques explicitly based on probability, like those used by professional blackjack players?
Probability is an epistemological concept - it pertains to our knowledge of things, not the things themselves. Once you have tossed a coin, there is a probability of 1 in reality that it will land (say) heads, but from our perspective the probability is 0.5 since we are ignorant of
all of the forces operating on the coin and can only use the evidence of past tosses to form a conclusion.
Note what I emphasized. All those forces operation on the coin are what caused it to be heads. Thus, it being heads is contingent upon all those forces that are distinct from the inherent properties of the coin in itself. That makes "The coin landed heads" a contingent truth.